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Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Model for light scattering and lasing in dye-dopednematic liquid crystals
A. Veltri, M. Infusino, S. Ferjani, G. Strangi
LICRYL (Liquid Crystals Laboratory),National Institute for the Physics of Matter (INFM-CNR), Center of Excellence
CEMIF.CAL and Department of Physics - University of Calabria, 87036Arcavacata di Rende (CS), Italy
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Lasing in Scattering Media
LasersImage from “Tunable photonic materials and random lasers” Stefano Gottardo - PhD Thesis
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Lasing in Scattering Media
All that you need
Random Lasers: A Scattering Medium A Laser-Active Dopant A bit of luck
Image from http://www.martin-klimas.de/
Image from http://www.greenbeans.co.nz/
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Lasing in Scattering Media
All that you need
Random Lasers: A Scattering Medium A Laser-Active Dopant A bit of luck
Image from http://www.martin-klimas.de/
Image from http://www.greenbeans.co.nz/
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Lasing in Scattering Media
All that you need
Random Lasers: A Scattering Medium A Laser-Active Dopant A bit of luck
Image from http://www.martin-klimas.de/
Image from http://www.greenbeans.co.nz/
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Lasing in Scattering Media
All that you need
Random Lasers: A Scattering Medium A Laser-Active Dopant A bit of luck
Image from http://www.martin-klimas.de/
Image from http://www.greenbeans.co.nz/
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
NLC as a Scattering Medium
Nematic Molecules and Photons
Light-Nematic InteractionNematic Length L ∼ 100nmLaser Wavelenght λ = [500 ÷ 600]nm
Director FluctuationInvolving ∼ 103 Nematic MoleculesDeformation Length ∼ Laser Wavelenght
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
NLC as a Scattering Medium
Director Fluctuations and Light Beams
Light-Nematic InteractionNematic Length L ∼ 100nmLaser Wavelenght λ = [500 ÷ 600]nm
Director FluctuationInvolving ∼ 103 Nematic MoleculesDeformation Length ∼ Laser Wavelenght
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
NLC as a Scattering Medium
Director Fluctuations and Light Beams
Light-Nematic InteractionNematic Length L ∼ 100nmLaser Wavelenght λ = [500 ÷ 600]nm
Director FluctuationInvolving ∼ 103 Nematic MoleculesDeformation Length ∼ Laser Wavelenght
Interaction Between Light Beams [N-photons] and Elastic Deformations
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Light in the Medium
Light and the Medium: Parameters
Light Beam position r(x , y , z)
polarization α = 1, 2 frequency ω
wave vector k
Nematic dielectric constants
ε⊥ and ε|| elastic constants κ1,2,3
temperature T
Images from http://www.geocities.com/ and http://it.wikipedia.org/wiki/Cristalli_liquidi
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Light in the Medium
Frames of reference
“Laboratory” Frame [x , y , z ]
H. Stark et al. “Light diffusion and diffusing-wavespectroscopy in nematic liquid crystal”J. Opt. Soc. Am. A, 14(1):156, January 1997.
y -axis perpendicular to the glass slabs
planar alignment n0 = (0, 0, 1)
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Light in the Medium
Frames of reference
“Impact” Frame [u1, u2, u3]
H. Stark et al. “Light diffusion and diffusing-wavespectroscopy in nematic liquid crystal”J. Opt. Soc. Am. A, 14(1):156, January 1997.
u2-axis perpendicular to [n0, k]-plane. u1-axis perpendicular to [u2, n0]-plane. u3 parallel to n0.
u2 =n0 × k|n0 × k|
u1 = u2 × n0
u3 ≡ n0
e1 is the electric field corresponding toextraordinary polarization (α = 1).
e2 is the electric field corresponding toordinary polarization (α = 2).
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Dealing with Impacts
Effect of Fluctuations
H. Stark et al. “Light diffusion and diffusing-wavespectroscopy in nematic liquid crystal”J. Opt. Soc. Am. A, 14(1):156, January 1997.
