Thèse - u-bordeaux1.frori-oai.u-bordeaux1.fr/pdf/2012/GAIKWAD_PREETI_2012.pdf · Thèse...
Transcript of Thèse - u-bordeaux1.frori-oai.u-bordeaux1.fr/pdf/2012/GAIKWAD_PREETI_2012.pdf · Thèse...
1
Thèse
Présentée à
L’Université Bordeaux 1
Ecole Doctorale des Science Physiques et de l’Ingénieur
par
Preeti Gaikwad
Pour obtenir le grade de
Docteur
Spécialité: Laser, Matiere et Nanosciences
Matériaux poreux multi-échelles pour la diffusion multiple/localisation de la
lumiere et les lasers aléatoires
English translation:
Multi-scale porous materials designed for multiple light
scattering/localization and random lasing
Soutenue le 13 Décembre 2012
Après avis de: DR Patrick Sebbah
Prof. Reinhard Höhler
Devant la commission d’examen formée de:
M. Bernard Pouligny DR, CNRS, CRPP Président
M. Patrick Sebbah DR, IL, ESPCI, Paris Rapporteur
M. Reinhard Höhler Professeur, INSP, UPMC, Paris Rapporteur
M. Peter Hesemann DR, Univ. Montpellier 2 Examinateur
M. Renaud Vallée CR, Habilitation, CRPP Directeur de thèse
M. Rénal Backov Professeur, Univ. Bordeaux 1 Codirecteur de thèse
Matériaux poreux multi-échelles pour la diffusion multiple/localisation de la lumiere et les lasers aléatoires
Résumé : Des matériaux poreux à architecture complexe et de couleur blanche ont été synthétisés, en combinant la physico-chimie des fluides complexes (émulsions, mésophase lyotropes) avec la chimie sol-gel. Ce procédé est connu sous le nom de chimie intégrative. En contrôlant la taille des objets diffusants (diamètres des pores) et en augmentant l’indice de réfraction, nous souhaitons augmenter le caractère diffusant de ces matériaux, générant ainsi diffusion et localisation de la lumière. Toutes les caractérisations structurales et optiques ont été réalisées. En utilisant des modèles physiques, nous avons analysé les résultats et obtenu les paramètres critiques de transport (transport moyen, longueur d’onde d’adsorption et constante du diffusion). Ces matériaux présentent un fort comportement multidiffusif et éventuellement de localisation de la lumière. Ces matériaux très diffusants sont des candidats pour la génération de lasers aléatoires. Dans cette optique, nous les avons infiltrés avec de la rhodamine-6G (chromophores) et quantifié leurs propriétés comme lasers aléatoires.
Mots clés : matériaux poreux multi-échelles, systèmes à diffusion multiple et lasers aléatoires
Multi-scale porous materials designed for multiple light scattering/localization and random lasing
Abstract : Disordered, porous, white, hierarchical materials have been synthesized using a sol-gel process combined with the physical chemistry of complex fluids (emulsion, lyotrope mesophase). The whole process is known as integrative chemistry. By tuning the size of the scatters (pore diameters) and increasing the refractive index contrast, we want to increase the scattering strength of our materials, thus promoting light scattering/localization. The structural and optical characterizations have been performed. By using well established theories, we have analyzed our results and obtain the transport parameters (transport mean free path, absorption length and diffusion constant). The materials exhibit a strong multiple-diffusive behavior and an eventual localization of light. These strongly scattering materials would be of potential interest for random lasing applications. Therefore, we infiltrated them with Rhodamine 6G laser dyes and quantified their random lasing performances.
Keywords : multiscale porous materials, multi-diffusive systems and random lasers
Equipe d’accueil : Univ. Bordeaux, CNRS, CRPP, UPR 8461, F-33600 Pessac, France.
3
Contents 3
Acknowledgement 7
Chapter I State of the Art 13
I Introduction 15
I.1 Light propagation through disordered media 15
I.2 Disorder materials as random lasers 20
I.3 Material aspects 23
II Problems and goals 29
III Description of the subsequent chapters 30
Chapter II Syntheses of Porous Materials and Structural
Characterisations 31
I Introduction 33
II Porous materials definition and their overall syntheses 34
II.1 Type of porosity 34
II.2 Dimension aspects 36
II.3 Porous materials syntheses 36
II.4 Inorganic polymerization; Sol-gel process 37
II.5 Soft templates using emulsion 38
II.6 Syntheses of SiO2(HIPE) 40
II.7 Syntheses of SiO2/TiO2 (HIPE) 41
III Structural characterizations 42
III.1 Macroscopic length scale: SEM 43
III.2 Mesoscopic and macroscopic length scale: Mercury porosimetry 44
III.3 Mesoscopic and macroscopic length scale: TEM-TED
and EDXS 45
III.4 Microscopic length scale: XRD 46
IV Conclusion 47
4
Chapter III Fundamentals of Scattering/diffusion/localization and random
lasing with their Optical Characterizations Tools 49
I Introduction 51
II Light propagation through disordered media 51
II.1Scattering of light 52
II.2 Multiple light scattering 53
II.3 Anderson localization of light 54
III How to probe the light propagation behavior? 55
III.1 Transmission versus Length (T (L)) measurements 55
III.2 Time of flight measurements 57
IV Theoretical approach 59
IV.1 Classical diffusion approximation 59
IV.1.1 Stationary solution of the diffusion equation 62
IV.1.2 Dynamic solution of the diffusion equation 64
IV.2 Pre-localized regime 65
IV.2.1 Stationary solution 65
IV.2.2 Dynamic solution 66
V.1 Dye Infiltration and Thermogravitometric analysis (TGA) 67
V.2 Experimental setup for random lasing 69
VI Conclusion 70
Chapter IV SiO2 (HIPE) for multiple scattering/localization
and random lasing 71
I Introduction 73
II Results and Discussion: All Characterizations 73
II.1 Structural Characterizations 74
II.1.1 Macroscopic Length Scale: SEM Image Analysis 74
II.1.2 Mesoscopic and macroscopic Length Scale: Mercury porosimetry 76
II.2 Optical Characterizations 77
II.2.1Transmission versus length measurements 77
II.2.1Time of flight experiments 80
III Random Lasing 86
5
III.1 TGA 87
III.2 Results and Discussion for random lasing 87
IV Conclusion 91
Chapter V SiO2/TiO2 (HIPE) for multiple scattering /localization and
random lasing 93
I Introduction 95
II Results and Discussion: All Characterizations 96
II.1 Structural Characterizations 96
II.1.1 Macroscopic Length Scale: SEM Image Analysis 96
II.1.2 Mesoscopic Length Scale: Mercury porosimetry 97
II.1.3 Mesoscopic Length Scale: TEM-TED and EDXS 99
II.1.4 Microscopic Length Scale: XRD 101
II.2 Optical Characterizations 102
II.2.1 Transmission versus length measurements 103
II.2.1 Time of flight experiments 106
III Random Lasing 108
III.1 TGA 108
III.2 Results and Discussion 109
IV Conclusion 114
Chapter VI Conclusions and perspectives 115
References 123
6
7
Acknowledgement
For their kind co-operation to the completion of my thesis work, I would like
to gratefully acknowledge the enthusiastic supervision of Dr. Renaud Vallée
and Prof. Rénal Backov and, also, for providing me financial support in the
Ph. D. fellowship. It has been an honor to be their Ph.D. student. On one
hand, Dr. Vallée taught me how good experimental optics can be performed
and, always taught me to double-check the obtained results, in order to
ensure reproducibility and, also to ensure that obtained results are correct in
all respects. On the other hand, Prof. Backov trained me with the skills for
chemical synthesis and helped me to understand ‘Integrative Chemistry’. Out
of his very busy schedule, Prof. Backov was frequently visiting all of his
students to motivate and support them for quality research work, which
remains one of his speciality. I appreciate their contributions in terms of
their valuable time, innovative ideas, to make my Ph.D. experience
productive and stimulating. The joy, enthusiasm, and dedication they have
for their research was contagious and motivational for me. They have real
qualities to furnish and/or polish a student. I am also thankful for the
excellent example they have provided as a successful scientist, teacher and
motivator.
I am really grateful to DR Patrick Sebbah for his kind help/guidance and his
kind permission to carry-out random lasing experiments in his laboratory. I
have never seen such a kind and generous scientist like him.
I also greatly acknowledge all jury members DR Bernard Pouligny, DR.
Patrick Sebbah, Prof. Reinhard Höhler, Prof. Peter Hesemann, Dr. Renaud
Vallée, and Prof. Rénal Backov. All jury members were so kind and
supporting and they really suggested me to improve the quality of presented
thesis.
8
The members of the NICE group have contributed immensely to my personal and
professional time at CRPP. This laboratory has been a source of friendship as well
as good advice and scientific discussions. I am especially grateful to Prof. Serge
Ravaine for his help/suggestions to better understand various chemical processes.
I am also thankful to all the members of NICE group, especially Béatrice
Agricole, Laurent Maillaud, Céline Leroy, Simona Ungureanu for their kind co-
operation.
I am also grateful to the Director of the CRPP lab, DR. Philippe Richetti, for his
kind permission to work in his laboratory. I am grateful to him to provide a very
positive and encouraging environment in his laboratory.
I am also very grateful to Isabelle Ly for her continuous help in extracting
beautiful SEM images of my samples. Without her dedication my thesis would
not be so attractive.
I am also thankful to the members of the Service Informatique especially Anne
Faq and Jean-Luc Laborde, for their constant help during my Ph. D. time. Their
help made me familiar to solve all software related problems. Special thanks to
Anne Faq for being kind friend whenever I needed her.
I am also grateful to the Mechanical Department of CRPP, especially Philippe
Barboteau and Jean-Yves Juanico, for their valuable contribution for
manufacturing all kinds of optical supports and stages. They were all the time
available to help us while we were setting up our optics laboratory.
Of course, without the library support, research work and thesis writing are not
possible and I am really grateful to Nadine Laffargue for her constant help for
providing journals/books when I needed them.
For my thesis, I have used various user facilities such as TGA, Mercury
9
porosimetry, TEM-TED and XRD etc. And, for that, quite a number of people
were involved. I am thankful to all of them: Marc Birot, Alain Derré, Frédéric
Louërat, Elisabeth Sllier.
I believe that, without friends, any good or bad things are not possible and for this
long journey I really was with many friends namely - Hrshita, Usha, Anirban ,
Shri bharani, Vivien, Richa, Indrani, Dalice, Besira, Sapana, Parantap, Rupali,
Sudha and many more. I really cannot list all of them and thank them for being
with me and making my journey easy and enjoyable.
Last but not least, my loving dad and, both of my brothers (Anand and Kapil),
who were a source of constant inspiration for this long journey…but it was my
dad’s dream to see me as a ‘Doctor’. I am really thankful to GOD that I am
daughter of you dad.
10
11
Dedicated
To
My Dad
12
13
Chapter I State of the Art
14
15
I. Introduction:
Electromagnetic radiation (light) shows a dual nature. It either consists of
waves (Christian Huygens) or particles (Isaac Newton). In the beginning of the
18th century, Young's double slit experiments showed clear evidence of the wave-
like nature of light (1). In the 19th century, the propagation of light was described
as a wave phenomenon. Through the work of Max Planck, Albert Einstein, Louis
de Broglie, Arthur Compton, Niels Bohr, and many others, it appeared that all
particles have a wave nature (and vice versa). From then, people started to explore
the benefits of light (photons) over the electrons for various applications. Since
the photon is a mass-less particle and can move faster than the electron, it is better
to use photons instead of electrons for various applications, i.e.
telecommunication purposes. The control of the light flow on a microscopic level
may equally well open a new era in the realms of computation, quantum
electronics, photonics, optical chips, and functional devices. E. Yablonovitch said
that everything we have done with the semiconductor will be done with the light
(2). Therefore, the aim is currently to control photons in the way that electrons
were controlled in microchips, or in integrated circuits. In 1987, E. Yablonovitch
and Sajeev John introduced the idea of photonic crystals where a control of the
propagation of light is possible (2, 3). These ordered (periodic) arrangements can
modify the transport of light and give rise to a photonic band-gap similar to the
electronic band-gap in semiconductors (2, 4). Due to the presence of the band-gap
in a photonic crystal, the propagation of light is inhibited at certain wavelengths
depending on the refractive index contrast and the geometry of the structure.
However, considering that the diversity of modern optical devices has
dramatically increased, there is now a plethora of new challenges in our quest for
new ways of controlling light.
I.1 Light propagation through disordered media:
Light can also be controlled in a non-periodic medium. Each non-periodic
medium is in a sense a unique structure. While, at first glance, it seems that no
‘universal behavior' can be traced with respect to light propagation in such a
medium, the definite laws of light propagation resulting from random scattering
16
can still be evaluated. There are analogies between the length-dependent
resistance (and conductivity) of a conductor, coherent backscattering and
Anderson localization of light. Furthermore, there are well-identified classes of
aperiodic media featuring definite geometrical regularities, like e.g. fractal media
with self-similar geometry. Some 'universal behaviors' of light propagation
through such aperiodic media with well- defined geometrical algorithms have
been discovered to date and are still an issue of current research.
When a pulse of light passes through a photonic crystal without scattering, it will
generally emerge from the crystal in much the same shape (with some broadening
of the pulse owing to dispersion). But if the pulse encounters defects in the
crystal’s structure, they will cause its photons to scatter. This can cause a
transition on the propagation of light through the crystal from a predominantly
ballistic to a diffusive regime. In this regime, the photons entering the crystal as a
short pulse will leave as a drawn-out exponential. The duration of this exponential
(characteristic time) is directly linked to the diffusion constant. Diffusive transport
of light energy allows for light ray trajectories to be implied in the consideration
of light propagation. If light scatters so frequently that light rays have no chance
to be plotted between two scattering events, i.e. if diffusive transport is no longer
possible since even a single oscillation cannot be performed by a wave between
successive scattering events, the wave appears to be confined within a portion of
space with a characteristic size of the order of the wavelength. This ultimate limit
is known as the Ioffe–Regel (localization) criterion for mean free paths versus
wavenumber k = 2π/λ: kl < 1 and means that the wave localizes in a random
medium.
In 1958, P. W. Anderson arrived at the conclusion that electrons cannot diffuse in
a strongly disordered potential (5). This phenomenon is among the cornerstone
concepts of the theory of disordered solids and its place in solid-state physics has
been recognized by the Nobel Prize awarded to P. W. Anderson in 1977. It is
referred to as the Anderson localization. While being first introduced for electron
conductivity processes, Anderson localization is possible for all types of waves
provided the localization criterion is fulfilled in terms of sufficiently strong
17
fluctuations of the physical parameters determining the speed of waves. For
electrons, fluctuation of potential is the proper physical parameter, whereas for
electromagnetic waves refractive index fluctuations are the relevant counterpart.
Generally, localization occurs more readily in space with lower dimensionality.
This is always the case for one-dimensional space provided a negligible disorder
is present. This is because there are no independent scattering processes in a one-
dimensional problem. In two dimensions, localization occurs under a certain
degree of disorder (depending upon system size and direction of observation),
whereas in three dimensions the disorder should be even stronger for localization
to occur. S. John was the first to outline the possibility of Anderson localization of
electromagnetic waves in 1984 (6). This report was followed promptly by the
elegant comment by P. W. Anderson (7) and since then localization of light has
become a challenge for experimentalists. However, experimental observation of
the Anderson localization of light is hard to perform and no straightforward report
on the observation of light localization has been reported up to now. The
principal obstacle is the relatively low refractive index of materials in the
optical range.
Experimental studies on Anderson localization of light have been reported in the
microwave regime (8-10), the near infrared regime (11), and the visible regime
(12-14).
For the near infrared, the highest refractive index values are inherent in Ge (n =
4), Si (n = 3.4), and GaAs (n = 3.37); for the visible these are GaP (n = 3.31),
ZnTe (n = 2.98), and TiO2 (n = 2.8). Not all of the above materials are readily
available in the form of a sub-micrometer powder. Not all of them are actually
suitable for experiment. For example, Si and Ge smaller particles readily acquire
an oxide shell in air.
D. Wiersma et al. (11) used GaAs powder samples with different average particle
diameters. A laser wavelength λ = 1064 nm was used, at which the absorption
coefficient of pure GaAs is α < 1 cm−1 and the refractive index is 3.48. Upon
reducing the average particle diameter, these authors found three distinctive
regimes of light propagation. The first one was the known T ∝ 1/L behavior
18
inherent in typical diffusive light transport (for 10 μm particles). The mean free
path evaluated from the backscattering data and from the T ∝ l/L dependence had
the same value l=9.8 μm. A deviation from this law for thicker samples (L > 500
μm) was interpreted as a signature of absorption and estimated to have a
characteristic length labs ≡ α −1, with an absorption coefficient value α < 0.13 cm−1.
When the particle mean diameter goes down to 1 μm, the T ∝ l/L law was no
longer valid. Instead, a quadratic dependence T ∝ L −2 emerged. This type of
behavior was predicted by the scaling theory of localization at the localization
transition (7, 15). Finally, for smaller particle diameters of about 0.3 μm, an
exponential transmission versus length law was observed: T (L) ∝ exp (− L/lloc),
which is a distinctive manifestation of the light localization regime. The
characteristic scaling length parameter lloc appearing in this exponential decay is
called the localization length, which in the case under consideration was found to
be lloc = 4.3 μm. However, this exponential law formally coincides with the Beer-
Lambert-Bouguer law inherent in inelastic (absorptive) losses, expressed in the
form T (L) = exp(−L/labs ) to emphasize this similarity.
After the GaAs paper (11) came out, comments were raised by Scheffold et. al.
(16) to question whether these phenomena were purely related to absorption in the
sample.
Scheffold et al. examined the behavior of samples of large GaP particles. In this
case, the absorption coefficient was found to be rather small. However, an
increase of this absorption coefficient for sub-micrometer powder entities could
not be excluded. These comments were countered in a reply (17) by pointing at
inconsistencies in the arguments used by Scheffold et al. In experiments with Ge
powders (with n =4.1 in the near infrared, Ge is the best candidate for light
localization experiments), this material exhibited a non-negligible absorption
which did influence the transmission of light and partially contributed to the
exponential T (L) law observed (18). Therefore the issue of absorption and
localization in GaAs powders was difficult to resolve by only performing T(L)
measurements.
Further signatures of light localization are to be searched for. An important
19
experiment would be to perform time-resolved transmission in which a drastic
reduction of the diffusion constant at the Anderson localization transition is
expected.
In the simulation done by Conti et al. (19) in the case of an inverse opal, for
moderate amounts of disorder above a certain value, the decay strongly deviates
from a single exponential and the distribution of characteristic times of the
emerging light splits into separate components with two different time constants.
The first component results from the expected delays induced by scattering. The
second component corresponds to a more pronounced critical slowing down of
photons arising from the population of localized states. Surprisingly, one finds
that this critical component only arises within a certain range of disorder, with the
localization length reaching a minimum at some optimal value and then
increasing once more with increasing disorder.
Back to experiments, Maret et al. (12, 20) performed experiments with dense TiO2
ground beads of a size close to the optical wavelength packed in dense layers of
1.2–2.5 mm thickness. They observed and reported increasing deviations at long
time from the exponential time dependence predicted by the diffusive transport
theory. For a sample with large kl value (as checked by coherent backscattering
experiments), the temporal profile of the output light pulse featured good
agreement with the theory of diffusive transport and exhibited an exponential tail
at long times. For smaller kl values, a discrepancy with the diffusive transport
theory manifested, which increased while kl was getting smaller and smaller. In
these cases, the transmission tail was found to be reasonably well described by a
modified diffusion equation taking into account a time-dependent diffusion
coefficient D (t). They found that D (t) beared witness to a decrease with time as
1/t, as expected from the theory of the localization regime.
The above results indicate that time-resolved light flight measurements offer
further insight towards discrimination of light propagation regimes near the
localization threshold.
Very recently, Beek et. al. showed that both the continuous wave and time-
resolved transports of light through GaAs powders can be fully described using
20
the diffusion model (21). They observed very small absorption length (6.1 ± 1.9
μm) and transport mean free path (0.6 ± 0.2 μm). These results shed new light on
the absorption and localization debate from more than two decades ago (16, 20).
