OF n-wires & µ-wires - Fabrication and Apps.pdf

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ptical fiber nanowires and microwires:abrication and applications

ilberto Brambilla,1,* Fei Xu,1 Peter Horak,1 Yongmin Jung,1

umihito Koizumi,2 Neil P. Sessions,1 Elena Koukharenko,3 Xian Feng,1

anapathy S. Murugan,1 James S. Wilkinson,1 and David J. Richardson1

Optoelectronics Research Centre, University of Southampton,outhampton SO17 1BJ, UK

Asahi Glass Co. Ltd., Kanagawa-ku, Yokohama 221-8755, Japan

School of Electronics and Computer Science, University of Southampton,outhampton SO17 1BJ, UK

Corresponding author: [email protected]

eceived August 21, 2008; revised November 17, 2008; accepted November 17, 2008;osted November 18, 2008 (Doc. ID 100357); published January 30, 2009

Microwires and nanowires have been manufactured by using a wide range ofbottom-up techniques such as chemical or physical vapor deposition andtop-down processes such as fiber drawing.Among these techniques, themanufacture of wires from optical fibers provides the longest, most uniformand robust nanowires. Critically, the small surface roughness and thehigh-homogeneity associated with optical fiber nanowires (OFNs) providelow optical loss and allow the use of nanowires for a wide range of newapplications for communications, sensing, lasers, biology, and chemistry. OFNsoffer a number of outstanding optical and mechanical properties, including(1) large evanescent fields, (2) high-nonlinearity, (3) strong confinement, and(4) low-loss interconnection to other optical fibers and fiberized components.OFNs are fabricated by adiabatically stretching optical fibers and thus preservethe original optical fiber dimensions at their input and output, allowingready splicing to standard fibers. A review of the manufacture of OFNs ispresented, with a particular emphasis on their applications. Three differentgroups of applications have been envisaged: (1) devices based on thestrong confinement or nonlinearity, (2) applications exploiting the largeevanescent field, and (3) devices involving the taper transition regions. Thefirst group includes supercontinuum generators, a range of nonlinear opticaldevices, and optical trapping. The second group comprises knot, loop, andcoil resonators and their applications, sensing and particle propulsion by opticalpressure. Finally, mode filtering and mode conversion represent applicationsbased on the taper transition regions. Among these groups of applications,devices exploiting the OFN-based resonators are possibly the most interesting;because of the large evanescent field, when OFNs are coiled onto themselvesthe mode propagating in the wire interferes with itself to give a resonator.In contrast with the majority of high-Q resonators manufactured by othermeans, the OFN microresonator does not have major issues with input–output coupling and presents a completely integrated fiberized solution. OFNscan be used to manufacture loop and coil resonators with Q factors that,although still far from the predicted value of 109, are well in excess of 105.

dvances in Optics and Photonics 1, 107–161 (2009) doi:10.1364/AOP.1.000107 107

2009 Optical Society of America

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The input–output pigtails play a major role in shaping the resonator responseand can be used to maximize the Q factor over a wide range of couplingparameters. Finally, temporal stability and robustness issues are discussed, anda solution to optical degradation issues is presented.

OCIS codes: 060.2310, 060.2370, 230.3990, 230.2285, 160.2290, 160.4236.

. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

. Manufacture of OFNs and OFMs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

. Properties of OFNs and OFMs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1113.1. Loss. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1113.2. Spot Size and Mode Confinement. . . . . . . . . . . . . . . . . . . . . . . . . . 1113.3. Mechanical Strength. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

3.3a. The Big Issue. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1163.3b. Embedding. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

. Applications. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1174.1. High-Q Resonators. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

4.1a. Single-Loop Resonators. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1184.1b. Coil Resonators. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

4.2. Particle Manipulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1284.3. Sensors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

4.3a. Resonating Sensors: Schematic and Manufacture. . . . . . . . . 1324.3b. Resonating Sensors: Theory. . . . . . . . . . . . . . . . . . . . . . . . . . 1344.3c. Resonating Sensors: Sensitivity. . . . . . . . . . . . . . . . . . . . . . . 1364.3d. Resonating Sensors: Detection Limit. . . . . . . . . . . . . . . . . . . 1394.3e. Resonating Sensors: Experimental Demonstration. . . . . . . . . 140

4.4. Supercontinuum Generation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1424.5. Particle Trapping. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1444.6. Mode Filtering. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147

4.6a. Mode Filtering: Theory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150. Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153cknowledgments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153eferences. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153



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ptical fiber nanowires and microwires:abrication and applications

ilberto Brambilla, Fei Xu, Peter Horak, Yongmin Jung,umihito Koizumi, Neil P. Sessions, Elena Koukharenko, Xian Feng,anapathy S. Murugan, James S. Wilkinson, and David J. Richardson