Input Beam wavevector k polarizarion α
Output Beam wavevector q polarizarion β
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Dealing with Impacts
Effect of Fluctuations
H. Stark et al. “Light diffusion and diffusing-wavespectroscopy in nematic liquid crystal”J. Opt. Soc. Am. A, 14(1):156, January 1997.
Input Beam wavevector k polarizarion α
Output Beam wavevector q polarizarion β
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Dealing with Impacts
Effect of Fluctuations
H. Stark et al. “Light diffusion and diffusing-wavespectroscopy in nematic liquid crystal”J. Opt. Soc. Am. A, 14(1):156, January 1997.
Input Beam wavevector k polarizarion α
Output Beam wavevector q polarizarion β
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Dealing with Impacts
Effect of Fluctuations
H. Stark et al. “Light diffusion and diffusing-wavespectroscopy in nematic liquid crystal”J. Opt. Soc. Am. A, 14(1):156, January 1997.
Input Beam wavevector k polarizarion α
Output Beam wavevector q polarizarion β
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Dealing with Impacts
Effect of Fluctuations
H. Stark et al. “Light diffusion and diffusing-wavespectroscopy in nematic liquid crystal”J. Opt. Soc. Am. A, 14(1):156, January 1997.
Input Beam wavevector k polarizarion α
Output Beam wavevector q polarizarion β
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Dealing with Impacts
Effect of Fluctuations
H. Stark et al. “Light diffusion and diffusing-wavespectroscopy in nematic liquid crystal”J. Opt. Soc. Am. A, 14(1):156, January 1997.
Input Beam wavevector k polarizarion α
Output Beam wavevector q polarizarion β
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Dealing with Impacts
Structure Factor Bαβ
H. Stark et al. “Light diffusion and diffusing-wavespectroscopy in nematic liquid crystal”J. Opt. Soc. Am. A, 14(1):156, January 1997.
Input Beam wavevector k polarizarion α
Output Beam wavevector q polarizarion β
Bαβ(k, q) = ∆ε2kBTω4
c4
2∑δ=1
N(eα, eβ, uδ)
kδ(qS)
by defining kδ(q) = κδq2⊥ + κ3q2
|| and usingL = (κ3c2)/(∆ε2kBTω2) as the normalization lenght:
Bαβ(k, q) =ω2
c2
2∑δ=1
N(eα, eβ, uδ)[κδκ3
q2S⊥ + qS||
]
where N = [(n0 · eβ)(uδ · eα) + (uδ · eβ)(n0 · eβ)]2
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Results of the Model
After a Scattering Event
Path to cover until next scattering event: R Wavevector after the scattering event: q New polarization of the beam: β
R =lα
cos δ ln(
11−xr
) 1lα(k)
=nα(k)
4π
2∑β=1
∫dΩq
4πBαβ(k, q)n3
β(q)
xr is a random number ∈ [0 : 1],
cos δ = 1n2
hsin2 θε2⊥
+ cos2 θε||
iand θ is the angle between k and n0
where
H. Stark et al. “Light diffusion and diffusing-wavespectroscopy in nematic liquid crystal”J. Opt. Soc. Am. A, 14(1):156, January 1997.
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Results of the Model
After a Scattering Event
Path to cover until next scattering event: R Wavevector after the scattering event: q New polarization of the beam: β
∫q
Bαβd q ≥ Cαβzr
Cαβ =
Cα1, if β = 1Cα2, if β = 2
Cα1 =nα(k)
4π
∫dΩq
4πBα1(k, q)n3
β(q)
Cα2 =nα(k)
4π
∫dΩq
4πBα2(k, q)n3
β(q)
zr is a random number ∈ [0 : 1]
where
H. Stark et al. “Light diffusion and diffusing-wavespectroscopy in nematic liquid crystal”J. Opt. Soc. Am. A, 14(1):156, January 1997.