The scattering strength, expressed by the product of the wave vector and the
transport mean free path ‘l’ kl = 5.5 is, according to the Ioffe-Regel rule, not in
the regime where a transition into the Anderson localization is expected to take
place. They have used more than two types of samples: powder samples, porous
homogenous and inhomegenous ones. The homogenous sample has an average
pore size of 5 μm. Their time-resolved transmission profiles were exponential
decay curves, suggesting the absence of Anderson localization in the GaAs
ground samples. In their second step, they scratch the homogenous porous sample
(at the center of about 40 μm) to create the inhomogeneity. By using a position-
dependent time-resolved setup, they observed the scratched area of the
inhomogeneous sample. The obtained results showed a non-exponential decay at
long time scale and the value of the diffusion constant was varying (between 64
and 37 m2/s).
Therefore, up to now, only dense sample of TiO2 beads showed visible light
localization in three dimensional systems due to its high refractive index contrast
and absence of absorption in the visible. Our concern is to find other materials
suitable for light diffusion/localization purposes. In order to fulfill the Ioffe-Regel
criterion, material engineers should design materials with a strong scattering
strength which are non-absorbing.
I.2 Disordered materials as random lasers:
Scattering medias can be used to generate random lasing. To understand
the physics underlying the functioning of a random laser, fundamentals of
conventional lasers are required.
A conventional laser is typically constructed from two basic elements: a
material that provides optical gain via stimulated emission and an optical cavity
providing resonant feedback in order to trap light. When the total gain of the
cavity is larger than the losses, the system reaches a threshold and lases. The
21
cavity determines the modes of a laser, i.e. induces the directionality of the
emission and its frequency.
Coherence of a laser emission and its strong dependence on the properties
of the cavity present a severe drawback for certain applications where high spatial
uniformity of illumination and high stability of the emission wavelengths are
desired. The frequency of the laser emission mode is sensitive to optical
alignment, thermal expansion of the resonator, mechanical vibration, and so on.
In order to overcome these issues and other disadvantages caused by the spatial
coherence of a laser beam, Letokhov et.al. have proposed in 1966 a new type of
laser where a non-resonant feedback occurred via reflection off a highly scattering
medium used in place of the optical cavity (22).
In 1967, Letokhov made one step further and theoretically predicted the
possibility of generating laser light through multiple scattering media in which the
light wavelength is much smaller than the dimension of the system (23). In the
proposed system, the scattering material at the same time played the role of an
active laser medium and an effective resonator providing nonresonant feedback.
Letokhov found that the solution of the diffusion equation for propagation of
emitted photons in an amplified medium diverges at some critical value of the
gain ‘g’ depending upon the characteristic size of the pumped medium B (B is
different for different shapes of the pumped volume) and the diffusion coefficient
D, g=DB2. Therefore by increasing either D or B, the gain will increase. The
critical value of g is associated with the threshold of stimulated emission in a
medium with gain and scatterers. That was probably the first report of what we
now call a random laser or powder laser. The proposed applications of an
incoherent random laser include a highly stable optical frequency standard and
express-testing of laser materials, which could not be easily produced in the form
of homogenous large crystals.
Experimentally, the first random laser like emission and properties were observed
by Markushev in 1986 in the powder of neodymium-activated luminophosphors
(Nd:La 2O3, 24). He found that above a certain pumping energy threshold, the
duration of the emission pulse shortened by approximately four orders of
22
magnitude (this was at liquid nitrogen temperature). An approximately equally
strong enhancement was found in the intensity of the strongest spectral
component of the 4F3/2-4I11/2 emission transition (approx 1.06-1.08 µm), the line
width of which narrowed significantly (25). Only one narrow line is observed in
the spectrum above threshold (see Fig 1.1(b), (a) is the spectrum below
threshold). The intensity of this emission line plotted versus the pump energy
resembled the input-output characteristics of a conventional laser (fig 1.1 (c)).
Fig 1.1: Emission spectrum of Nd3+ transition at T=77k (a) below and (b) above threshold (c)
input-output power dependence curve of stimulated emission in Na5La1-x powder.
By increasing the scattering strength of a diffusive medium, one can enhance the
path of the pump light. These long paths are responsible for many of the salient
features of light in random media, such as enhanced backscattering and ultimately
light localization. In most cases, the light intensity is distributed throughout the
sample and the modes are extended. In others, light interference can lead to
Anderson localization for which the multiple scattering processes themselves are
inhibited. The average spatial extent of these localized modes defines the
localization length. Such localized states trap light and can lead to intense lasing
modes. Near the Anderson light localization, localized modes of the passive
system act like regular modes of a conventional cavity. They are not modified by
the presence of gain. By introducing local pumping to the system, selective
excitation of an individual localized mode is possible. Therefore, the emission
23
spectrum is quite narrow at a very low lasing threshold. Such observation
constitutes in fact another approach to determine the scattering strength of the
investigated system.
In the case of 3D system, the multiple scattering of the pump light restricts the
excitation to the proximity of a sample surface. The emitted photons readily
escape through the sample surface, giving a high lasing threshold. In such systems
lasing is an issue. Many lasing modes appear at discrete frequencies, in spite of
tight focusing conditions. Therefore, the overall emission spectrum is broadened
and sharp peaks will not be clearly visible above threshold. Also, in case of
moderately absorbing materials, the non-uniform distributions of gain and
absorption could result in spatial localization of lasing modes in the pumped
region. In other words, local pumping in an absorbing medium creates a
“trapping” site for lasing modes.
Our concern is to observe the random lasing characteristics in 3 dimensional
disordered systems in order to complement the characterization of
diffusion/localization regime exhibited by our materials, performed by other
techniques.
I.3 Material aspects:
The idea of material comes from the natural sources, where we have
variety of disorder materials. One such type of system is the foam/porous
materials, containing gaseous voids surrounded by a denser matrix. These
materials have been widely used in the variety of applications, for example,
insulation, cushioning, absorbents, and weight-bearing structures (26). Depending
on the composition, cell morphology, and physical properties, polymer foam can
be categorized as rigid or flexible foams. Solid foams have cellular structures: the
word cell derives from the latin word cella, which means small compartment.
Cellular structures are common in nature; diatoms, lumbar vertebra, lungs, cork,
wood, sponge, and coral are example of this type of materials. Some of the natural
porous materials are shown in Fig 1.2 (a and b are the Biddulphia reticulate and
Diatoms which is the species of algae and c is the glass sponge which is the
24
Fig.1.2: Biddulphia reticulate (a), Diatoms (b), glass sponge (c)
sponge with a skeleton made up of four and/or six-pointed SiO2 spicules (tiny
spike like structures). Mankind has used these natural cellular materials for
centuries and more recently has made its own cellular materials; polymers are the
most common, but now there are techniques allowing metal and ceramics to
fabricate in the cellular forms. The main areas of application of solid cellular
materials are buoyancy, thermal insulation, packaging, and structural uses,
catalysis, water cleaning, etc (27). Polymer foams represent a group of
lightweight materials that have been widely used in a variety of industries.
However, applications of foam are limited by their inferior mechanical strength,
poor surface quality, and low thermal and dimensional stability. Cellular polymers
are usually prepared by chemically-induced (effervescence), air injection foaming
or using biliquid foams as templates (28). In these cases, the control of the cell
size leads generally to the preparation of fully open-cell structures. Based on our
experience in air-liquid or biliquids foams used as templates we can estimate that
solid foams emerging from air-liquid foams are much more mechanically fragile
than the ones obtained though the use of biliquid foams. Therefore, the emulsion-
template approach to prepare polymer foam could represent an interesting
alternative. High internal phase emulsions (HIPEs) are an interesting class of
emulsions usually characterized by an internal phase volume fraction exceeding
0.74, the critical value of the most compact arrangement of uniform, undistorted
spherical droplets. Consequently, their structure consists of deformed (polyhedral)
and/or polydispersed droplets separated by a thin film of continuous phase, a
structure resembling gas-liquids foams. The internal or dispersed phase of HIPEs
25
can be either polar or nonpolar. Therefore they can be, as ordinary emulsion,
classified into two categories: water-in-oil and oil-in-water (29). Fig 1.3 shows
the hierarchically synthesized porous materials under the laboratory environments
by using emulsion-template. A SiO2 photonic crystal of pore diameter of about 1
µm has been shown in Fig 1.3 a, synthesized by emulsion templating (30). As
emulsions are made of liquids, the droplets are easily removed by evaporation or
dissolution after the templating has been accomplished. They propose a method to
synthesize quite polydisperse macroporous materials of titania, silica and zirconia
with pore sizes ranging from 50 nm to several micro-meters. This technique can
be applicable to a wide variety of metal oxides, as far as the sol-gel chemistry is
well controlled, and even organic polymer gels. The method takes advantage of
the fact that the oil droplets are both highly deformable and easily removable. The
high deformability allows the inorganic gel to accommodate large shrinkage,
which prevents cracking and pulverization during ageing and drying. These
materials with the pore diameter comparable to the optical wavelength are
predicted to have a unique and highly useful optical properties, e. g. - photonic
bandgap and optical stop bands (31). Owing to the sol-gel chemistry and direct
emulsion template F. Carn et. al. synthesized SiO2 monoliths type material with
controlling pore diameters from nm to several microns (Fig 1.3 b) (32). They
obtained a hierarchically organized porosity and high internal surface area. By
increasing the oil volumic fraction of the starting emulsion above the typical value
of 0.74, they increase both the polydisperse emulsion viscosity and the shear
strength, so minimizing both the macroscopic cell sizes and the external junction
sizes while keeping the window cell diameters almost constant. Due to the high
internal surface area in porous materials with dense inorganic walls, gives rise to
maximal contrast of the refractive index between the matrix and the pores of the
material, which is an important characteristic for reaching high-performance
photo-band gap properties. There are a number of reasons why porous materials
are important and are used in various application(s) starting from photonics
(band-gap materials) (31), soft chemistry (shape selective catalysis) (33),
chromatography (34), batteries (35, 36) and bone implants (37) etc. Moreover,
26
many physical properties of porous structure such as density, thermal
conductivity, the mechanical resistance, or the permeability, are closely related to
Fig 1.3: Porous materials synthesized under the laboratory environments (a) SiO2
photonic crystal, (b) poly-HIPEs of SiO2 by Carn et al (32).
the solids. Thus, the control and/or the hierarchisation of porosity represent a
fundamental challenge for making of band-gap materials, catalysts, adsorbents, or
electrodes. Due to high internal surface area porous materials can be used in bulk-
chemistry applications e. g. - catalysis, in which reactant molecules need to be
readily access the interior pore structure but at the same time the internal surface
area is maximized, a ramified pore structure with large pores leading to smaller
and smaller pores is desired (similar to the structure of human lungs). Indeed, it
can be shown that the largest pores should form a 3D grid with the grid sections
subdivided by a sub-grid of smaller pores, and so on. Consequently, there is a
need to have complete control not only of the pore sizes at each dimension but
also the interconnectivity of these pores. Furthermore, for bulk applications it is
important that the preparation of such materials is straightforward, scalable and
eventually fairly inexpensive. Recently Brun et. al. have designed enzyme-based
biohybrid foams for continuous flow heterogeneous catalysis and biodiesel
production (38). In this context, they prepared the functional ordered macro-
mesoporous materials according to the concept of ‘‘integrative chemistry’’ (39).
They prepared the long monolith (Fig 1.4 d) using stainless column (b, c) and the
set up (a) shown for continuous flow. Those features, when applied to
transesterification (biodiesel production) via enzyme catalysis, provide among the
27
top enzymatic activities displayed by the bio-hybrid catalysts bearing
unprecedented endurance of continuous catalysis for a two month of period.
Fig.1.4 (e) shows the SEM image of monolith. This has an advantages of covalent
Fig.1.4: Pictures of: (a) the continuous flow set-up; (b, c) the as-synthesized column after 60 days
stabilization of the enzymes, together with a low steric of continuous flow transesterification
catalysis within the stainless steel canister; (d) the biohybrid macrocellular column extracted from
its canister after 60 days of continuous flow esterification catalysis. The two set of columns used
in this study are labelled col [CCR- lipase]@gGlymo-Si(HIPE) and Col[C-TL-lipase]@gGlymo-
Si(HIPE), (e) shows the SEM image of monolith.
hindrance between proteins and substrates, optimized mass transport due to the
interconnected macroporous network and simplicity with regard to the column in
situ synthetic path. The concept of immobilized biocatalysts, and have designed a
new series of biohybrid materials.
Another important application of these materials has been addressed by
Brun. el. al group in heterogeneous catalysis, separation techniques, absorbers,
sensors, optics. By using the above synthetic route (Integrative Chemistry), they
prepared macro-mesocellular hybrid foams (Eu3+@Organo-Si(HIPE)) (Fig 1.5)
28
and characterized their optical properties (absorption and emission) (40). From
this work, it is clear that these materials are quite useful for light emitting device.
Therefore, synthesizing this SiO2 (HIPE) and using it for optics is quite
reasonable from on the above facts. Using the same strategy, they combined with
foams (Lipase@Organo-Si(HIPE)), showed high catalytic performances. There
are several pathways that intend to synthesize ordered and disordered porous
materials. The integration of the sol-gel process with lyotropic mesophases,
supramolecular architectures, air–liquid foams, bi-liquid foams, external fields,
organic polymers, nanofunctionalization and nanotexturation, are an emerging as
a broad area of research and offers the possibility of achieving new architectures
Fig 1.5: Synthesized Organo-Si(HIPE) monoliths. (a) Eu3+@gβ- diketone-Si(HIPE)
(bearing the yellow color of the β-diketone silane derivative) and Eu3+@gmalonamide-
Si(HIPE) (white as malonamide silane derivative is colorless), (b)
Eu3+@gmalonamide-Si(HIPE) when irradiated under UV light (350 nm), and (c)
Eu3+@gβ-diketone-Si(HIPE) when irradiated under UV light (350 nm).
at various length scales and with enhanced properties. Current approaches to
hierarchically structured inorganic materials include coupling of multi-scale
templating that make use of self-assembled surfactant with larger templates as
emulsion droplets (41), air-liquid foams (42), latex beads (43), bacterial threads
29
(44), organogelators (45), controlled phase segregation (46), and nano- and
macromolding (47) etc.
II. Problems and goals:
From the “state of the art” literature survey, we know that there is
currently no experimental proof of Anderson light localization in the visible light
spectrum for 3D systems, the reason being mainly the lack of available materials
fulfilling the requirements of the Ioffe-Regel criterion. Main hurdles are to
construct non dispersive, high refractive index materials. While different scientific
groups have presented various arguments in favour of a localization behaviour,
like i.e. the quadratic dependence of the inverse transmittance as a function of the
sample using semiconductor materials (in transmission versus length
measurements), it was realized later that this behavior could be due to absorption.
Due to the lack of optical materials able to localize light in the visible range of the
spectrum, this field is still being explored and new materials are probed. In the
same context, we have hunted some potential disordered materials for light
localization purposes and the idea of such material comes from the natural source,
presenting a variety of disordered materials. Carn et al. showed a potential method
to synthesize porous, disordered, white, hierarchical materials by using integrative
chemistry (a sol-gel process combined with the physical chemistry of complex
fluids (emulsion, lyotrope mesophase). This method gives rise to a full control of
the morphology of the structure. Also, by mixing high refractive index metal
oxides, it is possible to enhance the refractive index contrast in these materials.
In this thesis, we aimed to and have synthesized 3D SiO2 (HIPE) and SiO2/TiO2
(HIPE) materials with a given control of the pore diameters, by varying the oil
volumic fraction. We expect these materials to have a large scattering strength,
thus promoting light scattering/localization. Strongly scattering materials would
be of potential interest for random lasing applications. These materials are like
white paints, can be successfully applied for various applications such as display
and or integrated chip technologies. We have quantified their diffusive regime and
random lasing performances by infiltrating them with Rhodamine 6G dyes. The
30
investigation of the light diffusing and or random lasing properties of these new
materials are reported here for the first time.
III. Description of the subsequent chapters:
Chapter II presents an introduction to porous materials and the various
methods used to synthesize disordered porous materials. The procedures to
synthesize SiO2 (HIPE) and SiO2 /TiO2 (HIPE) are described in detail. All
structural characterization tools (SEM, mercury porosimetry, TEM, TED, EDXS,
and XRD) are then discussed.
In chapter III, we first provide a basic theoretical description of light propagation
in disordered media via scattering/diffusion/localization. Then we describe the
experimental tools (time of flight measurements, transmission versus length
measurements) used to probe such phenomena. Finally, we discuss the
fundamentals of regular lasers and random lasers and the experimental setup used
to measure the laser characteristics.
In chapter IV, we describe all results obtained from the structural and optical
characterizations of pure SiO2(HIPE), using the characterization tools described in
chapter II and III. These results are fitted/analysed by the appropriate theories.
Finally, random lasing experimental results are described and discussed in detail.
In chapter V, we describe all results obtained from the structural characterizations
(SEM, mercury porosimetry, TEM, TED, EDXS, and XRD) of the
SiO2/TiO2(HIPE) composites. Then we describe results obtained from the optical
characterizations. Finally, we discuss the random lasing performances of these
composites.
In chapter VI, we conclude and present some future perspectives.
31
Chapter II Syntheses of Porous Materials and Structural
Characterisations
32
33
I. Introduction:
According to the first chapter, we can assume that disordered porous
materials can be the candidates of choice to trigger novel optical properties. In the
present chapter, we describe the fundamental questions, asked by the general
reader on the definition of porous materials and how can they be synthesized.
Beyond, the structural characterization techniques addressed to assess these
foams’ specific surface as well as bulk and skeleton densities are provided. The
properties of such solid state macrocellular foams are commonly dedicated to
heterogeneous catalysis, sensor, photovoltaic, drug delivery etc.(31-37) In the
present study we will use them for the first time for light their light transport
properties and more precisely for localization/diffusion and random lasing
applications. We have used some experimental techniques to structurally
characterize these porous materials such as Scanning Electron Microscope (SEM),
mercury porosimetery, Transmission Electron Microscopy combined with
Transmission Electron Diffraction (TEM-TED), and X-Ray Diffraction (XRD) to
obtain complementary structural information on the synthesized porous materials.
In the first step, a state-of-the-art bottom up approach (molecular chemistry
combines with the emulsion template) has been used to design polymerized High
Internal Phase Emulsion (poly-HIPEs) exhibiting a strong disorder in terms of
refractive index contrast. Owing to this approach, we are able to engineer silica-
based materials bearing controlled morphologies and textures (wall thickness,
wall curvatures, wall textural topologies, wall degree of mesoporosity, cell
diameter etc.). This emulsion-based templating route allows generating porous
hierarchical structures where photons can penetrate these solid foams internal
voids. The pores sizes, the pore monodisperse or polydisperse characters as well
as the wall density can be controlled through the adjustment of the oil volumic
fraction ‘f’ and the shearing rate. In the next step we have added 10 weight % to
15 weight % of Titania during the synthesis, with an objective of increasing the
refractive index contrast between the SiO2/TiO2 walls and the void spaces.
Thereby, by adding TiO2 in to SiO2 matrix, we intend to enhance the multiple
scattering. It is worth mentioning that titania exists in a number of allotropic
34
forms, the most important for optical applications are the ‘anatase’ or ‘rutile’
phases, the last being the TiO2 stable allotropic form. In order to assess which
form is present in the material, we have performed TEM-TED and XRD
analuyses. All structural characterizations technique(s) will be discussed hereafter.
II. Porous materials definition and their overall syntheses.
Porous materials are bi-phase medium which are composed of one continuous
phase (which can be solid or liquid) and while the dispersed phase is gazeous. A
simple example of the disordered porous material is shown in Figure2.1. The
cavities, containing gas, are named ‘pores’. The pores have small macroscopic
pore windows connecting to the porous template cells which are known as the
‘cell windows’. The volume occupied by the available porous environment, is
called apparent volume, and is composed of a solid part and it is denoted by Vs.
The volume of the porous network containing the gas phase of total volume is
denoted as Vp. In order to describe porous materials, several parameters are
necessary. Thus, one of the essential characteristics is related to the pore volumic
fraction, or internal porosity which is noted as φ, and defined as:
φ=Vp/Vs+Vp = (pore volume/ total volume)
II.1. Type of porosity:
Two types of porosities are described here at the macroscopic length scale.
The first one is known as “opened” or “connected” porosity where the cell walls
are broken and the structure consists of the ribs and struts. This type of porosity is
accessible to an external fluid. Other type of porosity is “closed” porosity where
the voids are isolated from each other and cavities are surrounded completely by
the cell walls. This type of porosity does not take part toward mass transport
properties. This topological distinction of porosity is intrinsically connected to the
type of applications when using these materials.