. Introduction

n the past decade nanowires have attracted much attention because of thenique properties that materials display on the nanoscale [1]. A vast variety ofaterials have been studied, including carbon nanotubes [2], single-element

anowires (Si, Ge, Cu, Au, and Ag [3–7]), multicomponent structures (GaAs,aN, InP, CdS, SiC, Si3N4, SiO2, Al2O3, ZnO, SnO2, In2O3 [8–18]), and

ven organic materials [19,20]. Nanowires have been manufactured by using aide range of techniques: electron beam lithography [21], laser ablation

22], template-based methods [23], bottom-up methods such as vapor–liquid–olid techniques [24], chemical and physical vapor deposition [8,25], solgelethods [26], and top-down techniques such as fiber pulling [27–31] or direct

raw from bulk materials [20,32].

rior to 2003 only two attempts to manufacture submicrometer wires by usingtop-down process were reported in the literature [33,34]. Interest in opticalber nanowires (OFNs) has been limited mainly because of the perceivedifficulties in manufacturing suitably low-loss structures. Although severalFNs were fabricated by using a variety of bottom-up methods [35–42], all of

hem exhibited an irregular profile and a surface roughness that appear toave limited the loss levels that could be reliably achieved [43,44]. In 2003 awo-step process to fabricate low-loss submicrometric silica wires was presented27]; it involved wrapping and drawing a pretapered section of standardber around a heated sapphire tip. Although the measured loss was orders ofagnitude higher than that achieved later with flame-brushing techniques

28–31], it was low enough to allow the use of OFNs for optical devices andgnite interest in the technology. In the following years a spate of publicationsnvestigated novel properties and applications of OFNs. It has becomeommonly accepted to define optical fiber nanowires (or photonic nanowires)s fiber waveguides with a submicrometric diameter. In this paper wiresith diameter bigger than 1 µm will be referred to as optical fiber microwires

OFMs)

FNs and OFMs are of interest for a range of emerging fiber optic applications,ince they offer a number of enabling optical and mechanical properties,ncluding the following:

1. Strong confinement. Light can be confined to a very small area over long
evice lengths, allowing the ready observation of nonlinear interactions, such as


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upercontinuum generation [45–48], at relatively modest power levels.2. Large evanescent fields.A considerable fraction of the power can propagate

n the evanescent field outside the OFN physical boundary [28], and thisan be exploited for atom guides [49,50], particle manipulation [51,52], sensors53–58], and high-Q resonators [59–66].

3. Great configurability. OFNs can be easily manipulated and bent becausef their relatively high-mechanical strength. Bend radii of the order of a fewicrometers can be readily achieved with low induced bend loss [67],

llowing for highly compact devices with complex geometries, e.g., 2D [60]nd 3D [59] resonators.4. Low-loss connection. Low-loss connection to other optical fibers and

berized components is possible; since OFNs are manufactured by adiabaticallytretching optical fibers, they maintain the original fiber size at their inputnd output, allowing ready splicing to standard fibers and fiberized components.nsertion losses smaller than 0.1 dB are commonly observed.

n the next sections the properties of OFNs and OFMs will be introduced andhe fabrication methodologies discussed. Applications ranging from modelters to high-Q resonators and to sensors will be presented.

. Manufacture of OFNs and OFMs

FN and OFM tapers are made by adiabatically stretching a heated fiber,orming a structure comprising a narrow stretched filament (the taper waist),ach end of which is linked to an unstretched fiber by a conical section (the taperransition region), as shown in Fig. 1.

n the past few years, three different methodologies have been used to fabricateFNs and OFMs from optical fibers:

1. Tapering the fiber by pulling it around a sapphire rod heated by a flame,2. The flame-brushing technique,3. The modified flame-brushing technique.

he flame-brushing technique has been previously used for the manufacture ofber tapers and couplers [68]. A small flame moves under an optical fiber

hat is being stretched: because of mass conservation, the heated areaxperiences a diameter decrease. Controlling the flame movement and the fiber

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tretching rate lets the taper shape be defined to an extremely high-degree ofccuracy. This technique provides access to the OFN from both pigtailed ends.oreover, it delivers OFNs with radii as small as 30 nm [31], the longest

nd most uniform OFNs–OFMs [28] and the lowest measured loss to date29–31].

he third fabrication method is a modified version of the flame-brushingechnique in which the flame is replaced by a different heat source. Two typesf heat source have been used: a sapphire capillary tube hit by a CO2 laseream [59], and a microheater [69]. This method is not limited to silica butrovides OFNs and OFMs from a range of glasses including lead silicates [69],ismuth silicate [69], and chalcogenides [48].

. Properties of OFNs and OFMs

.1. Loss

or diameters of the minimum waist region comparable with the wavelengthof the radiation propagating in the OFNs, light is strongly guided. When, the mode is strongly affected by diameter fluctuations. It has been shown

70] that for very small the propagation loss is related to the propagationonstant k, the absolute value of the transversal component of theropagation constant and the characteristic length of diameter fluctuations Lf

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xperimentally, has been evaluated during and after fabrication by launchingight into the OFN pigtail from a laser diode and collecting the transmittedignal with an InGaAs photodiode connected to the output pigtail. A summaryf recorded losses in OFNs made from telecommunication optical fibersersus radius for =1.55 µm is reported in Fig. 2.