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Results of the Model
After a Scattering Event
Path to cover until next scattering event: R Wavevector after the scattering event: q New polarization of the beam: β
β =
1, if g ≤ Rαβ
2, if g > Rαβ
Rαβ =Cα1
Cα1 + Cα1
Cα1 =nα(k)
4π
∫dΩq
4πBα1(k, q)n3
β(q)
Cα2 =nα(k)
4π
∫dΩq
4πBα2(k, q)n3
β(q)
g is a random number ∈ [0 : 1]
where
H. Stark et al. “Light diffusion and diffusing-wavespectroscopy in nematic liquid crystal”J. Opt. Soc. Am. A, 14(1):156, January 1997.
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Results of the Model
The Path
H. Stark et al. “Light diffusion and diffusing-wavespectroscopy in nematic liquid crystal”J. Opt. Soc. Am. A, 14(1):156, January 1997.
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Model for Active Dopant
How many levels you said?
We are not interested on:
Internal conversion
Inter System crossing
Triplet triplet absorption
Phosporescence
Taking into account that:
Transition d → b is very fast
We can consider a base levelat timeTypical energy spectrum of a dye molecule
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Model for Active Dopant
How many levels you said?
We are not interested on:
Internal conversion
Inter System crossing
Triplet triplet absorption
Phosporescence
Taking into account that:
Transition d → b is very fast
We can consider a base levelat timeThree level approximation
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Model for Active Dopant
How many levels you said?
We are not interested on:
Internal conversion
Inter System crossing
Triplet triplet absorption
Phosporescence
Taking into account that:
Transition d → b is very fast
We can consider a base levelat timeThree level approximation
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Model for Active Dopant
How many levels you said?
We are not interested on:
Internal conversion
Inter System crossing
Triplet triplet absorption
Phosporescence
Taking into account that:
Transition d → b is very fast
We can consider a base levelat timeOur Choice
Two level approximation
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Model for Active Dopant
Gain Equation
Let’s consider a beam of N photons σ-polarized propagating in suchmedium(
∂
∂t+ vσ
g · ∇)
Nσ(k) = Aσab(k)
[(Nσ(k) + 1)nb − Nσ(k)
ga
gbna
]Hypothesis:
gbAσab(k) = gaAσ
ba(k)
∂∂t = 0 [Steady State Solution]
Intensity:
I = hω3Nσ/(2π)3c2
Analytic Solution:
Nσ(S) = (N0 + 1/γ)eγAσabS − 1/γ
where γ = 1 − gbna/ganb
Aσab = Aσ
abnb/vσg
A. Aspect, C. Fabre, G. Grynberg “Optique Quantique 1: Lasers”Majeure de Physique (2005).
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Gain on the Path
Fluorescence
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Gain on the Path
Fluorescence
nb > na → γ > 0nb < na → γ < 0
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Gain on the Path
Fluorescence
nb > na → γ > 0nb < na → γ < 0
Nσ(S) = (N0+1/γ)eγAσabS −1/γ
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Wavelength and length of Path
More the Scattering, Longer the Path
Taking into account that free main path R ∝ (κ3λ2)/(∆ε2kBT )
lower λ ⇒ lower R ⇒ higher number of scattering events ⇒ longer the path S
S1 < S2
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Wavelength and length of Path
More the Scattering, Longer the Path
Taking into account that free main path R ∝ (κ3λ2)/(∆ε2kBT )
lower λ ⇒ lower R ⇒ higher number of scattering events ⇒ longer the path S
S1 < S2
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Wavelength and length of Path
More the Scattering, Longer the Path
Taking into account that free main path R ∝ (κ3λ2)/(∆ε2kBT )
lower λ ⇒ lower R ⇒ higher number of scattering events ⇒ longer the path S
S1 < S2
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Wavelength and length of Path
More the Scattering, Longer the Path
Taking into account that free main path R ∝ (κ3λ2)/(∆ε2kBT )
lower λ ⇒ lower R ⇒ higher number of scattering events ⇒ longer the path S
S1 < S2
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Wavelength and length of Path
More the Scattering, Longer the Path
Taking into account that free main path R ∝ (κ3λ2)/(∆ε2kBT )
lower λ ⇒ lower R ⇒ higher number of scattering events ⇒ longer the path S
S1 < S2
longer path
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Wavelength and length of Path
More the Scattering, Longer the Path
Taking into account that free main path R ∝ (κ3λ2)/(∆ε2kBT )
lower λ ⇒ lower R ⇒ higher number of scattering events ⇒ longer the path S
S1 < S2
longer path
γ > 0
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Wavelength and length of Path
More the Scattering, Longer the Path
Taking into account that free main path R ∝ (κ3λ2)/(∆ε2kBT )
lower λ ⇒ lower R ⇒ higher number of scattering events ⇒ longer the path S
S1 < S2
longer path
γ > 0γ < 0
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Monte Carlo Simulation
Initial Conditions
Randomly generatedinitial position r0and direction k
Parameters for the Medium E7 nematic liquid crystal
Dielectric Constants ε⊥ = 2.31526656 ε|| = 3.04921444
Elastic Constants κ1 = 10.3 · 10−12N κ2 = 7.21 · 10−12N κ3 = 16.5 · 10−12N
Temperature T = 300K
Parameters for Light λ ∈ [540 : 620]nm
α =
(1, 50%
2, 50%
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Monte Carlo Simulation
Initial Conditions
Randomly generatedinitial position r0and direction k
Parameters for the Medium E7 nematic liquid crystal
Dielectric Constants ε⊥ = 2.31526656 ε|| = 3.04921444
Elastic Constants κ1 = 10.3 · 10−12N κ2 = 7.21 · 10−12N κ3 = 16.5 · 10−12N
Temperature T = 300K
Parameters for Light λ ∈ [540 : 620]nm
α =
(1, 50%
2, 50%
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Monte Carlo Simulation
Initial Conditions
Randomly generatedinitial position r0and direction k
Parameters for the Medium E7 nematic liquid crystal
Dielectric Constants ε⊥ = 2.31526656 ε|| = 3.04921444
Elastic Constants κ1 = 10.3 · 10−12N κ2 = 7.21 · 10−12N κ3 = 16.5 · 10−12N
Temperature T = 300K
Parameters for Light λ ∈ [540 : 620]nm
α =
(1, 50%
2, 50%
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Monte Carlo Simulation
Outputs
Sample Thickness 1mm
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Monte Carlo Simulation
Outputs
Sample Thickness 1mm
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Monte Carlo Simulation
Outputs
Sample Thickness 1mm
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Monte Carlo Simulation
Outputs
Sample Thickness 1mm
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Monte Carlo Simulation
Outputs
Sample Thickness 1mm
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Monte Carlo Simulation
Outputs
Sample Thickness 1mm
Path λ-dependent
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Monte Carlo Simulation
Outputs
Sample Thickness 100µm
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Monte Carlo Simulation
Outputs
Sample Thickness 100µm
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Monte Carlo Simulation
Outputs
Sample Thickness 100µm
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Monte Carlo Simulation
Outputs
Sample Thickness 100µm
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Monte Carlo Simulation
Outputs
Sample Thickness 100µm
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Monte Carlo Simulation
Outputs
Sample Thickness 100µm
Path λ-independent
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Discussing the Results
No Lasing in 100µm Samples?
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Discussing the Results
No Lasing in 100µm Samples?