35
Fig 2.1: Represent the SiO2 disordered porous material (poly-HIPEs).
In the field of catalytic supports, the chromatographic filters, electrodes or
columns “open” porosity is useful. On the other hand, for their use as structural
material, where a “closed” porosity would be of use are - in soundproofing,
thermal or of mechanical energy absorption, and also for the light diffusion a
“closed” porosity would be of use. The second important parameter, directly
connected to the ratios of porosity, relates to the density of porous material.
Various type of densities, provide additional informations. The ‘skeleton’ density
is known as the real density of the materials. The skeleton density is defined as
the ration of the mass of the particle to the skeleton volume of the pores. Another
type of density is the bulk density, which is defined as the ration of the mass of
many particles of the material to the total volume they occupied. In this case, the
total volume includes particle volume, inter-particle void volume and internal
pore volume. Basically, each density is relative, and would represent different
values according to the characterization technique employed. Beyond the basic
concepts, it is of primary importance to define precisely the dimensional,
topological and morphological aspects of the pores, in order to be able to correlate
and capture the properties of materials.
36
II.2 Dimension aspects:
In natural porous materials the pore sizes can vary from angstroms (in zeolite
minerals) to nanometers (in leaf cellular structures) and to microns in diatom
skeletons for instance. The pores can be very uniform in shape and can cover a
wide range of pore sizes. The wall structure can be organized (crystalline) or
disorganized (amorphous). Finally, the chemistry (composition) of the wall can
vary enormously from oxide structures to functionalized polymers. According to
recommendations of International Union of Pure and Applied Chemistry
(IUPAC), three categories of the pores will be distinguished:
→The macropores, whose “diameter” is higher than 50 nm; and flow through the
macropores is described by the convection.
→ the mesopores, whose “diameter” lies between 2 and 50 nm; and flow through
mesopores is described by Knudsen diffusion (dispersion: a fluid is moving
through a weak convection in which molecules are diffusing).
→ the micropores, whose “diameter” is lower than 2 nm. Movement in
micropores is governed by activated diffusion (convection is negligible).
Our interest of pore sizes are lies in macroporous regime because our aim is to
enhance light-matter interaction for strong scattering. Therefore, we need a pore
diameter comparable to the light wavelengths.
II.3 Porous material syntheses:
Current approaches to synthesize hierarchically structured inorganic
materials include coupling of multi-scale templating that makes use of self –
assembled surfactant with larger templates as emulsion droplets, air-liquid foams
(41), latex beads(42), bacterial threads(43), organogelators (44), controlled phase
segregation(45) and nano macrmolding(46). Several synthetic methods to produce
hierarchical structures are multi-step processes and consequently there is an
impetus for low cost, one-pot, room temperature synthesis. In this regard, one
synthetic path was first published by Stucky and co-workers (47) using an
emulsion method to synthesize mesoporous silica. Using an emulsion method,
Imhof and Pine (30) has also reported the synthesis of ordered macroporous
37
materials. Subsequently, different research groups published various syntheses of
ordered macroporous materials using a mono-dispersed polystyrene monolith as a
template (48). Most of the methods allows producing an ordered macroporous
solid without meso- or microporosity or micro-mesoporous matter without the
macroporosity. The use of an emulsion makes the aim of producing materials
bearing hierarchical porosity (both macro-, meso and microporous) possible
where the macroscopic voids diameter falling into the range 50 nm - 50 μm (32).
II.4 Inorganic Polymerization: Sol-gel Process:
This reaction mechanism is quite popular in the polymerization of a silicon
alkoxyde and to control the morphology of the gel formed during the synthesis.
The latter point is of prime importance because it determines what will be the
final microporosity of the solid objects. The reaction pathways that we will
presents mainly are based on the work reported by Brinker et al (49). The sol-gel
process, as the name implies, involves the evolution of inorganic networks
through the formation of a colloidal suspension (sol) and gelation of the sol to
form a network in a continuous liquid phase (gel). The precursors for synthesizing
these colloids consists a metal or a metalloid element surrounded by different
reactive ligands. The starting material is processed to form a dispersible oxide and
forms a sol in contact with water or dilute acid. Removal of the liquid from the sol
yields the gel, and the sol/gel transition controls the particle size and shape. After
calcination of the gel to remove organic template we can produce the inorganic
oxides. Sol-gel processing refers to the hydrolysis and condensation of alkoxide-
based precursors such as Si(OEt)4 (TetraEthoxy-OrthoSiliane, or TEOS).
Materials prepared using this process when conbined with emulsions as template
are called, when dealing with silica, Si(HIPE) the acronym pending for High
Internal Phase Emulation (HIPE) due to high internal surface area. The reactions
involved in the sol-gel chemistry is based on the hydrolysis and condensation
reactions of metal alkoxides M(OR)z can be described as follows:
MOR + H2O → MOH + ROH (hydrolysis)
38
MOH+ROM→M-O-M + ROH (condensation)
Finally, resultant synthesis will provide metal oxides (M-O-M). Sol-gel method
of synthesizing nanomaterials is popular amongst chemists and is used to prepare
oxide materials. The sol-gel process can be characterized by a series of distinct
steps.
Step 1: Formation of different stable solutions of the alkoxide or solvated metal
precursor (the sol) where hydrolysis and condensation occurs.
Step 2: Gelation resulting from the formation of an oxide- or alcohol- bridged
network (the gel) by a poly-condensation reaction that results in a strong increase
in the viscosity.
Step 3: Aging of the gel, during which the poly-condensation reactions continues
until the gel transforms into a solid mass, accompanied by contraction of the gel
network and expulsion of solvent from gel pores. Ostwald ripening (also referred
to as coarsening, is the phenomenon by which smaller particles are consumed by
larger particles during the growth process) and phase transformations may occur
concurrently with aging. The aging process of gels can be completed, ranging
between 7-15 days and is critical for the prevention of cracks in gel(s) that have
been cast.
Step 4: Drying of the gel, when water and other volatile liquids are removed from
the gel network. This process is complicated due to fundamental changes in the
structure of the gel. The drying process has itself been broken into four distinct
steps: (i) the constant rate period, (ii) the critical point, (iii) the falling rate period,
(iv) the second falling rate period.
Step 5: Sintering of the gels at high temperatures (T>600°C).
Thus, depending on template, pore diameters greater than 100 microns can
be easily achieved. There are various hard and soft templates are discussed in the
literature such as phase separation, soft templates via emulsion, hard via polymer
beads (48) etc. Soft template approach(es) has been discussed in detail.
II.5 Soft templates: using emulsion:
39
An emulsion is a mixture of two or more liquids which are immiscible and
these are the part of a more general class of bi-phase systems of matter called
colloids. Although the terms colloids and emulsion are sometimes used
interchangeably, emulsion is used when both the dispersed and continuous phases
are liquids. In a direct emulsion, one liquid dispersed phase (oil) is dispersed in
the other continuous phase (water) (See Fig2.2 a). An emulsion is not
thermodynamically stable because of its high interfacial energy between the two
phases of water and oil. Several phenomenon as Ostwald ripening, coalescence,
Fig 2.2: Schematic representation of emulsion (a) and surfactant molecules (b).
drainage, will promote fast macroscopic phase separation between the oil and
water. Therefore, the stability of emulsions is defined kinetically, which means
that the rate of phase separation (relaxation) is slow in stable emulsions where
surfactant entities are used.
Indeed surfactant plays a significant role for the stability of an emulsion.
Surfactants are organic compounds that are amphiphilic, they contain both the
hydrophobic groups (in their tails) and the hydrophilic groups (in their heads)
(See Fig 2.2 b). The surfactant end with hydrophilic nature dissolves into the
water phase and the ends with hydrophobic nature dissolves into the oil phase.
Therefore, a surfactants are contains both water insoluble and oil soluble
components. Consequently, the hydrophilic and hydrophobic nature must be
balanced in the surfactant molecule and for this it has to work well as a good
40
emulsifier. Therefore, to obtain the stable emulsions without coalescence,
surfactant molecules must adsorb efficiently at the interface between the water
and oil phases. A good surfactant can lower the surface tension and the interfacial
tension between the two liquids. At low oil concentration the surfactant
molecules, if their concentration is posted above the critical micellar
concentration (C.M.C.), form micelles where oil droplets acts as a swelling agent.
The TEOS (TetraEthylOrthoSilane) will hydrolyse and condense and then will
bind to the swollen micelles so that the ultimate material is either a mesoporous
silica or a meso-cellular foam. There are various techniques to create templates
such as air-liquid foam, liquid-liquid foam etc. To prepare the monolith type
material, emulsion templates are quite promising and they can control the
morphology of the structure. Therefore, we have used emulsion template to
synthesize our porous materials.
II.6 Syntheses of SiO2(HIPE):
A sol-gel process has been used to obtain inorganic poly-HIPEs with a
procedure based on the use of both micelles and direct concentrated emulsion
templates (32). Tetraetoxy-orthosilane (Si(Oet)4, TEOS),
tretradecyltrimethylammonium bromide 98% (C14H29NBr(CH3), TTAB) were
purchased from Fluka, HCl 37% and dodecane 99% were purchased from
Prolabo. For the basic SiO2(HIPEs), typically 5 g of tetraethoxy-orthosilane
(TEOS) is added to 16.5 g of tetradecyltrimethyl ammonium bromide (TTAB)
aqueous solution at 35% in weight. The aqueous mixture is then brought to a pH
values close to 0 (by adding 6.7 ml of 37 % HCl). This aqueous phase was
continuously stirred for approximately 10 minutes in order to perform TEOS
hydrolysis. Then the emulsion was stirred manually using mortar by adding 35 g
of dodecane drop-by-drop in the as-prepared aqueous medium. This final
emulsion was then transferred into a long cylindrical container (or spread it to
obtain film) and left in this state for a period of one-week (shown in Fig 2.3). The
resulting material was then washed and calcined. To wash the monolith we have
used acetone/THF (1:1) mixture three times over a 24 hour period. Finally, to
41
remove the organic supramolecular-type templates, the hybrid organic-inorganic
materials were then calcined at 600°C for a period of six hours. The heating rate
was monitored at 2°C/min with a first plateau at 200°C for 2 hours. This basic
Figure: 2.3: One pot synthesis of HIPEs. (a) Adding oil drop by drop in continuous aqueous
phase (in mortar). (b) Spreading emulsion for condensation (c) Monolith of poly-HIPE sample.
materials are labeled as SiO2(HIPE). In this study we have performed the
syntheses of two pure SiO2(HIPE) foams emerging from the use of starting
concentrated direct emulsion at two different oil volumic fractions (f ) where 35 g
(f = 0.67) and 60 g (f = 0.78) of dodecane respectively are emulsified. Finally,
silica macrocellular foams are labeled as 35- SiO2(HIPE) and 60- SiO2(HIPE),
respectively.
II.7 Syntheses of SiO2/TiO2(HIPE):
In the second synthetic step, we have synthesized SiO2/TiO2(HIPE) by adding
titanium (IV) isopropoxide inorganic precursor with TEOS. The hydrolysis-
condensation reactions involved in silica polymerization are much easier to
control than that of SiO2/TiO2(HIPE). To obtain monolith-type material is the
difficult task for this composite material due to high shrinkage caused by sintering
effect in titania (discussed later). To prepare such hybrid structure, we have taken
a fixed oil volumic fraction (where f=0.67 means 35g of dodecane oil were used).
Titanium (IV) isopropoxide has been added in the aqueous solution of TTAB and
42
HCL and was stirred for minimum of 1 hour. Then TEOS was added in this
aqueous phase and was stirred for a minute and then emulsification process was
started by adding oil drop-by-drop. This final emulsion was then transfer into a
long cylindrical tube/ or spread like films and kept in this condition for more than
15 days in order to have condensation. We have applied thermal treatment to the
emulsion to enhance condensation process. We kept this cylindrical container in
an oil bath at 35° C for a period of 7 days prior to keeping it at room temperature
until completion. The resulting material was then washed with acetone and THF
(1:1) as mentioned above. Finally, to remove the organic supramolecular-type
templates, the hybrid organic-inorganic materials were calcined at 800 °C for a
period of 12 hours. The temperature used here is higher (800 °C) than the one
used for silica (600 °C), because we intend to obtain the rutile allotropic form of
titania. The main aim is to obtain rutile form is related to its refractive index.
Rutile form (2.6) of titania has higher refractive index than anatase form (2.4) of
titania. This higher refractive index material may improve multiple scattering. By
adding TiO2, we have synthesized two types of materials where 10 % and 15 % of
titanium (IV) isopropoxide weight added in 90 % and 85 % of TEOS weight
respectively. The samples are then labeled as 85/15-SiO2/TiO2(HIPE)and 90/10-
SiO2/TiO2(HIPE) where 85 and 90, 15 and 10 represents SiO2 and TiO2 weight
respectively. During the calcinations, these hybrid materials undergo strong
shrinkage. This high shrinkage is induced by the sintering effect, enhanced for
TiO2 by crystallization, where the amorphous microstructure switches towards the
ordered one. As we increase TiO2 in silica, shrinkage is further increased and it is
difficult to obtain a monolith or film after 15 % of TiO2. Therefore, we have only
synthesized upto 15 % of titania in 85% of silica matrix.
III. Structural characterization:
Structural characterizations have been performed on three scales: macroscopic,
mesoscopic and microscopic length scales. All the experimental techniques, used
for characterization of both type of HIPEs (SiO2 (HIPE) and SiO2/TiO2(HIPE))
are described in this section.
43
III.1 Macroscopic length scale; via Scanning Electron Microscopy (SEM):
A scanning electron microscope (SEM) is a type of electron microscope that
produces images of a sample by scanning over it with a high energy focused beam
of electrons. The electrons interact with electrons in the sample, producing
secondary electrons, back-scattered electrons, and characteristic X-rays (shown in
fig 2.4). Secondary electrons and backscattered electrons are commonly used for
imaging samples: secondary electrons are important for showing morphology and
topography on samples and backscattered electrons are important for illustrating
contrasts in the composition in multiphase samples (i.e. for rapid phase
discrimination via elemental analysis using EDAX). The electron beam is scanned
in a raster scan pattern, and the beam position is combined with the detected
signal to produce an image (shown inside computer in Fig 2.4). The electron
Fig 2.4: Schematic of scanning electron microscope.
beam can be focused on to a spot of approximately 1 nanometer in diameter, and
microscopes are able to resolve details ranging from 1–20 nm in size. To avoid
accumulating charge on the surface, samples must be electrically conductive; non-
conducting samples are often coated with an ultrathin coating of carbon or gold
44
materials. SEM analysis is considered to be "non-destructive"; that is, electron
beam generated by electron interactions do not lead to volume loss of the sample,
so it is possible to analyze the same materials repeatedly. We have performed
SEM observations with a Jeol JSM-840A scanning electron microscope, operating
at 10 kV. In our case, the specimens were carbon-coated prior to examinations.
We have also performed elemental analysis (using EDAX) along with SEM
observation on our silica/titania composites. All results are discussed in chapter V
and IV.
III.2 Macroscopic length scale; Mercury porosimetry:
In order to provide foams skeleton, bulk densities and to quantify the
macroscale void windows distributions, we have performed mercury intrusion
porosimetry (MIP) measurements. At this point we have to specify that this
technique measures the size of the macroscopic pore windows between the
emulsion template cells and not the diameter of the cells themselves. This
technique is based on the premise that a non-wetting liquid (one having a contact
angle greater than 90°) will only intrude pore windows under pressure. The pore
size can be determined based on the external pressure needed to force the liquid
into a pore against the opposing force of the liquid's surface tension. The
relationship between the pressure and pore windows diameter is described by
Washburn as:
P*=-4γ cosθ/d
Where P is pressure, g is surface tension of the liquid, θ is the contact angle of the
liquid and d is diameter of the pore windows. Total porosity is determined from
the total volume intruded. The MIP technique is widely used because of its ease
and simplicity. Since the technique is usually done under the vacuum, the gas
pressure remains zero. The contact angle of mercury with most solids is between
135° and 142°. The surface tension of mercury at 20 °C under vacuum is 480
mN/m. Obtained values from MIP are given in chapter IV and V for all our
samples.
45
III.3 Mesoscopic length scale; TEM-TED, HR-TEM and EDXS:
High resolution transmission electron microscopy (HR-TEM) have been
performed on SiO2/TiO2(HIPE) composites. We have performed HR-TEM using a
JEOL JEM 2200FS microscope operating at an accelerating voltage of 200kV
with a resolution down to the nanometer scale (~ 0.19 nm). The samples for
electron microscopy were prepared by grinding and subsequent dispersal of the
powder in ethanol and applying a drop of very dilute suspension on carbon-coated
grids. The suspension was then dried by slow evaporation at ambient temperature.
In the transmission electron microscope (TEM), electrons are transmitted through
a thinly sliced specimen and form an image on a fluorescent screen or
photographic plate (Fig 2.5). Those areas of the sample that are more dense will
transmit fewer electrons (i.e. will scatter more electrons) and will therefore appear
darker in the image. TEM’s can magnify up to one million times and are used
exclusively in Biology and Medicine to study the structure of viruses and the cells
of animals and plants. The following diagram shows the basic structure of a
TEM. This HR-TEM has a resolution down to nanometer range and can form an
highly resolved image (shown on computer screen in Fig 2.5). This HR-TEM
provides two modes for obtaining diffraction patterns from individual crystallites.
This technique provides a two-dimensional pattern of diffraction spots, which can
be highly symmetrical when a single crystal is oriented precisely along a
crystallographic direction (see inset of Fig 2.5 shown on computer screen). This
HR-TEM utilizes a new, rotation-free image-forming optical system which not
only facilitates acquisition of TEM images and diffraction patterns but also
produces elemental analysis with higher accuracy than the SEM with EDXS.
From this HR-TEM we have performed elemental analysis on our samples using
Energy-dispersive X-ray spectroscopy (EDXS). It relies on the investigation of an
interaction of X-ray with the sample. Its characterization capabilities are due in
large part to the fundamental principle that each element has a unique atomic
structure as a unique set of peaks in its X-ray spectrum. To stimulate the emission
of characteristic X-rays from a specimen, a high-energy beam of charged particles
such as electrons, or a beam of X-rays, is focused onto the sample under
46
investigation. At rest, an atom within the sample contains ground state (or
unexcited) electrons in discrete energy levels or electron shells bound to the
nucleus. The incident beam may excite an electron in an inner shell, ejecting it
from the shell while creating an electron hole. An electron from an outer, higher-
energy shell then fills the hole, and the difference in energy between the higher-
energy shell and the lower energy shell may be released in the form of X-rays.
The number and energy of the X-rays emitted from a specimen can be measured
Fig 2.5: Schematic of Transmission Electron Microscope.
by an energy-dispersive spectrometer. As the energy of the X-rays is characteristic
of the difference in energy between the two shells, and of the atomic structure of
the element from which they were emitted, this allows the elemental composition
of the specimen to be measured. EDXS via TEM is much more accurate than the
EDXS with SEM because it has higher energy and really can deal with the atomic
levels.
III.4 Microscopic length scale; XRD:
X-ray diffraction techniques are a family of a non-destructive analytical
technique which reveals information about the crystal structure, chemical
47
composition, and physical properties of materials and thin films. These techniques
are based on observing the diffracted intensity of an X-ray beam hitting a sample
as a function of incident and scattered angle, polarization, and wavelength or
energy. In order to determine the allotropic form of titania in SiO2/TiO2(HIPE)
composites, we have performed XRD on these samples. The diffraction patterns
were collected on a PANalitycal X'pert MPD Bragg-Brentano θ-2θ geometry
diffractometer equipped with a secondary monochromator over an angular range
of 2θ = 8-80°. Each acquisition was completed in 34 minutes. The Cu-Kα
radiation was generated at 40 KV and 40 mA (lambda = 0.15418 nm). The
powder samples were kept on the sample holders made up of silicon wafer and
flattened with a piece of glass. Results are discussed in chapter IV and V.
IV. Conclusion
In the first part of this work, we have synthesized SiO2 (HIPE) and SiO2/TiO2
(HIPE)s using the so-called integrative chemistry synthetic path, combining sol-
gel process, emulsions and lytropic mesophases. Details on synthetic paths and
characterization tools have been described in this chapter. Results for all structural
characterizations performed on the materials are given in chapter IV and V.