.2. Spot Size and Mode Confinement

he spot size of the light propagating in the taper is also strongly dependent on[71] through the V factor:

V =2

2NA, 2

here NA denotes the numerical aperture. Equation (2) provides the claddingVcl or core Vco V numbers, when the cladding or the core co diameters

The flame-brushing and modified flame-brushingtechniques provide the lowest loss across a wide raof .

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re used, respectively. The relationship between the spot size and Vcl during



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apering for a standard single-mode fiber (SMF) is shown in Fig. 3. Vcl haseen calculated from Eq. (2) for a mode confined by the silica–air interfaceNA1 if the silica and air refractive indices are taken to be 1.444 and 1,espectively).

conventional optical fiber falls at the right in this figure. The label SMF inig. 3 represents the value of Vco for a telecom optical fiber at 1.55 µm. When theptical fiber diameter decreases, V decreases and initially decreases untilminimum point (B) is reached. After that, the mode is no longer guided in theore, and suddenly increases to a maximum associated with claddinguiding. For even smaller diameters decreases with decreasing V until iteaches a minimum (A) for Vcl2, and then it increases again. This region at

cl2 is typical of OFNs: the mode is only weakly guided by theaveguide, can be orders of magnitude bigger than the physical diameter of

he OFN, and a larger fraction of the power resides in the evanescent field.

igure 4 shows the evanescent field at the surface of an OFN with various waistiameters simulated by using the beam propagation method. Simulations werearried out by using a full 3D vectorial method, and the electric field E wasormalized to unit power. The propagating mode of untapered optical fiber isompletely confined within the physical boundary of the fiber, and whenhe fiber is tapered below a certain diameter a considerable fraction of the powerropagates in the surrounding medium. The electric field at the interfacehows a maximum around the waist diameter of about 0.7 µm, below whicht sharply decreases. This can be explained by the increased , whichffectively decreases the power density in the OFN. The decrease at larger isscribed to the increasing mode confinement into the core.

t is interesting to note that the minimum beam waist depends on theladding material, and the minimum beam size is ultimately limited by

Figure 2

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ummary of optical loss achieved in OFNs and OFMs for the threeanufacturing techniques presented in Section 2: 1, the two stage process

nvolving a sapphire rod heated by a flame [27]; 2, the flame-brushing technique28–31]; 3, the modified flame-brushing technique [this work, 30, 71].



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elationship between the spot size (defined as the radius where the intensityas dropped to 1/e2 [71]), the cladding Vcl and core Vco V numbers of aapered telecom fiber. Labeled points are the points of maximum confinement,, in the cladding and, B, in the core and, C, the beginning of claddinguiding. Vcl and Vco are related to the cladding and core co diameters by Eq.2). SMF and OFN represent the V numbers of a common telecom opticalber and an optical fiber nanowire with r=500 nm in air at 1.55 µm.

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elationship between the electric field at the OFN surface and the OFNiameter . The wavelength and the refractive indices of the silica OFN wereaken to be 1.047 µm and 1.45, respectively. Water was taken as theurrounding medium with a refractive index of 1.33.



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iffraction. Figure 5 compares the dependence of on the cladding diameteror three different fiber glasses: silica, lead silicate (F2, Schott glass) andismuth silicate (Asahi glass). in bismuth silicate is nearly 40% smaller thann silica, and the OFM diameter at which the minimum occurs is nearly0% smaller.

n Fig. 5, it is possible to identify two regions: the high-confinement region (I)nd the large-evanescent-field region (II). In the high-confinement region s comparable with , the beam has its minimum waist diameter, and the opticalonlinearity reaches its maximum. is a figure of merit that is related tohe material nonlinear refractive index n2 and the beam size Aeff =2 /4 byhe following equation:

=2

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standard telecom SMF has 1 W−1 km−1, while typical silica OFMs canave as high as 100 W−1 km−1. OFNs made from highly nonlinearaterials such as lead silicate, bismuth silicate, and chalcogenide glasses can

e used to produce OFNs with maximum values of of the order of 1000,000, and 80,000 W−1 km−1 respectively. OFMs with diameters in this regionan be used for a wide range of nonlinear applications, includingupercontinuum generation, particle trapping at the nanowire end facet, andonlinear switching (see Subsections 4.4 and 4.5).

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=1.444), aead silicate glass nF2

=1.597, and a bismuth silicate glass nBS=2.02. Forncreasing refractive indexes, the minimum becomes smaller and occurst smaller diameters .



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y contrast, in the evanescent field region OFMs and OFNs have diametersmaller than the waist of the propagating modes. can be orders of magnitudeigger than , and a considerable fraction of the power propagates in thevanescent field outside the fiber physical boundary. OFMs and OFNs withiameters in this region can be used for high-Q resonators (knot, loop, and coil),article manipulation, and sensing (Subsections 4.1–4.3).