"contra facta non est argumentum" [you can’t deny the facts]
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Discussing the Results
The Rutherford Syndrome
We have to find a different description for the scattering centers distribution
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Discussing the Results
The Rutherford Syndrome
We have to find a different description for the scattering centers distribution
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Hunting Down the “bug”
Fluctuation Spectrum
Calculation of structure factor Bαβ isbased on the fluctuation spectrum:
〈|δn(qS)|2〉 ∼ kBT/κq2S
where qS is the wavevector associatedto director fluctuation
Large fluctuations are statistically favorite
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Hunting Down the “bug”
Fluctuation Spectrum
Calculation of structure factor Bαβ isbased on the fluctuation spectrum:
〈|δn(qS)|2〉 ∼ kBT/κq2S
where qS is the wavevector associatedto director fluctuation
Large fluctuations are statistically favorite
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Hunting Down the “bug”
Fluctuation Spectrum
Calculation of structure factor Bαβ isbased on the fluctuation spectrum:
〈|δn(qS)|2〉 ∼ kBT/κq2S
where qS is the wavevector associatedto director fluctuation
Large fluctuations are statistically favorite
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Hunting Down the “bug”
Fluctuation Spectrum
Calculation of structure factor Bαβ isbased on the fluctuation spectrum:
〈|δn(qS)|2〉 ∼ kBT/κq2S
where qS is the wavevector associatedto director fluctuation
Large fluctuations are statistically favorite
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Hunting Down the “bug”
Fluctuation Spectrum
Calculation of structure factor Bαβ isbased on the fluctuation spectrum:
〈|δn(qS)|2〉 ∼ kBT/κq2S
where qS is the wavevector associatedto director fluctuation
Large fluctuations are statistically favorite
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Hunting Down the “bug”
Fluctuation Spectrum
Calculation of structure factor Bαβ isbased on the fluctuation spectrum:
〈|δn(qS)|2〉 ∼ kBT/κq2S
where qS is the wavevector associatedto director fluctuation
Large fluctuations are statistically favorite
Hypothesis:Fluctuations Spatially uncorrelated
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Hunting Down the “bug”
Non Linear Interactions
Used spectrum describe director fluctuationsinteracting with a pure, uniform alignedmedium
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Hunting Down the “bug”
Non Linear Interactions
Used spectrum describe director fluctuationsinteracting with a pure, uniform alignedmedium
Fluctuation could also interact eachothers giving rise non-linear terms
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Hunting Down the “bug”
Non Linear Interactions
Used spectrum describe director fluctuationsinteracting with a pure, uniform alignedmedium
Fluctuation could also interact eachothers giving rise non-linear terms
This could change the slope of the spectrum at some scales
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Hunting Down the “bug”
Non Linear Interactions
Used spectrum describe director fluctuationsinteracting with a pure, uniform alignedmedium
We are using a dye doped nematicliquid crystal.We should have to take into accountsome kind of Janossy effect.Again non linear terms.
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Hunting Down the “bug”
Non Linear Interactions
Used spectrum describe director fluctuationsinteracting with a pure, uniform alignedmedium
We are using a dye doped nematicliquid crystal.We should have to take into accountsome kind of Janossy effect.Again non linear terms.
This could change the slope of the spectrum at some scales
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Conclusions
We have explored scattering in nematic liquid crystal as awavelength selector for random lasing in this medium
The idea works well for ideal thick samples, but isinappropriate for the thin ones utilized in experiments
The model represents a good diagnostic tool studying physicalphenomena occurring in this kind of systems
As a future develop, we plan to realize a more complex modeltaking into account spatial correlation for director fluctuationand/or interactions with dye molecules.
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
Introduction Scattering in NLC A Laser Active Medium Results Future Development Conclusions
Thank you for your attention!
Presentation made in LATEX
Alessandro Veltri LICRYL, INFM-CNR, Department of Physics UNICAL
Model for light scattering and lasing in dye-doped nematic liquid crystalselectronic-
Liquid Crys
tal Prese
ntations
electronic-
Liquid Crys
tal Prese
ntations
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55
http://w
ww.e-lc.org/prese
ntations/d
ocs/2007_10_09_12_07_55