48
49
Chapter III Fundamentals of multiple scattering/localization and random lasing with
their Optical Characterizations Tools
50
51
I. Introduction:
Experimental investigations of light propagation through disordered
materials are discussed in the current chapter. The various types of poly-HIPEs,
introduced in chapter II, are highly disordered, porous and poly-dispersed
materials. These materials are white and thus highly diffusive. To enhance
multiple scattering and promote localization of light, some fundamental
requirements have to be fulfilled such as i) scatters must have a size comparable
to the wavelength of light and ii) the refractive index contrast must be high
enough. We give in this chapter the details of the diffusion/localization theories
that will be used later to characterize our disordered materials. Two types of
characterizations have been performed: i) Transmission versus length (T(L))
measurements which allow us to determine the transport mean free path lt and
absorption length la of the material and ii) Time of flight measurements, which
allow us to determine the diffusion coefficient D0 of the material. Using our
dedicated code written in Octave/Matlab, we have analyzed/fitted the
experimental data with the expressions derived from the relevant
diffusion/localization theories and obtained ls, la, and D0 of the various materials.
In a subsequent section, we provide the details of the experimental setups that
have been used to perform the T (L) and time of flight measurements. Synthesized
materials have also been investigated for their potentialities in random lasing
applications. We finish this chapter with a description of the experimental setup
used for random lasing, experiments performed in the group of Dr. P. Sebbah at
ESPCI (Paris) and describe the analysis of the data obtained.
II. Light propagation through disordered media:
Non-periodic (disordered) structures can strongly affect light transport.
For particles that do not mutually interact (i.e. photons), transport through a
disordered medium is described by multiple scattering, due to the
inhomogeneities of the medium. Here are some fundamental processes described
to understand light propagation.
52
II.1 Scattering of light:
Scattering is a general physical process where some forms of radiation,
such as light, sound, or moving particles, are forced to deviate from a straight
trajectory by one or more localized non-uniformities in the medium through
which they propagate. Scattering of light will lead to diffraction or transmission
depending upon the medium characteristics (shape, size and arrangement of
particles). If radiation is only scattered by one localized scattering center, it is a
single particle scattering (see Fig. 3.1).
Fig 3.1: Schematic representation of single particle scattering. a is the size of the scatterer.
In general two types of scattering phenomena occur; one is elastic scattering and
the other one is inelastic scattering. In the process of elastic scattering, the kinetic
energy of the incident particle is conserved (no exchange of energy to or from the
electromagnetic fields) and only their direction of propagation is modified by the
interaction with other particles. However, in the case of inelastic scattering, the
kinetic energy of an incident particle is not conserved (i.e. there is exchange of
energy to or from the electromagnetic fields). In the later case, some energy of the
incident particle is lost or gained. Furthermore, scattering is characterized by two
important parameters: the size of the scatterer ‘a’ and the refractive index contrast
between the scatterer and the background medium. Depending upon the size of
the scatterers three types of scatterings process are described below.
1. Rayleigh scattering: Scattering of light by particles (i.e. atoms, molecules, and
53
very fine dusts) much smaller than the wavelength (a <<λ) is called Rayleigh
scattering. Its hallmark is the proportionality of the scattering cross section to
1/λ4. As is well known, scattering of light in the atmosphere is accurately
described by Rayleigh scattering. The strong dependence on the wavelength
causes blue light to be scattered more efficiently than red light, accounting for the
blue sky and the red sun at the sunset.
2. Mie scattering: Particles with a size of about a wavelength (a ~ λ) can produce
strong resonances due to interference in the scattered field.
3. Geometric optics: For scatterers much larger than the wavelength, geometric
(ray) optics can be used and light is pictured as a ray inside the material. This type
of scattering is witnessed by natural marvels like the rainbow.
II.2. Multiple light scattering:
When light travels through a disordered/inhomogeneous system, it is multiply
scattered. Straight or ballistic propagation cannot accurately describe the transport
of light in such a system. Anything turbid like e.g. clouds, fog, white paint, human
bones, sea coral, and white marbles scatter light multiply. The multiple scattering
process can be easily understood by the following picture (Fig 3.2) representing
the complicated path followed by light in a disordered medium (cloud). The
Fig 3.2: Light multiple scattering (a) and schematic representation of a disordered medium where
ls is the average distance between two scatters (b).
scattering strength depends upon various parameters such as the size of the
54
scatter, the wavelength of interest, and the average distance between two
scatterers (mean free path ‘ls’ shown in Fig 3.2 b). If the scatterers are identical
and can be characterized by a scattering cross-section σ, the mean free path is
equal to (N*σ)-1 where N is the scatterers concentration. White light undergoes a
random walk and, if the scattering strength is not very large (relatively low
refractive index contrast), the whole transport regime can be accurately described
as a diffusion process.
In our study, we aim to determine the transport parameters ls, and D pertaining to
our samples. From them, we will determine the transport regime followed by light
in these samples: multiple scattering in the case of weak scattering and
localization in the case of strong scattering.
II.3. Anderson light localization: This phenomenon is named after the American
physicist P. W. Anderson, who was the first one to suggest the possibility of
electron localization inside a semiconductor, in case of sufficiently large
randomness of the impurities or defects (5). Beyond the critical amount of
impurity, scattering, diffusion, zigzag motion of the electron is not just reduced, it
can come to localization and the conductivity vanishes. Therefore, the conductor
becomes an insulator. The key concept in that description was the mean free path
‘ls’, the average length over which an electron travels before it collides with an
ion. According to the classical theory, the electronic conductivity is directly
proportional to the electron mean free path. Thus, the larger the number of
impurities presents in the material, the smaller is the mean free path and,
accordingly, the lower is the conductivity. To distinguish diffusion and
localization on the basis of the scattering strength, Ioffe & Regel have given
limiting criteria. They predicted a localization to occur, featuring a transition from
metal to insulator when k*ls ≤ 1 (where k = 2π/λ) is satisfied (50). Anderson
localization is a general wave phenomenon that applies to the transport of any
kind of waves, would it be acoustic, spin etc. In the optical regime, anything
turbid scatters light diffusively. The scattering strength of natural disordered
materials is too weak to obtain Anderson light localization.
55
Our aim is thus to synthesize materials with a large scattering strength and
avoiding light absorption, in order to localize light. Up-to-now, this is a very
challenging and tricky task in case of three dimensional systems.
III. How to probe the light propagation behaviour:
There are various experimental techniques which allow one to investigate
light diffusion/localization behavior. In this section, we are describing two types
of experimental techniques: transmission versus length and time of flight
measurements. These techniques have been shown to be successful in
discriminating between diffusion, absorption, and or localization processes (12).
III.1 Transmission versus length T (L) measurements:
In such measurements, the static transmission through various samples of
different thicknesses is collected. Figure 3.3 schematically sketches the setup used
to perform the transmission versus length measurements. Material slabs with
different thicknesses are placed on the entrance aperture of an integrating sphere
and illuminated with a white light lamp (fiber coupled white light HL-2000-HP-
FHSA, Ocean Optics). The integrating sphere (fiber coupled integrating sphere
FOIS-1, Ocean Optics) consists of a hollow cavity with its interior coated for high
reflectance. The output is recorded by a spectrometer (fiber spectrometer
USB2000+VIS-NIR, Ocean Optics) and the data are sent to the computer. Fig
3.4.a shows the bare transmission signal S collected from L=1 to 10 mm sample
thicknesses for 1 second acquisition time. These samples are optically very thick.
It can therefore be assumed that only diffusive light comes out at any angle from
the sample and enters in the integrating sphere. This bare transmission S is
normalized by the reference (R) and dark signals (D) (shown in Fig 3.4.b) by
using the following formula
The reference signal is the signal of the white lamp used and the dark
signal the one recorded in absence of incidence light. Such signals are obtained
56
Fig 3.3: Schematic representation of the setup used to perform the static light measurements. A
slab of poly-HIPE with thickness L is placed at the entrance of an integrating sphere and
illuminated with white light. Diffuse light is measured at the detector, integrated over all angles.
Fig 3.4: a. Bare transmission S for various sample lengths (from L=1 to 10 mm) and b shows the
normalized transmission properly defined as T= S-D/R-D.
57
for all wavelengths extending from 450 nm to 850 nm. Taking two particular
wavelength (500 and 700 nm), we then plot the inverse transmission 1/T as a
Fig 3.5: Inverse transmittance for all sample thicknesses (from L=1 to 10 mm) at two wavelengths
500 (red stars) and 700 nm (blue stars).
function of thickness L in Fig. 3.5.
From such a plot, and by using the stationary solution of the classical
diffusion equation as a fitting equation (Section IV), we are able to obtain the
transport mean free path and absorption length of this type of diffusive samples.
III.2 Time of flight measurements:
In these measurements, the time-dependent transmission of the incident
pulse is collected through the sample. Our aim here is to determine the diffusion
coefficient. Fig 3.6 shows the schematic of the time-resolved system in which we
have used a combination of a femtosecond laser in the excitation path and a streak
camera in the detection path. The femtosecond laser source (from Amplitude
System) delivers pulses of 300 fs with a repetition rate of 10 MHz at a wavelength
of 1030nm.
58
Fig 3.6: Schematic representation of the experimental setup used to perform time-resolved light
measurements. A femtosecond laser pulse is sent to the sample. A spectrometer collects the pulse
temporally spread by the sample and sends it to the streak camera.
By doubling this wavelength of 1030 nm owing to a SHG (Second Harmonic
Generation) crystal, we can get the output in the visible range (at 515nm). The
laser beam is then focused onto the disordered material. Due to multi-diffusion in
our material, the output pulse is spread in time (depicted in Fig 3.6 inside the
computer image). The temporally spread pulse is then collected by the
spectrograph (from Princeton) and sent to the streak camera. The Hamamatsu
streak camera (HAMAMATSU Streak scope C10627), has a temporal resolution
of around 20 ps. From this geometry, we thus get the time of flight of outgoing
photons from the structures (a time profile is shown in Fig 3.7 for a diffusive
sample of Polystyrene beads of 1 micrometer diameter in solution in a 1 mm thick
cuvette in red circles). To obtain the material dynamic parameters, the
experimental data are fitted by the time-dependent solution of the classical
diffusion equation (in blue). Due to the experimental acquisition procedure, a
59
slight deviation appears at long times with respect to the behavior predicted by the
classical diffusion model, which is not a sign of pre- localization, since this type
of sample is not subject to localization.
Fig 3.7: Transmition versus time of a diffusive sample of PS beads in solution.
IV. Theoretical approach:
As explained in the previous sections, in order to determine the transport
parameters, the data originating from the T (L) and time of flight measurements
must be fitted. In order to provide the functions to be fitted, we describe in this
section two theories applying respectively to the multi-diffusive (or weakly
scattering) regime and to the pre-localization (or strongly scattering) regime. Both
theories are considered in static and dynamic perspectives. The goodness of the
fits originating from one or the other theory will give us an idea of the transport
regime obeyed by our samples.
IV.1 Classical diffusion approximation:
The multiple scattering of light is a very complicated solution of Maxwell
equations, when many scatterers have to be taken into account. The diffusion
approximation considers a random walk of photons and imposes a continuity
equation for the light intensity I(r, t) (where r is space and t is time), disregarding
the interference effects. Propagation of light can, therefore, be viewed as a
diffusion process such as gasses which diffuse in a partial pressure gradient. The
60
diffusion equation can be derived in a straightforward way from the continuity
equation, which states that a change in density in any part of the system is due to
inflow and outflow of material into and out of that part of the system. Effectively,
no material is created or destroyed:
where ϕ(r, t) is the density of the diffusing material at location r and time t and j
is the flux of the diffusing material. The diffusion equation can be obtained easily
from this when combined with the phenomenological Fick’s first law, which
assumes that the flux of the diffusing material in any part of the system is
proportional to the local density gradient:
3.2
If D (diffusion coefficient) is constant, then:
3.3
In the case of light diffusion, ϕ(r, t) is replaced by I (r, t), which is the light
intensity. In disordered materials, the light intensity will decay for various
reasons. The most important parameter is the scattering mean free path ‘ls’ which
is the average distance between two consecutive scattering events. This parameter
sets the limits of the diffusive approximation as λ<< ls<< L: many scattering
events occur before the light leaves the system, where L is the length of the
system while the medium is still diffuse. After several scattering events, the light
propagation is completely randomized. The transport mean free path ‘lt’ is defined
as the average distance after which the intensity distribution becomes isotropic
and is the characteristic length in the regime of multiple scattering. The transport
mean free path ‘lt’ is related to the scattering mean free path ‘ls’ as lt=ls/(1-cosθ)
61
where θ is the average angle between incident light and scattered light. If one
consider the transport of ballistic or un-scattered light in a medium at position (r)
and time (t), it follows the Lambert-Beer equation where the intensity is
maximum at r=0 and exponentially decaying with li, the absorption length
3. 4
By using Eq. 3.3, in a diffuse system, light propagates according to the diffusion
equation as follows:
3. 5
where S(r, t) is the light source (given later), νe is the energy velocity (velocity of
the transported energy given by the ratio of the energy flux to the energy density
at any point in the sample) and li is the absorption length, over which light is
attenuated by a factor e−1. This equation describes how light intensity spreads
through the system with a rate of transport dictated by the diffusion constant, D.
The larger the diffusion constant, the faster is the transport process. The whole
diffuse transport propagation will be truncated by an absorption term which
is the characteristics time over which light is absorbed in the system. Multiple
light scattering increases the interaction between light and the disordered medium.
The diffusive absorption length, la, is the distance light propagates diffusively
before being absorbed. Inside a diffusive and absorbing material, la is the
penetration depth of the diffuse light. Diffuse light propagates a greater distance
than in a homogeneous material to reach the same depth because of the random
walk performed by light. For this reason, la is shorter than li ( ).
The experimental systems treated in this work have a slab-like geometry which
imposes some boundary conditions on the diffusion equation: the system can be
considered infinite for x and y directions and limited between z = 0 and z = L.
Within the diffusion approximation, only diffusive light can be handled and,
62
therefore, an incident plane wave cannot be inserted as source in the diffusion
equation: it decays exponentially inside the system. The incoming coherent flux is
replaced by a source of diffusive radiation at the plane z = zp , where zp is the so
called penetration length. A common phenomenological way to introduce a source
(51) is to consider an exponentially decaying one,
or a delta function that is infinite at z=zp,
Two types of boundary conditions exist, Dirichlet and Neumann boundary
conditions. Dirichlet boundary conditions, imposed on either an ordinary or a
partial differential equation, specify the values a solution needs to take on the
boundary of the domain while Neumann boundary conditions specify the values
that the derivative of a solution is to take on the boundary of the domain. In our
case, Dirichlet boundary conditions are appropriate and imposed to the diffusion
equation as follows:
3. 6
where ze1,2 are the extrapolation lengths, of the order of ‘lt‘, which are the
positions where the diffusive light intensity would be zero if the light source
would be placed inside the system and, eventually, may be different at the front
and back surfaces (if their reflectivities are different).
IV.1.1 Stationary solution of the diffusion equation:
The stationary solution of the diffusion equation (3.5) with boundary
conditions as given in (3.6) and for a delta source leads to the total transmission of
light through a sample slab given by (52):
63
3.7
Where
and 3. 8
In the solution, α = 1/ li is the inverse absorption length and R is the
polarization and angular averaged reflectivity of the boundaries (53). Figure 3.8
represents a scheme of the light intensity versus distance I(z), assuming a delta
source (vertical black line) for a slab geometry system with the parameters related
to the diffusion equation such as ze and zp, which are typically set to be identical
(ze = zp).
A very important function to take into account is the total transmission of
light integrated over all angles, which is defined as the total flux at z= L divided
by the incident flux S(0):
3.9
In the absence of absorption and for L>>lt, we can expand sinh(x) in a Taylor
series limited to the first order term to obtain the total light transmission.
= 3.10
where ze ˜ lt since, by definition, lt at the order of the length for which the light
intensity is completely randomized.
Therefore the total transmission (equation 3. 10) reduced as:
3.11
64
Figure 3.8: Plot of the light intensity vs. distance in a slab of a poly-(HIPE). The dash line
represents the solution to the diffusion equation assuming a delta source placed at Z=Zp.
Extrapolation length Ze and penetration length Zp are shown.
The total light transmission through a multiple scattering slab in the
absence of absorption is directly proportional to the transport mean free path lt
and inversely proportional to the slab thickness. Doubling the thickness of the
(optical) conductor halves the transmission. This is known as the photonic Ohm’s
law.
In the case of an absorbing sample, by using Eq. 3.9 as the fit function of
the inverse light transmission versus sample thickness in T(L) measurements, it is
possible to obtain the absolute values of the transport mean free path lt and
absorption mean free path la.
IV.1.2 Dynamic solution of the diffusion equation:
The full solution of the time-dependent diffusion equation (eq. 3.5) with
boundary conditions is given by (54):
65
3. 12
where
and 3. 13
is the absorption or inelastic time. The rate of diffuse light transport in such a
disordered system is defined by the diffusion constant D, given by the Fick’s law
(55).
The dynamic solution of the diffusion equation including absorption is a sum of
exponentially decaying functions. Absorption in homogeneously absorbing
sample simply introduces a multiplicative exponential factor. The physical
meaning of the summation in equation (3. 12) can be understood as follows: light
which follows the shorter optical paths through the slab is transmitted at earlier
times while the light which performs longer random walks emerges much later.
The total transmission is therefore, given by the sum of all these contributions.
This produces a time-spread of the initial pulse, which depends on the diffusion
constant. This time dependent solution of the diffusion equation (Eq 3.12) is an
exponential decay at long time, with the asymptotic form:
3. 14
IV.2 Pre-localized regime:
In the case of a pre-localization (strong scattering) regime, the stationary
and dynamic solutions show different features. In this section, we describe the
solutions modified by the local scale theory of localization as introduced by
Berkovits and Kaveh (56).
IV.2.1 Stationary solution:
As discussed earlier, light diffusion in a disordered, non-absorbing multi-
66
diffusive dielectric slab, leads to the photonic Ohm’s law. In a moderately
absorbing system, Ohm’s law will not hold anymore. Furthermore in case of
strong scattering (k.ls ≥1) the system is predicted to exhibit a quadratic
dependence of inverse transmission (1/T ∝ L2) with respect to the system size,
according to the scaling theory of light localization at the localization transition
(16). The averaged transmission coefficient of a wave near the transition will thus
change from T = ls/L in the weak-disorder limit (ls >>λ) to
T=( ls/L)2 in strong-disorder limit, ls ~λ. 3.15
Observing such a quadratic dependence in the T(L) measurement could be the
signature of the light localization transition. However, moderately absorbing
sample may also show such kind of quadratic dependence. Therefore to
investigate the exact reason of an observed quadratic dependence of inverse
transmittance versus thickness, we must proceed to further investigate.
IV.2.2 Dynamic solution in the pre-localization regime:
In their local scaling theory of localization (56), Berkovits and Kaveh have
calculated the time dependence of transmitted pulses through the slab geometry.
The diffusion constant has been shown to be time-dependent and follows the law
(57-60)
3.16
where τ is the elastic scattering time ls/c, D0=(1/3)c*ls and ξ is the correlation
length.
According to this time-dependent diffusion constant, Berkovits and Kaveh
predicted a time dependence of the transmitted wave for an initial injected narrow
pulse of the form
3.17
An asymptotic form of T(t) near the transition is given by
3.18
This form features a departure from the single exponential decay at long time.
67
To analyze the time of flight experiments, we fitted the decay profiles with
both equations 3.14 and 3.18. If, at long times, the obtained decay profile is a
single exponential form, the scattering is weak and the sample is simply,
classically multi-diffusive. In that case, it is best fitted by the function 3.14. On
the contrary, if the long time decay presents a departure from the single
exponential behavior, it will be best fitted by function 3.18, as shown in chapter
IV and V. This departure from the single exponential law then points to as system
more likely to be in the pre-localization regime.