.3. Mechanical Strength

lthough they have an extremely small diameter, OFNs can be handledelatively easily because of their exceptional mechanical strength. Their ultimatetrength fract, defined as the maximum stress a material can withstand, cane measured in a simple static experiment by adding milligram masses at theower extremity of the vertically held fiber pigtail until fracture occurs.he mass m can then be measured and fract can be derived from the relation

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here A is the OFN cross section.

igure 6 shows a summary of the results carried out on OFNs with radii r /2 in the range from 60 to 300 nm. The tapers were produced with theodified flame-brushing technique by scanning a microheater (NTT-AT, Japan)

ver 6 mm along the optical fiber. For OFNs with r200 nm fract is in

In other words, a chalcogenide OFN at maximumconfinement has a nonlinearity that is 105 timehigher than that observed in conventional telecomfibers.

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xcess of 10 GPa. Although this value is slightly smaller than that measuredor carbon nanotubes (fract=21–63 GPa [72,73]), it is still considerably largerhan the values recorded for commercially available high-strength materialsike Kevlar fract=3.88 GPa [74] and the high-strength steel ASTM514 fract=0.76 GPa.

fract for OFNs is also higher than the measured fract5 GPa of bare telecomptical fibers, where the radius is up to 3 orders of magnitude larger r62.5 µm [75,76]. It is interesting to note that OFNs fabricated by the modified

ame-brushing technique seem to have a considerably better mechanicaltrength than those manufactured by the two-step technique, for which theeported tensile strength was 2.5–5 GPa [27]; this can be explained by the betterurface quality. Nanowires manufactured by the modified flame-brushingechnique also provide a better mechanical performance than thoseanufactured by the conventional flame-brushing technique because of the

ower water content in the nanowires. The flame produces a considerable amountf OH groups that then diffuse in the nanowire at high temperatures, and its known from experiments on optical fibers that the water content in silicaeduces the overall mechanical strength.

.3a. The Big Issue

urfaces degrade with time, and they need protection for long-term applications.ince OFNs have a large ratio between surface and volume, the effect ofegradation is considerably more pronounced than in bigger specimens, i.e.ptical fibers. Experiments have been conducted to quantify the long-termegradation of optical and mechanical properties of optical fiber nanowires andave shown a considerable difference between the nanowires preserved in aleanroom environment and those kept in a conventional optics laboratory; in aonventional optics laboratory a group of OFNs manufactured by theame-brushing technique with r375 nm experienced a decay approximatedy the relation [31]

fract = 10.4 − 0.172 t GPa, 5

here t represents the time from fabrication in days.

he decrease in fract has been related to optical properties, and it was foundhat an average decrease of 1.34 GPa in fract was associated with an averagenduced loss of 1 dB/mm. This connection was explained by the continuousormation of cracks, which simultaneously degrade the optical and theechanical properties of the OFNs. This effect is well known to the opticalber industry, where optical fibers are coated immediately after their fabrication

o protect them from mechanical degradation. Some means to protect theurface of the nanowire is therefore required.

.3b. Embedding

he acrylic coating used to protect optical fibers has a higher refractive indexhan silica because it has the additional purpose of stripping the modesropagating in the cladding. In OFNs the propagating mode has a significantntensity at the interface between silica and air, and the only approach to avoidonfinement losses is to use low-refractive-index materials, such as silicone
ubber [77], Efiron halogenated polymers, [78,79] and Teflon [66,80], which


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ave refractive indices n of 1.4, 1.373 and 1.3 at =1.55 µm, respectively.ilicone rubber is a thermocurable polymer that has been used to embed.5 µm OFMs and OFM resonators [77]. The Efiron UV37x family consists ofV-curable polymers manufactured by Luvantix (South Korea) [81] widelysed to coat fibers used in optical fiber lasers. Teflon is a fluoropolymer withxtremely low solubility in most chemicals. Still, a modified version existshat can be dissolved in fluorinated solvents [82]. This represents the best optiono achieve high-confinement in embedded OFN or OFMs because of its lowefractive index: the mode confinement is significantly higher than that achievedith other polymers because of the large refractive index difference between

he OFN or OFM and the Teflon coating. The temporal stability of OFNsmbedded in Teflon has also been studied over a period of time longer than00 h, and no change in transmitted power was observed [80]; for comparison,ver the same time period a 20 mm long uncoated sample with the same xperienced an induced loss in excess of 30 dB. Similar experiments carried outn silicon rubber and Luvantix polymers showed that all the above-mentionedaterials successfully protect OFNs and OFMs from degradation. For this

eason, sensors and applications are based on embedded OFNs or OFMs.

. Applications

pplications of OFMs and OFNs can be classified into three main groupsccording to what property they exploit:

Evanescent fieldConfinementTransition regions

vanescent field applications take advantage of the power propagating outsidehe physical boundary of the wire and include high-Q knot, loop, and coilesonators (Subsection 4.1), particle manipulation (Subsection 4.2), and sensorsSubsection 4.3).

pplications exploiting the confinement properties of OFMs correspondpproximately to region I in Fig. 5 and include supercontinuum generationSubsection 4.4), particle trapping (Subsection 4.5), and nonlinear switching oristability [83,84].

inally, transition regions have been exploited to convert and filter modes.pplications will be presented in Subsection 4.6.