V.1 Dye infiltration and TGA for random lasing: For the sake of random lasing
investigations, we have infiltrated an active medium in our bare SiO2 and
SiO2/TiO2(HIPE)s. We have chosen Rhodamine 6G laser dyes (shown in Fig 3.9)
as a gain medium because its optical properties such as quantum efficiency,
emission and absorption spectra etc. are well-known. Rhodamine 6G is a laser dye
which is commercially available. This dye is pumped by the second (532 nm)
harmonic from a Nd:YAG laser. The dye has a remarkably high photo-stability,
high fluorescence quantum yield (0.95), low cost, and its lasing range has close
proximity to its absorption maximum (approximately 530 nm). The lasing range
of the dye is between 555 to 585 nm with a maximum at 566 nm.
In order to infiltrate dye molecules in our HIPEs, we have dipped our materials in
the dye solution. However, we have observed that their surfaces are only
absorbing the dye molecules but dye is not able to penetrate the material. When
we drop HIPEs in the dye solution, we have observed that the sample was lying
on the top of the solution. The main reason is that these HIPEs are full of air and
to infiltrate them by the dye first we have to extract the air. Therefore, we have
applied vacuum of 10 mbar for 2 hrs to extract the air from the HIPEs and allow
the out flow of the dye solution from material. To confirm HIPEs infiltration, we
have cutted our sample in two pieces (so that we can see an inner part of the
sample) and kept under the UV lamp to observed irradiance. We have taken fixed
initial concentration (2*10-3 Mol/liter) for all HIPEs. But different structure
absorb different amount of dye depending upon their bulk densities. Therefore, in
68
order to know the exact amount of dye molecules within the structure, we have
Fig 3.9: Rhodamine 6G dye molecule.
performed thermogravitometric analysis (TGA). Thermal gravimetric analysis is a
type of testing performed on samples to determine changes in weight in relation to
a temperature program in a controlled atmosphere. Such analysis relies on a high
degree of precision in three measurements: weight, temperature, and temperature
change. To determine composition and purity one must take the mass of the
substance in the mixture by using thermal gravimetric analysis. In the first step,
we heat our composite at high temperature so that one of the components
decomposes into a gas and dissociates into the air. It is a process that utilizes heat
and stoichiometry ratios to determine the percent by mass ratio of a solute. If the
compounds in the mixture that remain are known, then the percentage by mass
can be determined by taking the weight of what is left in the mixture and dividing
it by the initial mass. Knowing the mass of the original mixture and the total mass
of impurities liberating upon heating, the stoichiometric ratio can be used to
calculate the percent mass of the substance in a sample. In our case, increasing the
temperature Rhodamine molecule decomposes and SiO2(HIPE) or
SiO2/TiO2(HIPE)s materials remains indestructible. Therefore from the weight
loss (in percentage) caused by the dye molecules represent the amount of dye
within the structure. Using bulk density and weight loss, we are able calculate dye
molecules per unit volume. Results of thermogravitometric analysis have been
given in chapter IV and V.
69
V.2 Experimental setup for random lasing:
We have explained the working principle of random lasers as well as their
typical characteristics in chapter I. In this section, we will discuss the
experimental setup (Fig 3.10) used at IL-ESPCI to investigate random lasing. The
second-harmonic output of a nanosecond Nd3+: YAG laser (at wavelength: 532
nm, pulse duration: 6ns, repetition rate: 5 Hz) was focused at the front surface of
Fig 3.10: Schematic representation of the experimental setup used to perform random lasing. A
nanosecond laser pulse is sent to the poly-HIPE sample. The output emission is collected in the
backward scattering geometry using a fiber placed at 45 degrees with respect to the normal of the
spectrometer. A filter F is used to cut the pump beam.
the poly-HIPEs self standing film by a lens of 10.0 cm focal length to excite R6G
molecules embedded in the HIPEs. The sample is placed beyond the focal point
of the lens to avoid damage and/or bleaching of dye. The emission of the dye
molecules from the sample is then collected in the backward scattering geometry
using a fiber placed at 45 degrees with respect to the normal to the sample
surface, and recorded using an Ocean Optics HR4000 spectrometer. This
spectrometer has a peak-to-peak spectral resolution of about 0.11 nm. Before the
spectrometer, we have used the band pass filter F (to cut the line 532nm and allow
long-pass emission from 540nm) to cut the pump beam. Recorded spectra will
70
give us the output intensity counts versus wavelength. An energy meter
(resolution 5 µJ) has been used to record the input energy. Using this geometry we
have systematically investigated the occurrence of random lasing and the
input/output characteristics of the materials. The obtained experimental data of
output versus input intensities have been fitted to obtain lasing threshold (in
chapter IV and V).
VI Conclusion:
In this chapter, we have developed a fundamental understanding of how
light propagate through disordered materials. The first part of this chapter was
specifically devoted to the theoretical and experimental approaches for
investigating scattering/diffusion/localization and random lasing. We have shown
the experimental setups allowing us to collect the transmitted light in disordered
media. The obtained results are discussed in chapter IV and V.
71
Chapter IV SiO2 (HIPE) for multiple scattering/localization and random lasing
72
73
I. Introduction:
Among the various materials available for photonics, SiO2 is probably one of
the most promising and renowned candidate for various optical applications. It is
important because of its low cost, compatibility with electronics, and established
fabrication techniques (30, 31, 39, 61). This material can be grown in a ordered or
disordered form using various effortless procedures. In chapter II, we have described
the sol-gel process allowing us to synthesize porous disordered SiO2 structures.
Generally, this material is white and non-absorbing in the visible range of the light
spectrum. It is white for large enough thicknesses and thus is beneficial for
localization/diffusion processes. In the current chapter, we discuss the optical properties
of SiO2 (HIPE)s. Two type of materials, namely 35-SiO2(HIPE) and 60-SiO2(HIPE),
have been structurally and optically characterized. Structural information on these
materials was obtained on macroscopic length scales using SEM and mercury
porosimetry. Results are discussed in the current chapter. After reporting on the
structural characterization results, we report on the light transport parameters of these
materials. Optical measurement, combining steady-state and time-resolved detections,
in the far field, are used to characterize the photon transport parameters (e.g., mean free
path, absorption length, diffusion coefficient, etc.). We show that a reduction in size of
the pores and an increased monodispersity of their distributions occur as the oil volumic
fraction (f) is increased, leading to a decrease of the transport/absorption mean free
paths and diffusion coefficient. The stationary solution of the diffusion equation has
been used to fit the static experimental data and results are discussed in detail. Two
different theoretical approaches have been used to fit the dynamic experimental data:
one is the classical diffusion approximation and the other one is the scaling theory near
the localization transition. Both approaches were discussed in detail in chapter III. From
this study, we are able to understand/characterize our highly complex disordered
materials. In a next step, we have used these materials for random lasing investigations.
By minimizing the transport mean free path and diffusion constant, we expected to
lower the random lasing threshold. Performance on random lasing and complete set of
results are shown in the subsequent sections.
II. Results and discussion; All characterizations:
74
Two types of materials (35-SiO2 (HIPE) and 60- SiO2 (HIPE)) are characterized
structurally and optically. Experimental details of the characterization setups are
described in chapter II and III. The experimental results are fitted using the theories
discussed in chapter III.
II.1 Structural characterizations:
Structural characterizations were performed using SEM and mercury
porosimetry. Both types of structural characterization are given in this section in detail.
II.1.1 Macroscopic length scale via SEM:
Owing to scanning electron microscopy (SEM), we have obtained structural
information, mainly the pore size distributions. The SEM has been described in chapter
II. Obtained SEM images are shown in Fig 4.1. An inorganic film-type material (Fig.
4.1.a) depicts the polymerized (HIPE) type interconnected macroporous texture with
poly-disperse cellular sizes within the micrometer range (4.1. b and 4.1.c). At this point,
we would like to mention that we call “windows” the holes, which separate two
adjacent macroscopic cells. To measure the pore diameters distribution, SEM image
analyses have been performed. As we increase the starting emulsion oil volumic
fraction (f), the macro-cellular cell sizes diminish drastically (see Fig. 4.1 b to c) and
the size, mono-dispersity of their distributions is reduced from 10 − 40μm to 1 − 3.5μm
(shown in Fig. 4.2, SEM image analysis data). In fact, considering the emulsion
rheology, it is well known that the viscosity of the direct emulsions increases
dramatically when the oil volumic fractions access the value 0.74 (62, 63). For the
starting emulsions of the materials 35-SiO2(HIPE) and 60- SiO2(HIPE), this
phenomenon increases the shear applied on the oily droplets minimizing thereby their
sizes.
Furthermore, as seen in Figs. 4.1 b, the macroporous monolithic texture resembles
aggregated hollow spheres. Indeed, in such low pH (0.035) conditions, the
polycondensation is strongly Euclidian (49) (dense) and starts at the oil/water interface.
In fact, the oil-water interface is promoting silica condensation by minimizing the
nucleation enthalpy, acting so as a defect (64). We may argue that this feature is valid at
75
FIG. 4.1: SEM micrographs of the 35-SiO2(HIPE) (b) and 60-SiO2(HIPE) (c).(a) shows a 35- SiO2(HIPE)
monolith.
the micelles interface too, but the Euclidian character of the on growing network is
addressed with solubilization-reprecipitation, the recipritation (nucleation) will occur at
Fig 4.2: Normalized size distributions (dotted red lines: 60-SiO2(HIPE); solid black lines: 35-
SiO2 (HIPE)) of pore diameters.
76
the interface bearing the lower curvature, this is to say the oil/water interface droplets
and not the micelles interfaces, if working above the critical micellar concentration
(CMC). Also, it the oil-water interface of an emulsion is associated to a higher
surfactant concentration than the core of the continuous aqueous phase (64). In our case,
this specific region of high surfactant concentration is also enhancing silica
condensation through minimizing electrostatic repulsions or achieving faster inorganic
precursors electroneutrality favoring the nucleation. As a consequence of the reduction
of the macroporous void space diameters from the 35- SiO2(HIPE) foam to the 60-
SiO2(HIPE), we expect the light transport parameter to decrease in the 60-SiO2(HIPE)
structure with respect to those of the 35-SiO2(HIPE) .
II.1.2 Macroscopic length scales via mercury porosimetry:
In order to provide foam skeletal, bulk densities and to quantify the
macroscale void windows distributions, we performed mercury intrusion
porosimetry measurements. At this point we have to specify that this technique
measures the size of the macroscopic pore windows between the emulsion
template cells and not the diameter of the cells themselves. Overall, if we increase
the condensation at the interfaces by minimizing the oil droplet diameters and by
optimizing the droplets number, we increase the number of cell walls per unit of
volume, leading to formation of a material with a larger bulk density (Table 4.1)
Materials Oil volumic Porosity Skeleton Bulk
fraction (%) density density (g/cm3) (g/ cm3)
35-SiO2(HIPE) 0.67 91 1 0.083
60-SiO2(HIPE) 0.78 77 0.98 0.23
TABLE 4.1: Mercury intrusion porosimetry data of two samples (35-SiO2 (HIPE) and 60- SiO2 (HIPE)).
and larger shrinkage. The skeleton densities are smaller than 1.2 (silica density)
77
because the foam walls are indeed bearing a large degree of meso-porosity (Fig.
4.1b, spheres have small pores). Increasing the oil volumic fraction, the porosity
of the material is reduced in 60-SiO2(HIPE) as compared to 35-SiO2(HIPE). The
60-SiO2(HIPE) is thus denser than the 35-SiO2(HIPE). For denser sample, a
stronger multiple scattering is expected. Furthermore, due to the the high bulk
density of the denser sample, this material will also absorb more dye molecules,
i.e. the amount of gain medium to promote random lasing.
II.2 Optical characterization:
Two types of materials (35-SiO2 (HIPE) and 60- SiO2 (HIPE)) are
characterized on the steady-state level and dynamically. Results are reported in
this section. Experimental details of the setups are described in chapter III. The
experimental results are fitted with the equation originating from the various
theories mentioned in chapter III.
II.2.1 T(L) experiments:
White light transmission versus length experiments, T (L), have been
performed on the two types of samples with more than 20 thicknesses ranging
between 1 and 10 mm. Figs 4.3.a and b exhibit the conductance versus thickness
behavior for the (35-SiO2(HIPE) and 60-SiO2(HIPE)) samples at two different
wavelengths (blue stars: 500nm and red stars: 700 nm). These experimental
results have been fitted by the stationary solution of the diffusion equation (Eq
3.9) including absorption (blue and red solid lines in Fig. 4.3). Using this fitting
function, we obtained the transport mean free path lt and the absorption length la
for the full range of wavelengths displayed by the white light illumination (from
500 to 800nm). The obtained values of lt and la are plotted in Fig 4.4 and 4.5. The
transport mean free paths at 515 nm of 35-SiO2(HIPE) and 60-SiO2(HIPE) are 86
μm and 19 μm respectively. Their absorption mean free paths at 515 nm are 2.9
and 1.5mm, respectively. A common behavior for transport mean free path is to
vary with frequency. However, both Fig. 4.4.a and 4.5.a exhibit a rather flat
dependence of lt on wavelength (especially around 515 nm, which we will use
78
Fig 4.3: Inverse transmittance versus thickness behavior for 35-SiO2(HIPE)(a) and 60-
SiO2(HIPE)(b) at λ=500 nm (blue circle) and at λ=700 nm (red circle) fitted by the stationary
solution of diffusion equation (blue and red solid line respectively) as well as by the 1/T∝ L2 law(
dotted lines). Inset shows the residuals of the fits.
79
Fig 4.4: Wavelength dependent transport mean free path (a) and absorption length (b) of 35-SiO2(HIPE).
later as excitation wavelength for dynamic measurements and random lasing
experiments), excluding the possible occurrence of a wide variety of T(L) due to
the large spectral width of the incident light. As expected, the transport mean free
path is shorter for the HIPE presenting the smaller pore sizes. Also, the latter
being the denser sample, it exhibits the shorter absorption length. The stationary
solution of the diffusion equation including absorption fits particularly well the
experimental data, providing values for the transport mean free path such that k*lt
>> 1. Although these values are inherent to diffusive light transport, the plots
shown in Fig. 4.3 exhibit a quadratic dependence (1/T ∝ L2) (black dash lines in
Fig. 4.3) rather than a linear relationship, expected from the classical diffusion
(equation 3.11) in the absence of absorption. At first, E. Abrahams et al. and later,
Wiersma et al. used the scaling theory of localization and predicted that this type
of quadratic dependence may appear near the localization transition. This
observation lifts the issue of whether the quadratic dependence 1/T ∝ L2 provides
evidence that the described systems are near the localization transition or simply
reflects the diffusive behavior in moderately absorbing samples. In order to solve
this issue, we performed dynamic measurements of pulse transmission through
80
the samples.
Fig 4.5: Wavelength dependent transport mean free path (a) and absorption length (b) of 60- SiO2(HIPE).
II.2.2 Time of flight experiments:
The experimental setup used to perform time resolved measurements is
described in chapter III (Fig. 3.6). Using this experimental setup, we have
performed time of flight experiments on various samples, with thickness ranging
from 1 to 10 mm in the case of 35-SiO2(HIPE) and from 1 to 4 mm for 60-
SiO2(HIPE). Figure 4.6 shows typical results for three 35-SiO2(HIPE) samples of
thicknesses 2.26, 4.05, 5.84 mm. The insets exhibits a part of the corresponding
measured streak plots. These plots are bi-dimensional with the horizontal and
vertical axis being wavelength and time delay between excitation and detection,
respectively. The top left plot displays the pulse characteristics with a spectral and
temporal width of 1.4 nm around 515 nm and 80ps, respectively. Clearly, the
samples exhibit a strongly multi- diffusive character, with photons being
significantly delayed in the samples in all cases. As the thickness of the sample
increases, the mean exit time of the photons also increases, and the pulse is
delayed more and more in time. The insets from Fig 4.6 clearly indicate a
broadening of the spectral width with respect to pulse profile shown on the top
left of the Fig 4.6.a. This broadening is of course not related to the mixing of
81
frequencies originating from the source but merely results from the multiple
scattering of light within the sample, leading to divergent outgoing beams focused
by the lens at slightly different positions on the entrance slit of the spectrograph.
Furthermore, there is a huge strengthening of the multi-diffusive process while
densifying the sample. The dynamic measurements of 60-SiO2 (HIPEs) for three
different thicknesses are shown in Fig 4.7 a, b, c, with thicknesses of 1, 2.71, 3.49
mm, respectively. The 60-SiO2(HIPE) with a thickness L = 3.49 mm (Fig 4.7 c)
shows a time profile more extended than to the one exhibited by the 35- SiO2
(HIPE) with a nearly similar thickness L = 4.05 mm ( fig 4.6 b), indicating that
the time delay (i. e. the multiple scattering path) is more important in the denser
sample.
We have chosen time windows of 2ns, 5ns, 10ns or 20ns, depending on the
samples characteristics. For all time windows, we have a fixed number of data
points equal to 240. If the time window is too short with respect to the typical
time spent by the photons in the sample, we loose the information pertaining to
the tail of the time profile. On the contrary, if the time window is too long, we
loose the temporal resolution on the measurement. For example, Fig 4.8. a and b
show the same sample measured on two different time scales (2 ns and 5 ns).
From Fig 4.8 a, the relevant part of the decay profile is clearly longer than 2 ns.
We thus loose the long time behavior of the multi-diffusive process. By choosing
a time window of 5 ns, we evidence the long time behavior while keeping enough
data points to have a good resolution (Fig 4.8 b). All time profiles have been fitted
by the asymptotic form of the classical diffusion equation mentioned in Eq 3.14
(blue dashed-dotted lines). Clearly, substantial increases in transmission relative
to that predicted by the diffusion model are observed at long times. Measurements
in the time domain make it possible to unravel the effects of absorption.
Absorption in homogeneously absorbing samples simply introduces a
multiplicative exponential factor in time. All photon paths emerging from the
sample at a given delay time t have the same length and have suffered the same
diminution due to absorption. Because the weight of the path distribution is not
changed by the absorption at a given t, and since all partial waves arriving at a
82
fixed time are equally suppressed by the absorption, weak localization is not
Fig 4.6: Time of flight experiments (red circles with black connecting line) performed on 35-SiO2
(HIPE). Figures a, b, c correspond to samples of 2.26, 4.05, 5.84 mm thicknesses, respectively.
The pulse temporal profile is shown in the top figure (a, solid black line). The fits corresponding
to the asymptotic form of the time dependent diffusion equation (blue dashed) and to the
asymptotic form of T(t) near the localization transition (green dashed lines) are also shown. The
insets show the streak plots from which the profiles are built (pulse streak plot on the top left).
83
Fig 4.7: Time of flight experiments (red circles with black connecting line) performed on 60-SiO2
(HIPE). Figures a, b, c correspond to samples of 1, 3.71, 3.49 mm thickness, respectively. The fits
corresponding to the asymptotic form of the time dependent diffusion equation (blue dashed) and
the other fit corresponding to the asymptotic form of T(t) near the localization transition (green
dashed lines) are also shown. The insets show parts of the streak plots from which the profiles are
built.
84
Fig 4.8: Time of flight experiments (red circles with black connecting line) performed on 60-Si
(HIPE). Figures a, b correspond to samples of 2.05 mm recovered with time windows of 2 ns and
5 ns respectively. The fits corresponding to the asymptotic form of the time dependent diffusion
equation (blue dashed) and the other fit corresponding to the asymptotic form of T(t) near the
localization transition (green dashed lines) are also shown.
affected by absorption in the time domain. The influence of a kind of pre-
localization regime can be seen as a reduction of the decay rate with increasing
time delay. As this is precisely what is seen in Fig 4.6 and Fig 4.7, we have fitted
the experimental results with the asymptotic form of T(t) near the localization
transition, mentioned in Eq. 3.18 of chapter III, featuring a time dependent
diffusion constant D(t) = D0(τ/t)1/3, where τ is the elastic scattering time. These
asymptotic forms (green-dashed lines) provide better fits of the recorded data then
85
Scholar no. 35-SiO2 (HIPE) 60-SiO2 (HIIPE)
L D0 L D0
Thickness (in mm) (in m2/s) Thickness (in mm) (in m2/s)
1. 2.26 2858 1 360
2. 3.21 3780 1.67 600
3. 4.05 4224 1.89 650
4. 5.84 4350 2.05 790
5. 6.25 6520 2.63 760
6. 6.27 6577 2.71 820
7. 7.91 8050 3.49 1110
8. 9.45 9730
9. 10.4 9930 Table 4.2: Diffusion constant versus thickness of 35-SiO2 (HIPE) and 60-SiO2 (HIIPE).
the asymptotic blue-dashed forms. The values of the diffusion coefficients
extracted from the asymptotic forms (from Eq 3.18) are given in table 4.2 for both
SiO2 (HIPE)s. Obtained diffusion constants versus thickness are plotted in fig 4.9.
These plots show that the diffusion constants of 35-SiO2(HIPE) and 60-
SiO2(HIPE) are linearly dependent functions of the thickness. Other materials, for
example biological membranes, have been reported to exhibit size-dependent
diffusion constants (65, 66). The obtained values of both diffusion coefficients
and transport mean free paths, in this study, are nearly two orders of magnitude
larger than those measured by Storzer et al. in very dissimilar structures (67). It is
very remarkable that our very low refractive index n ~ 1.1 SiO2(HIPE)s exhibit
time transmission profiles with clear deviations from diffusive regime. Taken
together, the quadratic dependence 1/T ∝ L2 observed in Fig. 4.3 and the long
time departure from a single exponential decay observed in our time of flight
experiments, clearly indicate a non-standard diffusive transport regime of our
samples. Since the value of the diffusion constant and the transport mean free path
are far from the localization criteria, we cannot univocally certify that the non-
86
classical diffusion regime that we observe is a true pre-localization regime. In all
respect, the complexity certainly originates from the hierarchical porosity of our
material.
Fig4.9 Diffusion constant versus thickness behavior for the 35-Si(HIPE) (black star) and 60-
Si(HIPE) (blue star) fitted by using linear fit (in red solid line).
III Random lasing:
In order to perform random lasing experiments in our highly disordered
systems, we have infiltrated samples with Rhodamine 6G. The dye infiltration
method is described in chapter III. We have performed random lasing experiments
on the two type of samples: 35-SiO2 (HIPE) and 60-SiO2(HIPE). After optical and
structural characterizations, we know that 60-SiO2 (HIPE) has smaller pore
diameters and lower tansport parameters (lt and D0) than the 35-SiO2 (HIPE).
Therefore we expect to have lower lasing threshold in the former sample. TGA
analysis and random laser properties are discussed in this section in detail.
III.1 Thermogravitometric analysis:
From TGA measurements, we can obtain the percentage of weight loss
within the structure. From the weight loss, we can calculate the number of dye
87
molecules per unit volume. The data are given in table 4.3. Once we know the
amount of dye molecules within the structure, we can normalize the random
lasing data for each material. TGA analysis reveals that 60-SiO2 (HIPE)s has less
weight loss than 35-SiO2 (HIPE) (table 4.3); these structures thus contain a
smaller amount of dye molecules. By taking into account the bulk density of the
structure (which is higher for the denser sample), we have however obtained a
number of molecules per unit volume larger for 60-SiO2 (HIPE) (given in table
4.3).
35-SiO2 (HIPE) 60-SiO2 (HIPE) Weight loss No of molecules/volume Weight loss No of molecules/volume
(in %) mol/cm3 (in %) mol/cm3
7.9 0.15*10-4 6 0.31*10-4 Table 4.3: TGA data of two samples 35-SiO2 (HIPE) and 60-SiO2 (HIPE).
III.2 Results and Discussion for R.L.:
The experimental setup is described in chapter III (Fig 3.14). We have
performed random lasing experiments on two types of samples: 35-SiO2 (HIPE)
and 60-SiO2 (HIPE) with, for example, 4.66 and 4.74mm thicknesses. Results are
shown in Fig 4.10 and 4.11. the emission spectra of 35-SiO2 (HIPE) shown in Fig
4.10.a clearly show that, with increasing the input intensity, the output intensity
also increases. It is clear that the line-width narrows as a function of increasing
pump power. For large enough input power, narrow spikes appears on top of the
emission spectra (in Fig 4.10.b). At three points, we have calculated the Full
Width at Half Maxima (FWHM) (bottom, middle and top which are 12.11, 5, 0.6
nm, respectively). On top of the emission profile (in Fig 4.10.b), the FWHM
reduces to less than a nanometer, featuring random laser spikes in our material.
The characteristics output versus input pump energy (Fig 4.10c) looks like a
conventional laser characteristics (see chapter III in Fig 3.9). Fitting these
experimental results, using linear fits, we are able to obtain lasing thresholds as
88
Fig 4.10: Random lasing performed on 35-SiO2(HIPE) @4.66 mm thickness. Emission spectra are
shown in (a). Narrow spikes on the top of the emission profile are zoomed in (b). Input/output
power dependence is shown in (c); black stars are the experimental data points and red solid lines
are linear fits.
the cross-sections (in red solid lines) of horizontal and vertical lines from Fig
4.10c. These linear fits match well with the experimental data, with an accuracy in
the determination of the parameters larger then 98% for the horizontal (Horizontal
regression coefficients; H.R.C.) and vertical regression coefficients; V.R.C.) (see
table 4.4).
89
Fig 4.11: Random lasing performed on 60-SiO2(HIPE) @4.74 mm . Emission spectra are shown
in (a). Narrow spikes are zoomed in (b). Input/output power dependence is shown in (c); Black
stars are the experimental data points and red solid lines are horizontal and vertical linear fit.
In a second step, repeating the measurements on the same spot of the sample, we
have replicated the experimental data. Our results are thus fully reproducible and
further indicate that the dyes are not bleaching too fast. Off-course illuminating
the sample with a high power for more than 2-3 minutes leads to a bleaching of
the dyes in our materials. We have observed that the HIPEs themselves are not
damaged by continuous exposure to the high intensity pump beam: they are hard
enough to sustain the large excitation. We have also performed these experiments
while changing the spot position on the same sample and observed similar results.
The random lasing thresholds determined for all our experiments on this sample
are given in table 4.4. Similar experiments have been performed on 60-
SiO2/TiO2(HIPE) sample. Results are shown in figure 4.11. These samples also
90
show random lasing characteristics (i. e. narrowing of the emission lines as a
function of power (Fig. 4.11 a) and threshold behavior (Fig. 4.11 c)) and exhibit
very sharp peaks on top of the emission profiles (see the zooming area Fig 4.11
b).
Repeating the similar measurements as described above at the same spot position,
we are able to reproduce the results. The lasing characteristics are collected in
table 4.4. By changing the spot position, we repeated the measurements and
observed almost similar lasing thresholds in all cases. We have compared the
results of the 35-SiO2 (HIPE) and the 60-SiO2 (HIPE) on the basis of lasing
performances, shown in table 4.4. Clearly, the threshold values are larger for the
60-SiO2 (HIPE)s than for the 35-SiO2 (HIPE)s. These observations are
counterintuitive with the facts that the denser 60-SiO2 (HIPE)s have i) smaller
pore size distributions and ii) more dye molecules per unit volume than 35-SiO2
(HIPE)s. The lasing threshold is higher in the denser sample (average value of
141 µJ for the 60-SiO2(HIPE) while it is 90 µJ for the 35-SiO2(HIPE)). In three
35-SiO2(HIPE) @ 4.66mm 60-SiO2 (HIIPE)@ 4.74mm
Threshold H. R.C. V. R.C. Threshold H. R.C. V. R.C.
(in µJ) (in %) (in µJ) (in %)
1. 77.5 99.6 99.7 139 99.8 99.4
2. 85 99.5 99.7 84 99.5 98.8
3. 100 99.1 99.5 202 98.8 99.5
4. 100 98.8 99.5
Av.V. 90.62 141.6 Table 4.4. Random lasing threshold for 35-SiO2(HIPE) @ 4.66mm and 60-SiO2 (HIIPE)@
4.74mm. The values of Horizontal and vertical regression coefficients (H.R.C. and V.R.C.) for fits
are given.
dimensional systems this unexpected results may depend upon various issues.(i)
The multiple scattering of the pump light might restrict the excitation to the
proximity of a sample surface. The emitted photons from this sample surfaces
91
might readily escape through the sample surface, leading to a high lasing
threshold. (ii) We have observed that, for the denser sample, the absorption length
is smaller. Due to absorption, local pumping in an absorbing medium might create
a spatial “trapping” of the lasing modes. (iii) It is also possible that due to strong
scattering/localization, the pump beam itself gets trap within the system
producing a delayed emission from another mode later in time. Therefore, we
may have a larger lasing threshold for the highly scattering sample (in 60-
SiO2(HIPE)). Finally, in 3D systems, a large number of modes are involved in the
lasing action leading to a difficult observation of intense narrow lasing spikes.
IV. Conclusion:
Two types of samples (60-SiO2 (HIPE) and 35-SiO2 (HIPE)) were
investigated structurally and optically. Structural information shows that by
increasing the oil volumic fraction, we were able to decrease the pore diameters
and the porosity of the material. We found that 60-SiO2(HIPE) is denser than 35-
SiO2(HIPE). Static and Dynamic measurements were performed for more than 10
thicknesses. Both types of measurements provide us with the material transport
parameters. These slabs have lateral dimensions of a few cm2 (Fig. 4.1a) and are
thus really three-dimensional system. According to the expectations, the denser
samples exhibit the smaller transport and absorption mean free paths as well as
the smaller diffusion coefficients. Unexpectedly, both types of samples exhibit a
non-standard light diffusion behavior, clearly manifested by the observation of a
quadratic dependence 1/T ∝ L2 and by the reduction of the decay rate with
increasing time delay in the time transmission profiles. Such features cannot be
totally explained by absorption, as this would only lead to an additional
exponential decrease in the time of flight measurments. Such observations
performed while the Ioffe-Regel criterion is not fulfilled point to a peculiar
behavior being mainly due to the extremely disordered aspect and hierarchical
porosity of the structures.
Random lasing experiments were performed on the two types of samples
with almost similar thicknesses. Typical laser characteristics, i.e. input/output
92
power dependences, have been noticed in our materials. The narrowing of the
line-width of the Rh6G emission spectra and narrow spikes developing on the top
with increasing pump power have been observed. These features clearly point to
the large potential of our structures to be used as random lasers. The denser
sample shows a larger lasing threshold pointing to the fact that the pump beam
may be trapped in a mode within the material prior the emission can be released
in another mode later in time. More fundamental studies are however needed to
clearly unravel and allow us to understand the occurrence of the lasing threshold
with respect to the material hierarchical structure. Also, the observed increase of
the diffusion constant with the thickness of the sample has to be elucidated by
further investigation.
93
Chapter V SiO2/TiO2 (HIPE) for multiple scattering/localization and random lasing
94
95
I. Introduction:
Titanium dioxide is a semiconductor (with band gap at 3.27 eV) which
crystallizes in three polymorphic forms: rutile, anatase and brookite (68). Rutile is
the only stable form, whereas anatase and brookite are metastable phases and
transform to rutile phase, upon annealing. Nanosized titanium dioxide based
materials have been in the focus of researchers because they exhibit modified
physico-chemical properties in comparison with their bulks. Titania nanocrystals
have received great attention in recent years for their extensive applications in
conventional catalyst support, optics, cosmetics, white paint and solar cells (69,
70).
Titania is a common constituent of ceramics and glasses. Silica, with a few
percent of TiO2 (71), is used for length standards and astronomical mirror blanks
(72). Titania-doped silica materials played a crucial role in the development of
optical fibers (73) due to higher refractive index contrast between SiO2/TiO2
ordered composites. Also the high refractive index material leads to higher
multiple scattering in the case of disordered systems. Inspired from the above
specifications, we have synthesized SiO2/TiO2 hybrid, macro-cellular foams,
poly-HIPEs to enhance multiple scattering. Syntheses procedures of these
composites have been discussed in chapter II. Structural information on these
materials was obtained on various length scales using SEM, mercury porosimetry,
TEM with TED and XRD. Results are discussed in the current chapter. The
‘anatase’ and ‘rutile’ forms of titania are the most abundant. These forms have a
slightly different refractive index (2.4 for anatase and 2.6 for rutile). To know
which form is present in our composite, we have performed XRD and TEM-TED
measurements using the tools described in chapter II. In order to know the
material transport properties, we have performed transmission versus length and
time of flight measurements. Finally, in order to test these materials as potential
random lasers, we have infiltrated the samples with Rhodamine 6G laser dyes.
The infiltration method has been given in chapter II. After infiltration, in order to
determine the amount of dye molecules absorbed, we have performed
Thermogravitometric analyses (TGA). Results and discussion on random lasing
96
performances are given in detail in this chapter as well.
II Results and discussion; All characterizations:
Two types of materials (85/15-SiO2/TiO2(HIPE) and 90/10-
SiO2/TiO2(HIPE)) have been synthesized and characterized both structurally and
optically. The results are reported in this section. The experimental details of the
setups are described in chapter II and III.
II.1 Structural characterizations:
Structural characterizations were performed on three different length
scales. The macroscopic length scale has been characterized by SEM and mercury
porosimetry. The mesoscopic length scale has been characterized by TEM-TED,
EDXS. The microscopic characterization has been performed by XRD. All the
three types of characterization techniques are given in this section.
II.1.1 Macroscopic length scale via SEM:
SEM images of 90/10-SiO2/TiO2(HIPE) and 85/15-SiO2/TiO2 (HIPE) are
shown in Fig 5.1. An inorganic monolith-type material of 85/15-SiO2/TiO2(HIPE)
is shown in Fig. 5.1.a. Fig 5.2 shows the SEM image analysis performed on these
two samples. The pore sizes of 90/10-SiO2/TiO2(HIPE) and 85/15-
SiO2/TiO2(HIPE) are distributed between 2 to 44 μm and between 1.17 to
2.22μm, respectively. Fig 5.1 clearly illustrates that the 90/10-SiO2/TiO2(HIPE) is
bearing larger pore sizes than those of the 85/15-SiO2/TiO2(HIPE). By increasing
titania by a small weight percentage (from 10 % to 15 %) we are able both to
reduce the pore diameter and to increase their mono-dispersity. By adding titania,
we intend to increase the refractive index contrast between pores and their
surroundings. We have observed that this addition of titania also reduces the pore
diameters due to higher shrinkage during the polycondensation, and strong
sintering when the thermal tretament is applied, a process based on atomic
diffusion. In most sintering processes, the powdered material is mold in a
particular shape and then heated to a temperature below its melting point. The
atoms in the powder particles diffuse across the boundaries and thus, fusing the
97
particles together and creating a single solid piece. Because the sintering
temperature should be lower than the melting point of the material, sintering is
often chosen as the shaping process for materials. After this sintering, we have
observed shrinkage and reduced pore diameter caused by titania due to fusion of
many atoms in the particle under the high temperature thermal treatment. Here, it
is very important to notice that the 85/15- SiO2/TiO2(HIPE) sample is highly
mono-dispersed. The observed narrow distribution of pore sizes and the random
positioning of these pores makes, our material an excellent candidate for light
multi-diffusion/localization.
II.1.2 Macroscopic and mesoscopic length scale via Mercury porosimetry:
In order to provide foams skeletal, bulk densities and to quantify the mesoscale
void windows distributions, we have performed mercury intrusion porosimetry
measurements. Overall, if we increase the amount of titania, due to the shrinkage
caused by titania and sintering effect, the pore diameters will reduce. By
increasing the amount of titania, we have reduced the pores diameters and
increased the number of pores. Hence the number of cell walls per unit volume is
increased causing an increase of the bulk as well as the skeleton densities (given
FIG. 5.1: SEM images of 90/10-SiO2/TiO2(HIPE) (b) and 85/15-SiO2/TiO2(HIPE) samples (c) are
shown. (a) shows a 85/15-SiO2/TiO2(HIPE) monolith sample.
98
FIG. 5.2: Normalized pore size distribution for the 90/10-SiO2/TiO2(HIPE) (solid black line) and
85/15-SiO2/TiO2(HIPE) (dotted red line).
Materials Porosity Skeleton Bulk
(%) density density (g/cm3) (g/cm3)
90/10-SiO2/TiO2 (HIPE) 90.2 1.11 0.1086
85/15- SiO2/TiO2 (HIPE) 71.6 1.5 0.43
TABLE 5.1: Mercury intrusion porosimetry data of two samples (90/10-SiO2/TiO2 (HIPE) and 85/15- SiO2/TiO2 (HIPE)).
FIG. 5.3: Distribution of cell window sizes for the of 85/15-SiO2/TiO2(HIPE) (a) and the 90/10-
SiO2/TiO2(HIPE) (b).
99
in Table 5.1).The skeleton densities are smaller than the density of silica and
titania because the foam walls are indeed bearing a large degree of mesoporosity.
From this technique, we can measure the exact diameters of the cell windows, the
distribution of which is shown in Fig 5.3. In the case of the 85/15- SiO2/TiO2
(HIPE), the pore size distribution is very monodisperse around an average value
of 2 µm (Fig 5.2). From fig 5.3 the mean cell window diameter is close to 0.5 µm
for 85/15- SiO2/TiO2 (HIPE) and around 1.6 µm for 90/10-SiO2/TiO2 (HIPE).
II.1.3 Mesoscopic length scale via TEM-TED, HR-TEM and EDXS:
We have performed HR-TEM measurements on three types of samples: 90/10-
SiO2/TiO2 (HIPE), 85/15-SiO2/TiO2(HIPE) and 75/25-SiO2/TiO2(HIPE)
composites. In the case of the 90/10-SiO2/TiO2 (HIPE), due to the small amount
of titania present in the structure, results were not significant. A TEM image of
85/15-SiO2/TiO2(HIPE) samples is shown in Figure 5.4 a. On one hand, if the
material is amorphous, a light gray color will appear in the shown TEM image.
On the other hand, if the material is crystalline, it will appear as dark black color
Fig 5.4: Transmission electron micrograph of 85/15-SiO2/TiO2(HIPE) (a) gray color shown in
circle is SiO2 material and black color shown in another circle is TiO2. A TED pattern of the
85/15-SiO2/TiO2(HIPE) is shown in b. Inset in (b) shows the model representation of diffraction
pattern for amorphous material.
in the TEM image. In this composite, SiO2 is amorphous whereas TiO2 is in a
100
crystalline phase. A TED image of the 85/15-SiO2/TiO2(HIPE) is shown in Fig.
5.4.b. In this sample the amorphous state of silica is dominating on the crystalline
form of titania, only diffused rings with a centered dot in the diffraction pattern
are observed. A comparison with a numerical diffraction pattern calculated for an
amorphous material is shown in inset of Fig 5.4b. The TEM image of the 85/15-
SiO2/TiO2(HIPE) indicates that some crystalline form of TiO2 is also present
Fig 5.5: Transmission electron micrograph of 75/25-SiO2/TiO2(HIPE) (a) gray color shows SiO2
material and black color is TiO2 material. The TEM image of one TiO2 particle in the silica matrix
is shown in (b). A zoom on the TiO2 particle shows clear crystalline form (c). (d) The TED pattern
of the 75/25-SiO2/TiO2 (HIPE) reveals a tetragonal system.
(black spots in Fig. 5.4. a feature of a crystalline phase). To obtain a more
accurate information about which of the allotropic phase of titania is present in
101
our sample, we have also performed experiments on the 75/25-SiO2/TiO2(HIPE).
The TEM and TED images of this structure are shown in fig 5.5. Fig 5.5 (a)
confirms the presence of both silica and titania (indicated by gray and black
colors, respectively). On zooming down to the nanometer scale, we found that
TiO2 particles are dispersed in silica matrix (Fig 5.5 b) and the particle size ranges
between 10 to 15 nm in size. A further magnification allows us to see the
crystalline structure (fig 5.5 c) of the titanium dioxide nanoparticle. In order to
determine the allotropic form of this nanoparticle, we have performed TED
measurements (Fig 5.5 d). The obtained diffraction pattern demonstrates that TiO2
crystallizes in the tetragonal system, indicating the presence of the Anatase
allotropic form of Titania (68).
To obtain the atomic weight fraction of Ti and Si, we have performed elemental
analysis using EDXS. The EDXS results are given in table 5.2. The EDXS
analysis confirms that 85/15-SiO2/TiO2(HIPE) has as smaller amount of Ti (3.22
and 4.41) than 75/25-SiO2/TiO2(HIPE) (table 5.2).
Materials Atomic weight % of Si Atomic weight % of Ti
75/25-SiO2/TiO2 (HIPE) 95.59 4.41
85/15- SiO2/TiO2 (HIPE) 96.78 3.22
Table 5.2: EDXS elemental analysis data of two samples (75/25-SiO2/TiO2 (HIPE) and 85/15- SiO2/TiO2 (HIPE)).