.1. High-Q Resonators

igh Q resonators have been widely studied because of their broad range ofpplications [85] ranging from optical communications to nonlinearptics, cavity QED, and sensing. If an OFN (or OFM) is coiled onto itself, theodes in the two different sections can overlap and couple, creating a

esonator with an extremely compact geometry. A schematic of the transmissionpectrum of a high-Q resonator is shown in Fig. 7.

everal resonator parameters can be easily estimated from the transmissionpectra: quality factor (Q), free spectral range (FSR), and finesse (f) are the mostmportant. Q is proportional to the confinement time in units of the optical
eriod and can be expressed as [86]


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here res is the resonance wavelength and FWHM its full width atalf-maximum. The typical Q of OFN single-loop resonators is in the range03–106 [60,66,78,79].

he FSR is the inverse of the round-trip time (round-trip group delay) of anptical pulse. In the loop resonator spectrum, the FSR is the wavelength orrequency period of the peaks as shown in Fig. 7. It can be expressed as86]

FSRHz =c

2neffL7

where c is the light’s speed, neff the effective index of the mode propagating inhe OFM, and L the loop length). FSR can also be expressed as the difference of two adjacent resonator wavelengths near res:

FSR 2

4neffL. 8

inally, f can be evaluated from the ratio between FSR and FWHM [86]:

f =FSR

FWHM. 9

.1a. Single-Loop Resonators

ingle-loop resonators are the simplest resonators manufactured from OFNsnd OFMs. Two different single-loop resonators have been demonstrated: theoop resonator and the knot resonator. Figure 8 shows an example of aingle-loop knot resonator fabricated by knotting an OFM.

oop resonators can be easily manufactured by coiling an OFN or OFM. These of XYZ stages to coil the OFM allows a great deal of control of the

Figure 7

chematic of a spectrum with the related notation for FWHM, free spectralange (FSR), and resonant wavelength res.

esonator geometry. Still, the geometry stability is based on surface forces;



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hus loop resonators are compromised in terms of long-term reliability. Inontrast, knot resonators (like the one reported in Fig. 7) exhibit an enhancedemporal stability because of the friction that different sections of the OFMxert on one another. However, because the stiffness of the OFM is different thanhat of its pigtails, the bending curvatures needed to manufacture knotesonators induce an enormous stress in the OFM, which therefore breaks. Thenot resonator can be easily manufactured if the fiber taper presented in Fig.is broken; knotting is performed in the region of uniform waist (OFM), and no

xcess tension occurs. As a result, this type of resonator exhibits only onenput–output fiberized pigtail.

he optical properties of single-loop resonators can easily be recorded byaunching light from a broadband source into one of the OFM pigtails andnalyzing the transmitted light with an optical spectrum analyzer. A typicalransmission spectrum is shown in Fig. 9.

y using Eqs. (6)–(9), res1.55 µm and FWHM0.2 nm, the FSR, f, and Qere estimated to be 4 nm, 20, and 8103, respectively.

he loop resonator’s temporal stability can be addressed by using aerogel as aubstrate. Aerogel is very light, extremely low-density material withxcellent thermal insulating properties and a refractive index close to 1. Alsonown as “frozen smoke,” aerogel in its solid form has a texture similar tohat of foamed polystyrene and has a transparent optical spectral range similaro that of silica. As aerogel is mostly air, it has a refractive index very closeo that of air and a very small loss. It has been previously used [67] to fabricateinear waveguides, waveguide bends, and branch couplers.

igure 10 shows the transmission spectra of a loop resonator sandwichedetween two pieces of aerogel after 1 h, 2 h, and 1 day. Even after 1 day,here are no considerable changes in the spectral profile. This shows that aerogels a very good substrate material on which to assemble optical nanowireoop resonators into functional microphotonics devices. However, aerogel is

Figure 8

not resonator with radius R45 µm manufactured from an OFM with r1 µm.



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rittle and ultimately does not protect OFMs and OFNs from degradation inhe same way as the polymers considered in Subsection 3.3b.

he loop resonator transmission coefficient can also be obtained analytically60] by considering the output to be the sum of two interfering contributions: the

Figure 9

ransmission spectrum of a loop resonator as recorded from an opticalpectrum analyzer (OSA).

Figure 10

1534.4 1534.6 1534.8 1535.0 1535.2 1535.4 1535.6

-62

-61

-60

-59

-58

-57

-56

-55

-54

after 1 hourafter 2 hoursafter 12 hours

Wavelength (nm)

Tra

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issi

on(d

Bm

)

ransmission spectra of a loop resonator sandwiched between aerogelsecorded 1, 2, and 12 h after fabrication. The OFN radius is r=400 nm.