II.1.4 Microscopic length scale via XRD:
Titania is known for its allotropic phase transformation (from brookite to
anatase form then to rutile form) upon thermal treatment. At 800°C, various
scientific groups have observed the rutile form (68). From TEM with TED
measurements, it is clear that SiO2/TiO2(HIPE)s is present in the anatase form of
titania, even though we have used a high temperature (800°C) to calcine our
HIPEs. To clearly confirm this allotropic form of titania, we have performed X-
ray diffraction (XRD) on these hybrid materials. Results are shown in Fig 5.6.
102
From the available literature, we know that the anatase form of titania shows a
very sharp peak at 2θ = 25° (68) but, due to the small amount of titania present in
the 90/10-SiO2/TiO2(HIPE) and 85/15-SiO2/TiO2(HIPE), we have rather observed
a broad hump around 2θ =25°.
Fig 5.6: XRD of three samples 90/10-SiO2/TiO2(HIPE) in black, 85/15-SiO2/TiO2(HIPE) in red,
75/25-SiO2/TiO2(HIPE) in blue, black circle showing the peak at 25°.
By increasing the titania content in the composite (75/25-
SiO2/TiO2(HIPE)), we have observed a narrow peak around 2θ = 25°
superimposed to the broad bump. In fig. 5.6 the sharp peak superimposed to the
broad bump (see blue curve) shows the bi-phasic nature of the sample, consisting
of an amorphous phase and a crystalline phase: sharp peak (evidenced in the black
circle). Therefore, from both XRD and TEM-TED measurements, it is clear that
we have obtained the anatase form of titania embedded within an amorphous
network. The surrounding amorphous network is certainly locking the anatase
allotropic change toward the rutile one, as rutile, being the stable form, should be
present at 800°C.
II.2 Optical Characterizations:
103
The Two types of materials (90/10-SiO2/TiO2(HIPE) and 85/15-
SiO2/TiO2(HIPE)) were characterized by transmission versus length
measurements and time of flight experiments. The results are reported in this
section. The experimental details of the setups are described in chapter III. The
obtained experimental data were analyzed according to the theories mentioned in
chapter III.
II.2.1 Transmission versus length measurements:
White light transmission through samples of various versus lengths (T(L)) have
been performed on the two types of samples with more than 10-20 length
(thicknesses) ranging between 1 to 5 mm. Figs 5.7 (a) and (b) exhibit the
conductance versus thickness behavior for the two types of samples (90/10-
SiO2/TiO2(HIPE) and 85/15-SiO2/TiO2(HIPE)) at two different wavelengths (blue
stars: 500nm and red stars: 700 nm). From Fig 5.7, it is clear that our
experimental data do not follow a linear relationship between 1/T and L. The
samples are not following the Ohm’s law (it should be linear for diffusive sample
only if there is no absorption, see Eq 3.11). A quadratic dependence (1/T ∝ L2)
(black dotted lines in Fig. 5.7) better fits our experimental data. The experimental
results have been also fitted by the stationary solution of the diffusion equation
(see eq 3.9) including absorption (blue and red solid lines in Fig. 5.7). The insets
of Fig 5.7 exhibits the residuals of the fits as a function of the thickness. By using
this fitting procedure, we are able to obtain the transport mean free path ‘lt’ and
the absorption length ‘la’ for the full range of white light illumination (from 500 to
800nm). The obtained values of ‘lt’ and ‘la' are plotted in Figs 5.8 and 5.9. The
transport mean free path at 515 nm for the 90/10-SiO2/TiO2(HIPE) and 85/15-
SiO2/TiO2(HIPE) are 11.81 μm and 11.19 μm, respectively. Their absorption
lengths at 515 nm for the 90/10-SiO2/TiO2(HIPE) and the 85/15-SiO2/TiO2(HIPE)
are 3.33 and 2.52mm respectively. From the SEM analysis of these samples we
expect to have a lower lt and la for the 85/15- SiO2/TiO2(HIPE) than for the 90/10-
SiO2/TiO2(HIPE), since the 85/15-SiO2/TiO2(HIPE) has a distribution of more
monodisperse and smaller pore sizes (see Fig 5.2). The absorption lengths of these
104
Fig 5.7: Inverse transmittance versus thickness behavior for 85/15-SiO2/TiO2 (HIPE) (a) and
90/10-SiO2/TiO2 (HIPE) (b) at λ=500 nm (blue stars) and λ=700 nm (red stars) fitted by the
stationary solution of the diffusion equation, (fits are blue and red solid line, respectively) as well
as by the 1/T∝ L2 law (fits are black dotted lines). Insets of (a) and (b) show the residuals of the
fits.
105
Fig 5.8: Wavelength-dependent transport mean free path lt (a) and absorption length la (b) of a
90/10-SiO2/TiO2(HIPE).
Fig 5.9: Wavelength-dependent transport mean free path lt (a) and absorption length la (b) of a
85/15-SiO2/TiO2(HIPE).
samples are in good agreement with their bulk densities (denser sample has lower
la). However, lt is not significantly different for both samples. A common behavior
for the transport mean free path is to vary with frequency, which we observe in
Figs. 5.8 (a) and 5.9 (a) and contrarily to what we reported for 35-SiO2(HIPE) and
60-SiO2(HIPE) in chapter IV. By increasing the wavelength, lt increases in both
samples. The experimental data in the case of 85/15-SiO2/TiO2(HIPE) are very
106
much scattered (Fig 5.7a). This may be attributed to randomly positioned TiO2
nano-particles, introducing some additional multiple scattering at random
positions from sample to sample or place to place in the same sample. The
stationary solution of the diffusion equation including absorption fits particularly
well the experimental data, providing the values of the transport mean free path
such that k*lt >> 1. These values are inherent to diffusive light transport.
However, the plots shown in Fig. 5.7 are also nicely fitted by a quadratic
dependence (1/T ∝ L2) (black dotted lines in Fig. 5.7), which might provide some
indication of light pre-localization.
II.2.2 Time of flight experiments:
The experimental setup used to perform time resolved measurements is
described in chapter III (Fig. 3.6). Using this experimental setup, we have
performed time of flight experiments on various samples with thicknesses ranging
between 1 to 5 mm for the 90/10-SiO2/TiO2(HIPE) and 85/15-SiO2/TiO2(HIPE).
Fig 5.10 shows typical results for samples 85/15-SiO2/TiO2(HIPE) and 90/10-
SiO2/TiO2(HIPE) at thicknesses 2.5 and 3.08 mm, respectively. The inset exhibits a
part of the corresponding measured streak plots. The samples exhibit a strongly
multi-diffusive character, with photons being significantly delayed in the samples
in all cases. From Fig 5.10 (a) and (b), it is clear that the time profile is more
extended in the 85/15-SiO2/TiO2(HIPE) with respect to the 90/10-SiO2/TiO2(HIPE)
((a) has smaller thaickness than (b)). This suggests that the delay develops more in
the denser sample as it is expected from longer paths performed by light in the
sample due to stronger multiple scattering. All traces have been fitted by the
asymptotic form of the diffusion equation described by Eq 3.14 (blue dashed-dotted
lines). Clearly, substantial increases in transmission relative to that predicted by the
diffusion model are observed at long times. Measurements in the time domain
make it possible to unravel the effects of absorption. The influence of localization
can be seen in a reduction of the decay rate with increasing time delay. As this is
precisely what is seen in Fig 5.10.b we have fitted the experimental results with the
asymptotic form of T(t) near the localization transition, described by Eq. 3.18,
107
featuring a time dependent diffusion constant D(t) = D0 (τ/t)1/3, where τ is the elastic
scattering time. These asymptotic forms (green dashed lines) provide slightly better
Fig 5.10: Time of flight experiments (red circles with black connecting line) performed on (a)
85/15-SiO2/TiO2(HIPE) and (b) 90/10-SiO2/TiO2(HIPE) at thicknesses 2.5 and 3.08 mm,
respectively. The fits corresponding to the asymptotic form of the time dependent diffusion
equation (blue dashed) and to the asymptotic form of T(t) near the localization transition (green
dashed lines) are also shown. The insets show parts of the streak plots from which the profiles are
built.
fits of the recorded data. Basically these theories were not developed for poly-
HIPEs. Therefore such kind of complex material is difficult to characterize using
the mentioned theories. The values of the diffusion coefficients extracted from the
Scholar no. 90/10- SiO2/TiO2 (HIPE) 85/15- SiO2/TiO2 (HIPE)
L D0 L D0
Thickness (in mm) (in m2/s) Thickness (in mm) (in m2/s)
1. 3.08 2000 1.5 1910
2. 3.94 1304 2.5 1030
3. ------ ------- 2.77 1010 Table 5.3: Thickness and diffusion constants of 90/10-SiO2 /TiO2(HIPE) and 85/15-SiO2/TiO2
(HIIPE).
108
asymptotic forms are given in table 5.3 for both SiO2/TiO2(HIPE)s. From these
values of diffusion constants, it is clear that the more we add titania in the
SiO2/TiO2(HIPE), the more we are able to reduce D0. This drop in D0 originates
from both a better monodispersity of the pore sizes and a larger refractive index
contrast in the case of 85/15-SiO2/TiO2(HIPE). Taken together, the quadratic
dependence 1/T ∝ L2 observed in Fig. 5.7, and the long time departure from a
single exponential decay observed in our time of flight experiments clearly indicate
that our samples follows a non-standard diffusive transport regime while not clearly
attributable to a pre-localization regime.
III Random lasing:
We have performed random lasing on both types of samples: 85/15-
SiO2/TiO2(HIPE) and 90/10-SiO2/TiO2(HIPE). In order to measure the amount of
dye molecules within the structure, we have performed TGA. The random lasing
properties of our samples and TGA results are discussed in this section in detail.
III.1 Thermogravitometric analysis:
From TGA measurements we can obtain the percentage of weight loss
within the structure as a function of temperature. From the weight loss, we can
calculate the number of molecules per unit volume. The data are given in table
5.4. The 85/15-SiO2 (HIPE) has less weight loss. A smaller amount of dye
90/10- SiO2/TiO2 (HIPE) 85/15- SiO2/TiO2 (HIPE)
Weight loss (in %) No of molecules Weight loss (in %) No of molecules
mol/cm-3 mol/ cm-3
12.8 0.33*10-4 8.9 0.88*10-4
Table 5.4: TGA data of 90/10-SiO2 /TiO2(HIPE) and 85/15-SiO2/TiO2 (HIIPE).
molecules is thus present per unit volume in this HIPE with respect to the 90/10-
SiO2 (HIPE). Taking into account the bulk density of the structure, which is larger
109
for the denser sample, we have more molecules per unit volume in this sample.
III.2 Results and Discussion for R.L.:
In order to test the potentialities of random lasing in our highly disordered
systems, we have infiltrated them with Rhodamine 6G dyes by the method
discussed in chapter II. The experimental setup is described in chapter III. Owing
to the mentioned experimental geometry, we have performed random lasing on
two types of samples 85/15-SiO2/TiO2(HIPE) and 90/10-SiO2/TiO2(HIPE) at two
different thicknesses (at 1.4 and 3.5 mm). Results are shown in Figs 5.11 and
5.12. Emission spectra of 90/10-SiO2/TiO2(HIPE) shown in Fig 5.11.a clearly
show that with increasing input intensity, the output intensity also increases. Also,
it is clear that the line-width gets significantly narrower with increasing pump
power. A magnification of a part of the emission spectra is shown in Fig 5.11(b).
The overall narrowing of the spectra occurs together with the narrow spikes
observed on the top. These spikes occur at random frequencies. At three points we
have calculated the Full Width at Half Maxima (FWHM) (bottom, middle and top
which are 10.9, 6.15, 0.42 nm, respectively). The top spikes exhibited in the
emission profile (Fig 5.11.b) have a FWHM that reduce to less than a nanometer,
featuring a random laser spike originating from our material. The characteristic
output versus input pump energy (Fig 5.11.c) looks like a conventional laser
characteristic. Fitting these experimental results, using linear fits, we are able to
obtain lasing thresholds at the cross-sections (crossing of the red solid lines) of
horizontal and vertical lines from Fig 5.11.c. This linear fit matches very well
with the experimental data. The majority of the plots are giving more than 95%
accurate values of regression coefficients for horizontal and vertical (Horizontal
regression coefficients (H.R.C.) and vertical regression coefficients (V.R.C.), (see
table5.5). In a second step, repeating the measurements on the same spot of the
sample, we have replicated the experimental data. Our results are thus fully
reproducible and further indicate that the dyes are not bleaching too fast. We have
also performed these experiments while changing the spot position on the same
sample and observed similar results. The random lasing thresholds determined for
110
all our experiments on this sample are given in table 5.5. Similar experiments
have been performed on a 85/15-SiO2/TiO2(HIPE) sample. Results are shown in
Fig 5.11: Random lasing performed on 90/10-SiO2/TiO2(HIPE) @1.43 mm thickness. a) Emission
intensity versus wavelength curves are shown. b) Narrow spikes appearing on the top of the
emission profile are zoomed. (c) Input/output power dependence curve is shown. The black stars
are the experimental data points and the red solid lines are linear fits to the data.
111
Fig 5.12: Random lasing performed on 85/15-SiO2/TiO2(HIPE) @1.44 mm . a) Emission intensity
versus wavelength curves are shown. b) Narrow spikes appearing on the top of the emission
profile are zoomed. (c) Input/output power dependence is shown. The black stars are the
experimental data points and the red solid lines are horizontal and vertical linear fits to the data.
figure 5.12. This sample also shows random lasing characteristics (fig 5.12.c) and
exhibit very sharp peaks on top of the emission profiles (see inset of Fig 5.12 b).
Repeating the measurements as described above at the same spot position, we are
able to reproduce the results. By changing the spot position, we repeated the
measurements and observed almost similar lasing thresholds in all cases. All
threshold values are collected in table 5.5. Since the average pore diameters in the
85/15-SiO2/TiO2(HIPE) are smaller than the one of the 90/10-SiO2/TiO2(HIPE),
we expect the lasing threshold to decrease in the denser sample. Also the high
refractive index contrast of titania should help to reduce the lasing threshold in
112
these denser materials. From the results in table 5.5, it is clear that the lasing
threshold is lower in the denser sample (average value: 235 µJ in 85/15-
SiO2/TiO2(HIPE) and 347 µJ in 90/10-SiO2/TiO2(HIPE)). This experiment clearly
confirms that the lowering of the transport parameters, observed in the T(L) and
time of flight experiments, is due to stronger scattering/localization, leading to a
reduction of the lasing threshold in the denser sample. We have performed similar
measurements on 85/15-SiO2/TiO2(HIPE) and 90/10-SiO2/TiO2(HIPE) with a 3.5
mm thickness. The results are given in table 5.6. By increasing the thickness, we
aim to decrease lasing threshold. But due to lack of time, we have measured only
two sample thicknesses, which is not sufficient to conclude on the performance of
random lasers as a function of thickness. From Fig 5.11.c and 5.12.c, it is clear
that 85/15-SiO2 /TiO2(HIPE) has a lower lasing threshold than the 90/10-SiO2
/TiO2(HIPE). For all 85/15-SiO2 /TiO2(HIPE) samples, we have observed a very
sharp peak centered around 573.5 nm superimposed to the emission spectra of
Rhodamine 6 G (Fig 5.13). the origin of this peaks, occurring systematically at the
same wavelength is not clear and cannot attribute to a random lasing effect.
90/10-SiO2 /TiO2(HIPE) @ 1.43 mm 85/15-SiO2 /TiO2 (HIIPE)@ 1.4mm
Threshold H. R.C. V. R.C. Threshold H. R.C. V. R.C.
(in µJ) (in %) (in µJ) (in %)
1. 338 92.1 99.9 202 94.5 99.4
2. 300 98.5 99.12 224 95.5 99.7
3. 390 98.1 99.6 265 96.6 99.6
4. 360 99.8 98.6 250 98.8 99.8
Av.V. 347 235.5 Table 5.5: Random lasing threshold for 90/10-SiO2 /TiO2 (HIPE) @ 1.43 mm and 85/15-SiO2
/TiO2 (HIPE) (HIIPE)@ 1.4 mm have been given. The value of H.R.C. and V.R.C. (Horizontal and
vertical regression coefficient) for horizontal and vertical fit have been given.
113
Fig 5.13: Emission intensity versus wavelength curves are shown for a 85/15-SiO2/TiO2(HIPE)
@3.5mm. Very sharp spikes at 573.52 nm have been observed.
90/10-SiO2 /TiO2(HIPE) @ 3.5 mm 85/15-SiO2 /TiO2 (HIIPE)@ 3.5mm
Threshold H. R.C. V. R.C. Threshold H. R.C. V. R.C.
(in µJ) (in %) (in µJ) (in %)
1. 340 98.1 99.6 115 98.5 99.6
2. 350 98.5 99.5 100 97.5 99.8
3. 400 98.9 98.7 121 96.6 99.8
4. 350 96.8 98.2
Av. V. 360 112 Table 5.6: Random lasing thresholds for 90/10-SiO2 /TiO2 (HIPE) @ 3.5mm and 85/15-SiO2
/TiO2 (HIPE)@ 3.5mm. The value of H.R.C. and V.R.C. (Horizontal and vertical regression
coefficient) for horizontal and vertical fits are also given.
114
IV Conclusion:
SiO2/TiO2 composites have been investigated structurally and optically
using various techniques. SEM analysis of two types of samples (85/15-
SiO2/TiO2(HIPE) and 90/10-SiO2/TiO2(HIPE)) shows that by increasing the
amount of titania, we are able to reduce the pore diameters. From TEM-TED and
XRD, we know that these composites combine an amorphous state of silica and a
crystalline phase of titania. T(L) measurement have been performed on different
thicknesses varying from L = 1 mm to 5mm. Dynamic measurements were also
performed for all the thicknesses. Both types of measurements provide us with the
material transport parameters. These slabs have lateral dimensions of a few cm2
and are thus really three-dimensional systems. According to the expectations, the
denser sample exhibits the smaller transport and absorption mean free paths as
well as the smaller diffusion coefficients. Unexpectedly, both types of samples
exhibit a non-standard light diffusion behavior, clearly manifested by the
observation of a quadratic dependence 1/T ∝ L2 and by the reduction of the decay
rate with increasing time delay in the time transmission profiles.
Random lasing was performed on the two types of samples with two
thicknesses. Typical laser characteristics, input/output power dependences, have
been noticed in our materials. As expected, the denser sample shows a lower
lasing threshold. The narrowing of the line width with increasing pump power has
been observed. An overall narrowing of the emission spectrum together with the
narrow spikes on the top, have been observed. The titania nano-particles embaded
in the silica matrix are 10 to 15 nm in size. These dimensions are not likely to
affect very much the light transport properties of the materials. Nevertheless, this
titania addition induced more monodisperse pore diameters distributions
responsible, with the larger dielectric contrast, to the observed behaviour of the
transport paramters.
115
Chapter VI Conclusions and perspectives
116
117
In this thesis, our aim was to probe new materials potentially able to
multidiffuse/localize light and act as random lasers. In this context, disordered,
porous, white, hierarchical materials have been synthesized by using a sol-gel
process combined with the physical chemistry of complex fluids (emulsion,
lyotrope mesophase). The whole synthesis process is known as integrative
chemistry and is a potential technique to control the morphology of the materials
at macro and mesoscopic length scales. The obtained self-standing slabs have
lateral dimensions of a few cm2 and a thickness ranging from 0.5 mm to several
mm. They are thus real three-dimensional systems. Due to the lack of materials
having a large refractive index in the visible range of the spectrum
electromagnetic, it is a very challenging task to obtain light localization in 3D
systems. In spite of this fact, we attempted to synthesized materials exhibiting this
behaviour. To determine the structure of our materials at the macro, meso, and
micro length scales, we have characterized them by SEM, mercury porosimetry,
TEM, TED, EDXS, and XRD. To determine the light transport parameters, we
have characterized these materials optically via transmission versus length
measurements and time of flight measurements. The investigation of the light
diffusing properties of these new materials is reported here for the first time.
In a first step, owing to the above mentioned technique, two types of
samples: 35-SiO2 (HIPE) and 60-SiO2 (HIPE) were synthesized by varying the
oil-volumic fraction of the emulsion. The structural characterizations (SEM) have
been performed on these samples. They revealed that we are able to reduce the
pore diameters distributions from 10 − 40μm to 1 − 3.5μm in the cases of 35-SiO2
(HIPE) and 60-SiO2 (HIPE), respectively, by increasing the oil-volumic fraction.
The mercury porosimetry measurements performed on these samples illustrate
that the 60-SiO2 (HIPE) sample has a larger bulk density than the 35-SiO2 (HIPE).
Therefore, 60-SiO2 (HIPE) is a denser sample than 35-SiO2 (HIPE).
Optical characterizations (T(L) and time of flight measurements) were
then performed. These complementary measurements provide us with the material
transport parameters: transport and absorption mean free paths, diffusion constant.
118
By using well established theories, we have analyzed our results and obtain the
transport parameters. The obtained T(L) data have been fitted with the stationary
solution of the classical diffusion equation. We observed that the inverse
transmittance has a quadratic dependence on thickness. This quadratic
dependence may be attributed either to absorption phenomenon or multiple
scattering inhibition close to the localization regime. According to the
expectations from the classical light diffusion theory, the denser samples must
exhibit the smaller transport and absorption mean free paths. We observed this
typical trend in our SiO2 (HIPE) materials. The obtained values of ‘lt’ is 86 µm for
35-SiO2 (HIPE) and is 19µm for 60-SiO2 (HIPE).
Time of flight experiments in the time domain must allow us to unravel
the effects of either absorption or scattering inhibition. Absorption in
homogeneously absorbing samples simply introduces a multiplicative exponential
factor in time. The influence of a pre-localization regime can be seen as a
reduction of the decay rate with increasing time delay, which would lead to a non-
exponential time tail at longer time scales. Times of flight measurements have
been performed: we observed a non-exponential decay tail. By using both the
diffusion and localization theories, we have fitted our results and observed that the
localization theory provides a better fit function with the experimental data.
However, due to the weak scattering strength measured in T(L) experiments, k lt
>> 1, we cannot simply ascertain that observe a pre-localization regime.
Furthermore, these theories are not fully appropriate for the analysis of our
complex materials. From the fitting results, we have obtained the values of the
diffusion constant and observed that it is a function of thickness (by increasing the
thickness, D0 is increasing), an unusual property of classically diffusing materials.
Therefore, there is a strong need nowadays to develop an appropriate theory for
our materials.
In a second step, we have synthesized 85/15-SiO2/TiO2(HIPE) and 90/10-
SiO2/TiO2(HIPE) samples by addition of a small amount of TiO2 in the SiO2
materials, to enhance the refractive index contrast. These materials have been
structurally characterized by various techniques such as SEM, mercury
119
porosimetry, TEM, TED, EDXS, XRD. Results obtained from TEM-TED and
XRD reveladed that these composites combine an amourphous state of silica and
a crystalline phase of titania. The SEM observations illustrate that the 85/15-
SiO2/TiO2(HIPE) has a very narrow pore size distribution as compared to the one
of the 90/10-SiO2/TiO2(HIPE): pore size ranging from 1.17 to 2.22 μm and from 2
to 44 μm, respectively. From the mercury porosimetry experiments, 85/15-
SiO2/TiO2(HIPE) has a higher bulk density. Therefore, it is a denser sample, than
the 90/10-SiO2/TiO2(HIPE).
T(L) measurements performed on different thicknesses exhibit a similar
quadratic dependence of inverse transmittance versus thicknesses as the SiO2
(HIPE)s. By applying diffusion theory, we have obtained the values of ‘lt’ for the
90/10-SiO2/TiO2 (HIPE) and 85/15-SiO2/TiO2 (HIPE). They are 11.81 μm and
11.19 μm, respectively. lt is not significantly different for both samples. This small
values of ‘lt’ in the case of the 90/10-SiO2/TiO2(HIPE) sample might originate
from the narrow cell windows size distribution centered around 1 μm.
Dynamic measurements were also performed and revealed that the denser sample
(85/15-SiO2/TiO2 (HIPE)) has a lower diffusion constant than that of the 90/10-
SiO2/TiO2 (HIPE). In these composites materials, we have observed that the long-
time departure from the single exponential decay is stronger than pure SiO2-
(HIPEs). Since we have not performed our measurements on many samples, we
are not able to establish a relation between the diffusion constant and the
thickness of these composites.
All types of samples investigated in our studies exhibit a non-standard
light diffusion behavior, both in the T(L) and in the time of flight measurements.
Such features cannot be explained by absorption, as this would only lead to an
additional exponential decrease in the time decay profiles. These features thus
constitute somewhat direct evidence for either the slowing down of photon
diffusion due to the approach to the Anderson localization transition or some
peculiar behavior due to the hierarchical porosity of our disordered structures.
Such observations performed while the Ioffe-Regel criterion is not fulfilled point
to observation being mainly due to the extremely disordered aspect and
120
hierarchical porosity of the structures.
In order to strengthen our observations and investigations, more evidence
is nowadays required, Speckle pattern analyses, measurements in the frequency
domain, and coherent back scattering experiments might help in fully elucidating
the observed behaviour. Also, the observed increase of the diffusion constant with
the thickness of the sample has to be elucidated by further investigation.
The disordered systems synthesized and characterize here above can act as
“random lasers”. Therefore, we have investigated their random lasing
performances by infiltrating the four types of aforementioned samples with
Rhodamine 6G laser dyes. Typical laser characteristics, i.e. input/output power
dependences, with lasing threshold, have been noticed in all materials. For each
sample, the narrowing of the line-width of the Rh6G emission spectra with
increasing pump power has been observed. For each sample, overall narrowing of
the emission spectrum with narrow spikes developing on top of the spectrum has
been observed. These features clearly point to the large potential of our structures
to be used as random lasers.
On the one hand, the denser (60-SiO2 (HIPE)) sample shows a larger
lasing threshold than the (35-SiO2(HIPE)) pointing to the potential fact that the
pump beam may be trapped in a mode within the material prior that the emission
can be released in another mode later in time.
On the other hand, as expected, the denser (85/15-SiO2/TiO2 (HIPE) as
compared to the 90/10-SiO2/TiO2 (HIPE)) sample shows a lower lasing threshold
in the case of SiO2/TiO2 (HIPE) composites. The 85/15-SiO2/TiO2 (HIPE) also
shows a very sharp shoulder peak which cannot be ascribe at the moment.
As perspectives, we can briefly mention:
1. More experimental proofs are needed to justify that the observed regime is
a “light pre-localization regime”. Therefore, speckle pattern analysis and
measurements in the frequency domain are suggested for our materials.
2. In order to fully analyze this new type of diffusing materials, it is required
121
to develop the appropriate theories for such complex materials.
3. To obtain the clear trend of random lasing threshold with thickness.
Experiments performed for more thicknesses are needed.
4. To avoid the dye bleaching problems within the materials during random
lasing experiments, quantum dots can be infiltrated and observed.
122
123
Reference
(1) T. Young, “A Course of Lecture on Natural Philosophy and the Mechanical
Arts.” (1807, replished 2002 by Thoemmes Press)
(2) E. Yablonovitch, "Inhibited Spontaneous Emission in Solid-State Physics and
Electronics." Phys. Rev. Lett., 58, 2059, (1987)
(3) S. John, "Strong localization of photons in certain disordered dielectric
superlattices." Phys. Rev. Lett., 58, 2486, (1987)
(4) P. Sheng, “Introduction to wave scattering, Localization, and Mesoscopic
Phenomena.” (Academic Press, San Diego, 1995)
(5) P. W. Anderson, “Absence of diffusion in certain random lattices.” Phys. Rev.
Lett., 109, 1492, (1958)
(6) S. John, “Electromagnetic absorption in a disordered medium near a photon
mobility edge.” Phys. Rev. Lett., 53, 2169, (1984)
(7) P. W. Anderson, “The question of classical localization: a theory of white
paint?” Philos. Mag. B, 52, 505, (1985)
(8) A. Z. Genack, N. Garcia, “Observation of photon localization in a three-
dimensional disordered system.” Phys. Rev. Lett. 66, 2064, (1991)
(9) A. Z. Genack, P. Sebbah, M. Stoytchev, and B.A. van Tiggelen, “Statistics of
Wave Dynamics in Random Media.” Phys. Rev. Lett. 82, 715, (1999)
(10) A. A. Chabanov, A.Z. Genack, “Statistics of Dynamics of Localized
Waves.” Phys. Rev. Lett. 87, 233903, (2001)
(11) D. S. Wiersma, P. Bartolini, A. Lagendijk, and R. Righini, “Localization of
light in a disordered medium.” Nature 390, 671, (1997)
(12) M. Störzer, P. Gross, C. M. Aegerter and G. Maret, “Observation of the
critical regime near Anderson localization of light.” Phys. Rev. Lett., 96, 063904,
(2006)
(13) F. J. P. Schuurmans, M. Megens, D. Vanmaekelbergh , and A. Lagendijk,
“Light Scattering near the Localization Transition in Macroporous GaP
Networks.” Phys. Rev. Lett., 83, 2183, (1999)
(14) C. M. Aegerter, M. Störzer, and G. Maret, “Experimental determination of
critical exponents in Anderson localisation of light.” Europhys. Lett. 75, 562
124
(2006)
(15) E. Abrahams, P. W. Anderson, D. C. Licciardello and T. V Ramakrishnan,
“Scaling theory of localization: absence of quantum diffusion in two dimensions.”
Phys. Rev. Lett., 42, 673, (1979)
(16) F. Scheffold, R. Lenke, R. Tweer and G. Maret, “Localization or classical
diffusion of light?” Nature, 398, 206, (1999)
(17) D. S. Wiersma, J. Gomez Rivas , P. Bartolini, A. Lagendijk, and R. Righini,
“Localization or classical diffusion of light?” Nature 398, 207, (1999)
(18) J. Gomez Rivas, R. Sprik and A. Lagendijk, “Optical transmission through
very strong scattering media”. Ann. Phys., (Leipzig) 8 Spec. Issue, p. I-77– I-80,
(1999)
(19) C. Conti and A. Fratalocchi, “Dynamic light diffusion, three-dimensional
Anderson localization and lasing in inverted opals.” Nature Phys. 4, 794 (2008)
(20) C. M. Aegerter, M. Störzer, S. Fiebig, W. Buhrer and G. Maret, “Observation
of Anderson localization of light in three dimensions”. J. Opt. Soc. Amer. A, 24,
A23–A27 (2007)
(21) T. van der Beek , P. Barthelemy, P. M. Johnson, D. S. Wiersma, and A.
Lagendijk, “ Light transport through disordered layers of dense gallium arsenide
submicron particles.” Phys. Rev. B, 85, 115401, (2012)
(22) R. V. Ambartsumyan, N.G. Bascov, P.G. Kryukov, and V.S. Letokhov, “Laser
with a non-resonant feedback”, [Pis’ma Zh. Eksp. i Teor. Fiz., 3: 261 (1966)
Russian ] JETP Lett., 3: 167 (1966).
(23) R. V. Ambartsumyan, N.G. Bascov, P.G. Kryukov, and V.S. Letokhov, “A
laser with a non-resonant feedback”, [Zh. Eksp. i Teor. Fiz., 51: 724-729 (1966)
Russian] Sov. Phys. JETP, 24: 481, (1967)
(24) V. M. Markushev, V.F. Zolin, and Ch. M. Briskina, “Powder laser.” Zh.
Prikl. Spektr., Russian. 45, 847, (1986)
(25) V. M. Markushev, V.F. Zolin, and Ch. M. Briskina, “Luminescence and
stimulated emission of neodymium in sodium lanthanum molybdate powder.”
Sov. J. Quantum Electron, 16, 281, (1986)
(26) D. Klemper, and K.C. Frcisch, (eds), “Handbook of polymeric Foams and
125
Foam Technology, Oxford University Press.” New-York (1991)
(27) M. E. Rosa, “An introduction to solid foams.” Philos. Mag. Lett., 88, 637,
(2008)
(28) S. T. Lee, and N.S. Ramesh, “Polymeric Foam: Mechanism and Materials.”
2nd edn CRC Press, Boca Raton, FL, (2009)
(29) F. Jahaniaval, Y. Kakuda, and V. Abraham “Characterization of a double
emulsion system (oil-in-water-in-oil emulsion) with low solid fats:
Microstructure.” J. A. O. Chem. Soc., 80, 1, 25, (2003)
(30) A. Imhof & D. J. Pine, “Ordered macroporous materials by emulsion
templating.” Nature, 389,948, (1997)
(31) C. Soukoulis, “Photonic Band Gap Materials”. (Kluwer, Dordrecht, 1996)
(32) F. Carn et al., “Inorganic monoliths hierarchically textured via concentrated
direct emulsion and micellar templates.” J. Mater. Chem., 14, 1370, (2004)
(33) F. Gillot, S. Boyanov, L. Dupont, M. L. Doublet, M. Morcrette, L.
Monconduit, J. M. Tarascon, “Electrochemical Reactivity and Design of NiP2
Negative Electrodes for Secondary Li-Ion Batteries.” Chem. Mater., 17, 6327,
(2005)
(34) C. Sarrazin, Piles électriques : Présentation générale, Techniques de
l’Ingénieur, D 3, 320, (2002)
(35) J. Koryta, J. Dvořák, L. Kavan, Principles of Electrochemistry (2nd edit.),
Wiley, Chichester (U.K.), (1993)
(36) D. Guyomard, J. M. Tarascon, “Rocking-Chair or Lithium-Ion Rechargeable
Lithium Batteries”, Adv. Mater. 6, 408, (1994)
(37) D. Guyomard, “Nouveaux matériaux d'électrode pour les batteries au
lithium.” L'actualité Chimique, 7, 10, (1999)
(38) N. Brun et al., “Enzyme-based biohybrid foams designed for continuous flow
heterogeneous catalysis and biodiesel production.” Energy Environ. Sci., 4, 2840,
(2011)
(39) R. Backov, “Combining soft matter and soft chemistry: integrative chemistry
towards designing novel and complex multiscale architectures.” Soft Matter, 2,
452, (2006)
126
(40) N. Brun, “Eu3+@Organo-Si(HIPE) Macro-Mesocellular Hybrid Foams
Generation: Syntheses, Characterizations, and Photonic Properties.” Chem.
Mater., 20, 7117, (2008)
(41) A. Imhof, D. J. Pine, “Uniform Macroporous Ceramics and Plastics by
Emulsion Templating.” Adv. Mater., 10, 697, (1998)
(42) (a) G. T. Chandrappa et al., “Green revolution: A mutant gibberellin-
synthesis gene in rice.” Nature 2002, 416, 702. (b) H. Maekawa, J. Esquena, S.
Bishop, C. Solans, B. F. Chmelka, “Meso/Macroporous Inorganic Oxide
Monoliths from Polymer Foams.” Adv. Mater., 15, 591, (2003) (c) L. Huerta, C.
Guillem, J. Latorre, A. Beltran, D. Beltran, P. Amoros., “Large monolithic silica-
based macrocellular foams with trimodal pore system.” Chem. Commun., 1448,
(2003) (d) F. Carn, et al., “Rational Design of Macrocellular Silica Scaffolds
Obtained by a Tunable Sol–Gel Foaming Process.” Adv. Mater., 16, 140, (2004)
(43) (a) B. T. Holland et al. "Synthesis of Highly Ordered Three- Dimensional
Mineral Honeycombs with Macropores." A. Science, 281, 538, (1998) (b) M.
Antonietti, B. Berton, C. Goltner, “Synthesis of Mesoporous Silica with Large
Pores and Bimodal Pore Size Distribution by Templating of Polymer Latices.”
Adv. Mater., 10, 154, (1998)
(44) S. A. Davis et al. “Bacterial templating of ordered macrostructures in silica
and silica-surfactant mesophases." Nature , 385, 420,( 1997)
(45) M. Llusar, C. Roux, J. L. Pozzo, C. Sanchez, “Design of organically
functionalised hybrid silica fibres through the use of anthracenic organogelators.”
J. Mater. Chem., 3, 442, (2003)
(46) K. Nakanishi, “Pore Structure Control of Silica Gels Based on Phase
Separation.” J. Porous Mater., 4, 67, (1997)
(47) P. Yang, et al. “Hierarchically Ordered Oxides.” Science, 282, 2244, (1998)
(48) Alexandre Desforges et. al., “Synthesis and fictionalization of poly-HIPE
beads.” Reactive and Functional Polymers 53, 183, (2002)
(49) C. J. Brinker, et. al. “Sol-Gel Science: The Physics and Chemistry of Sol-Gel
Processing.” (Academic Press)
(50) A. F. Ioffe and A. R. Regel, Progress in Semiconductors vol 4, ed A F
127
Gibson, F. A. Kroger and R. E. Burgess (London: Heywood) p 237, (1960)
(51) D. J. Durian, “Influence of boundary reflection and refraction on diffusive
photon transport.” Phys Rev. E 50, 857, (1994)
(52) N. Garcia, A. Z. Genack, A.A. Lisyansky, “Measurement of the transport
mean free path of diffusing photons.” Phys. Rev. B. 46, 14475 (1992)
(53) J. X. Zhu, D. J. Pine, D. A. Weitz, “Internal reflection of diffusive light in
random media.” Phys. Rev. A 44, 3948 (1991)
(54) M. S. Patterson, B. Chance, B. C. Wilson, “Time resolved reflectance and
transmittance for the non invasive measurements of tissue optical properties.”
Appl. Opt. 28, 2331 (1989)
(55) A. Fick, “Uber Diffusion”, Poggendorff’s Annalen der Physik and Chemie,
94, 59, (1855)
(56) R. Berkovits and M. Kaveh, “Propagation of waves through a slab near the
Anderson transition: a local scalling approach.” J.Phys. Condens. Matter 2 (1990)
(57) P. A. Lee and T. V. Raakrishnan, “Disordered electronic systems.” Rev.
Mod. Phys. 57, 287, (1985)
(58) Y. Imry and Y. Gefen, “Interaction effects in disordered conductors near the
metal–insulator transition.” Phil. Mag. B 50, 203, (1984)
(59) R. Berkovits and M. Kaveh, “Backscattering of light near the optical
Anderson transition.” Phys. Rev. B 36, 9322, (1987)
(60) R. Berkovits, M. Kaveh, and I. Edrei, “Critical behavior of the static and
dynamic correlation functions near the optical Anderson transition.” Phys. Rev. B
39 12250, (1989)
(61) M. Riordan, “The Silicon Dioxide solution: How physicist Jean Hoerni built
the bridge from the transistor to the integrated circuit.” IEEE Spectrum, (2007)
(62) M. Mooney, “The viscosity of a concentrated suspension of spherical
particles.” J. Colloid Interface Sci., 6, 162, (1951)
(63) M. P. Aronson and M. F. Petko, “Highly Concentrated Water-in-Oil
Emulsions: Influence of Electrolyte on Their Properties and Stability.” J. Colloid
Interface Sci., 159, 134, (1993)
(64) D. Barby and Z. Haq, Eur. Patent Appl. 60138, (1982)
128
(65) I. Yeh and G. Hummer, “System-Size Dependence of Diffusion Coefficients
and Viscosities from Molecular Dynamics Simulations with Periodic Boundary
Conditions.” J. Phys. Chem. B, 108, 15873, (2004)
(66) G. Guigas et al., “Size-dependent Diffusion of membrane Inclusions.”
Biophysical Journal, Vol 90, 7, 2393, (2006)
(67) M. Störzer, P. Gross, C. M. Aegerter, “Observation of the Critical Regime
Near Anderson Localization of Light.” Phys. Rev. Lett. 96, 063904, (2006)
(68) S. Bakardjieva et al., “Transformation of brookite-type TiO2 nanocrystals to
rutile: correlation between microstructure and photoactivity.” J. Mater. Chem., 16,
1709, (2009)
(69) R. Wang et al., “ Light-induced amphiphilic surfaces.” Nature, 388, 431,
(1997)
(70) P. A. Mandelbaum et al., “Photo-Electro-Oxidation of Alcohols on Titanium
Dioxide Thin Film Electrodes.” J. Phys. Chem. B, 103, 5505, (1999)
(71) M. E. Nordberg, U.S. Patent 2,326, 059 (1943); J. E. Nitsche, U.S. Patent
3,303,115 (1967)
(72) P. C. Schultz and H. T. Smyth, Amorphous Materials, edited by R. W.
Douglas and B. Ellis (Wiley-Interscience, London, 1972), p. 453
(73) H. M. Presby and 1. P. Kaminow, “Binary silica optical fibers: refractive
index and profile dispersion measurements.” App. Opt Lett. 15, 12, (1976)