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rst is represented by a fraction of the beam a1, which is transmitted fromnput to output without entering the resonator, while the second consists of theemaining fraction of the beam a2, which propagates through the coil. Thiseads to a simple relation for the transmitted power T as a function of theavelength [60]:

T = a1 + a2 expikL2, 10

here a1 and a2 represent the amplitudes of the two fractions of the beam, Lhe coil length, and k the propagation constant.

.1b. Coil Resonators

he flame-brushing or modified flame-brushing technique allows the fabricationf OFNs and OFMs with extremely long lengths. As a consequence, theyan be coiled in more complicated resonant structures to form microcoilesonators. This potentially provides Q factors much higher (in excess of 109

or losses approaching the material loss) and resonances much narrowerhan those presented in Figs. 9 and 10. The OFN microcoil resonator (OMR) is3D resonator consisting of many self-coupling turns (Fig. 11), and it cane created by wrapping an optical fiber nanowire on a low-index dielectric rod.

lthough there is no limit to the number of turns that the OMR can have,ractical technological issues (i.e., the OFN intrinsic propagation loss and theoss induced by wrapping the OFN around a support rod) limit the usefulumber of coils. In this subsection OMRs are studied with a particular focusn the three- and four-loop resonators.

he OMR spectral response can be derived analytically by solving the coupledave equations for the amplitudes Am of the light propagating in the mth

urn of the OMR (Fig. 12).

f coupling between nonadjacent turns is ignored, the propagation of lightlong the coil in an M-turn OMR is described [60,64,65] by the coupled wavequations for slowly varying pitches:

Figure 11

ptical fiber nanowire microcoil resonator (OMR). Light can both propagatelong the OFN (red arrow) or be coupled into an adjacent coil (green arrow).



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d

dA1

A2

¯

Am

¯

AM−1

AM

= i

0 R1 12 0 ¯ 0 0 0

R2 21 0 R2 23 ¯ 0 0 0

0 R3 32 0 ¯ 0 0 0

¯ ¯ ¯ ¯ ¯ ¯ ¯

0 0 0 ¯ 0 RM−2 M−1M−2 0

0 0 0 ¯ RM−1 M−2M−1 0 RM−1 M−1M

0 0 0 ¯ 0 RM MM−1 0

A1

A2

¯

Am

¯

AM−1

AM

, 11

here pq is the coupling between turns p and q of the resonator, defined as

Figure 12

ylindrical coordinates system used for the analytical description of the OMR.he angle continuously increases along the coil.



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pq = pqexpi0

2

pRpd − i0

2

qRqd. 12

p is the propagation constant in the pth turn, and pq is the coupling coefficientetween the pth and qth turns that is due to the overlap of the field modesetween neighboring turns [59].

efining the average coil radius R0 as

R0 =m−1

M 02Rmd

2M, 13

he average coupling parameter Kpq can be written as

Kpq = 2R0pq. 14

assumes values between 0 (when the coils are far apart and there is nooupling) and KMAX (maximum coupling, which occurs when the OFN coilsouch) with intermediate values obtained by controlling the spacing of adjacentoils.

he OMR transmissivity coefficient T is defined as

T =Am2

A10expi

0

2

MRmd , 15

nd it is calculated from Eqs. (11)–(15), assuming field continuity between theurns:

Am+10 = Am2expi0

2

MRmd 16

or m=1,2 . . .M−1.

he OMR spectrum is strongly dependent on its geometry; in particular, theesonance FWHM and FSR depend on the OMR geometry and the OFN sizehrough K.

MR Geometry and Coupling. The Q of the uniform OMR presented inubsection 4.1b is extremely sensitive to the coupling strength. In theory, theighest Q can be achieved by selecting a K for which the FWHM isinimized, but in practice this is difficult to realize because the FWHMuctuates considerably for small changes in K, and K has an exponential relation

o the pitch [48–50,54–56]. It is therefore desirable to find a geometry for

hich the FWHM is at its minimum and changes slowly with K.

everal different profiles have been studied in the literature [64,65] to find theptimum resonator shape that allows the easiest realization of OMRs with

A minute change in the coil distance implies anenormous change in the FWHM, and thus in Q.

igh Q. Figure 13 presents some of the geometries considered.



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he profiles have been described by the following mathematical formulas:

H uniform, Rm = R0, Kpp+1 = Kc. 17

V conical, Rm = R0 −M

2dR + m − 1 +

2dR, Kpp+1 = Kc.

18

X biconical, Rm = R0 + M + 1

2− m +

−

2dR −

M

4dR ,

Kpp+1 = Kc. 19

I incrementing, Rm = R0, Kpp+1 = Kc

p − 1 + /2

M − 1. 20

T triangular, Rm = R0, Kpp+1 = Kc1 − p − 1 + /2

M − 1/2− 1 ,

21

here m=1,2 , . . . ,M; p=1,2 . . .M−1; dR /R01; dR= Rm+1−Rm forny two adjacent turns; Kmn is the coupling coefficient between turns n and m;nd Kc is the maximum coupling parameter.

hese geometries can be realized by wrapping an OFN around a low-refractivendex rod, which is angled for the V and X geometries. Simulations showedhat the optimum fabrication tolerances are achieved with symmetriceometries, where the coil diameter increases from the center toward thextremities (X) or where the coupling is maximum at the center of the coil andecreases toward the extremities (T). For best performance, OMRs witharger numbers of turns are preferred, which imposes additional fabricationifficulties. Still, simulations on the T geometry showed that high-Q resonatorsan be obtained for nearly every value of the maximum coupling coefficient,ven for resonators with only three or four turns [65]. However, the fabrication ofMRs with well-defined varying pitch is likely to be a very challenging

Figure 13

II IIIH V X I T

Z

R

chematic of various OMR geometries. H represents the OMR with a constantoil radius (along Z) and coil pitch (along R). V and X have a constant coilitch and a variable coil radius; I and T a constant coil radius and a changing coilitch.

ask.



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or this reason, a simpler way to tune the resonator properties has beennvestigated. Since the slow change in coupling properties has been shown torucially affect Q, the possibility to easily achieve a high Q simply byuning the input–output pigtails has been investigated. To this end coupling haseen considered constant in the center [Kn=Kc for 2M−12)]nd variable only at the ends, going to zero at the pigtail ends K0=KM=0.

igure 14 shows five profiles of K for M=4. It was found [65] that sharp Krofiles [such as Figs. 14(a) and 14(e)] have a FWHM strongly dependent on

c, while smoother profiles [Fig. 14(c)] can achieve flat FWHM profiles,.e., high Q at nearly any Kc. Although the realization of an OMR with the exactrofile of Fig. 14(c) is challenging, an OMR can be practically manufacturedy wrapping the coils on a support rod and then tuning the input and outputigtails to achieve a slow decrease of coupling to zero.

Figure 14

Schematic of pigtail geometries in four-turn OMRs.



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hese results can be explained by noting that a resonance in the transmissionpectrum of an OMR occurs when there is a mode with light circulating inhe inner rings of the coil while the intensities at the input and at the output endanish. This requires two conditions to be fulfilled:

1. The circumference of the coil must be a multiple of the wavelength.2. In one round trip the light must be entirely coupled back to the previous

ing.

oreover, the conditions must be fulfilled simultaneously at both sides of theoil. It is believed that slowly varying profiles provide a range of differentoupling conditions for which condition 2 is more easily fulfilled. An increasef the coupling in the input–output pigtails with a small gradient ensureshat the condition of perfect coupling of light from an outer ring of the coil ton inner ring is met somewhere at the coil ends, thereby producing a low-lossigh-Q resonator mode inside the coil.

MR Internal Field Distribution. The field distribution inside an OMR haseen found to depend strongly on the OMR geometry. Simulations wereerformed assuming an OFM with r=1 µm, n=1.457, the effective index neff

1.182 at 1.55 µm, coil radius R0=62.5 µm, dR=0.05 µm, and K in theange 0–20. The field amplitudes A1, A2, and A3 were calculated for

for profiles H, V, and X in Fig. 13, choosing the wavelength and K thataximize the field amplitude. Figure 15 shows the dependence of the internaleld distributions on the angle in three coils.

he internal field amplitude in the H and X profiles is much larger than that inhe V profile, meaning that more energy can be stored in OMRs with the Hnd X geometries.

MR Manufacture. OMRs have been demonstrated in a liquid [79], in air [87],nd in Teflon [66]. In all cases an OFM and a support rod were used. In fact,ecause of the high value of the support rod refractive index or of the liquid oreflon refractive index, the V value experienced by the mode propagating inhe wire is low, and the fraction of power in the evanescent field is large even forelatively large diameters.

o test the resonator properties in real time during fabrication, the OFM hadts pigtails connected to an erbium-doped fiber amplifier (EDFA) and an opticalpectrum analyzer (OSA). Although early experiments were carried out byoiling the OFM on a low-refractive-index rod by hand with the aid of aicroscope [Fig. 16(a)], the demands of continuous uniform coupling over the

ntire coil length necessitated the use of automated setups including a rotationtage (which controls the actual coiling) and a translation stage (whichontrols the coil pitch). It is clear from Fig. 16 that the coil uniformity isonsiderably better in the latter case. In the last stage of fabrication, the OFM

In summary, very high fabrication tolerances can bachieved by microtuning the input and output pigtprovided that the change of the pitch in the inputand output ends of the OMR is sufficiently slow.

eails,



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igtails were fixed to 3D stages and were tuned to find the optimum resonatorpectrum.

f the coil was to be embedded, the fine tuning of the OFM pigtails waserformed on uncured polymer, and the curing was carried out by checking theesonator properties in real time as the pigtails were adjusted. The polymeras then cured when the suitable adjustment had been completed. OMRs wererapped on a low-refractive-index support rod to maximize the OMR

emporal stability and robustness. Losses can be significant because oficrobends and confinement losses. However, the loss can be minimized by

ncreasing the microfiber thickness and the rod diameter, by using aow-refractive-index material for the rod, and by improving the smoothness ofhe rod surface. It was found [87] that using a rod coated with Teflon AFDuPont, United States) or UV373 (Luvantix, Korea) provided goodonfinement because of the polymer’s low refractive index at the interface withhe microfiber (n1.3 and n1.37 at 1.55 µm, respectively). Supportods as small as 250 µm have been used without any significant observed loss.

ost recent results seem to show that the particulate nature of the Teflonsed in these experiments might induce higher losses than those observed forV-curable fluoropolymers. Micrometer-size Teflon particles can in fact

ncrease the Mie scattering and the overall OFM transmission loss [80].

Figure 15

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

5

10

15

A1

A2A3

I

a

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Amplitu

de

A1

A2A3

IIb

H

V

Amplitu

de

Amplitu

de

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

2

4

6

8

10

12

14

16

Angle(x2Pi)

Amplitu

de

A1

A2A3

III

c

X

Amplitu

de

θ/(2π)-(M-1)

θ/(2π)-(M-1)θ/(2π)-(M-1)

Internal field amplitude in three-turn OMRs for profiles H, V, and X (Fig. 13).



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.2. Particle Manipulation

he radiation pressure exerted by light on matter was demonstrated byebedev more than a century ago [88]. However, until the laser was invented,

ight sources with high intensity were not readily available, and the radiationressure was minute. Kawata and co-workers initially demonstrated theovement of dielectric microspheres initially by exploiting the evanescenteld produced on the surface of a high-refractive-index prism [89] andubsequently by using the evanescent field of a single-mode channel waveguide90]. Two effects take place: (1) the gradient force attracts and traps thearticles laterally with an action similar to optical tweezers [91] while (2) thexial force due to absorption and scattering propels the microspheres alonghe direction of propagation of light in a waveguide [92]. The drag force opposeshe propelling forces and acts to limit continuous acceleration, so that thearticles ultimately reach a terminal velocity. This method may simultaneouslyanipulate several particles and provides a way to sort micrometer-size

articles and biological cells. Driving microparticles by using the evanescenteld produced by various types of planar waveguides has been investigated

n more detail in the past two decades [93–96]. Recently, the evanescent fieldf an OFN has also been exploited to propel 3 µm [51] and 10 µm [52]iameter polystyrene microspheres and microsphere clusters with diametersarger than 20 µm. In Subsection 3.2 the beam size was shown to decrease forecreasing OFM–OFN diameters until a minimum for V2, after which

Figure 16

MRs manufactured (a) by hand and (b) by an automated stage. The numberf turns is three in (a) and two in (b).



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t sharply increases. For small sizes, a considerable fraction of the powerropagates outside the physical dimension of the OFN; the evanescent fieldan extend for several micrometers into the surrounding medium, and it can bexploited to propel particles.

he propulsion experiments were carried out by positioning OFNs on MgF2

ubstrates with their extremities fixed with adhesive tape. One of the pigtails wasonnected to a CW diode-pumped fiberized Nd:YLF laser. The powerropagating in the fiber before the OFN was estimated to be 400 mW at047 nm. While the power was completely confined within the fiber boundaryn the fiber pigtails Vcl2, in the liquid the OFN had 1 µm Vcl2;hus a considerable fraction of the power was propagating in the surroundingater. The water-based suspension containing polystyrene microspheres

refractive index nPS=1.59 and specific gravity PS1.05 g/cm3) was used tourround the OFN. Real-time monitoring was performed with a CCD cameraounted on top of the microscope with a 10 objective and connected to a

omputer. A diagram of the experimental apparatus is given in Fig. 17.

igures 18 (media 1) and 19 (media 2) show two movies taken by the CCDamera for suspensions of 3 and 10 µm spheres, respectively. Bright spotsppear in Figs. 18 and 19 because no filter was inserted into the microscope toeduce the collection of scattered laser light. The bright spots are explaineds the excitation of whispering gallery modes in microspheres whose size is inesonance with the laser beam launched in the OFN. When the laser iswitched on, the microspheres around the OFN were first attracted laterally tohe OFN and then driven along it in the direction of light propagation. Thearticle velocities were evaluated from a measurement of the averageisplacement over a few seconds and were estimated to be of the order of10 µm/s. It is notable that even clusters of 6–7 particles with overall diameters

arger than 20 µm can be propelled along the OFN (media 2).

he optical force experienced by particles is proportional to the opticalntensity at their surface; in Subsection 3.2 the electric field (E field) at the

Figure 17

Laser

Polystyrene spheresWater

10x

CCD

PC

Microscope

MgF2 Substrate

chematic of the experimental apparatus used to demonstrate optical propulsionf polystyrene microparticles.



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urface of the OFN has been evaluated, and Fig. 4 shows how there is aaximum at =0.7 mm. For a laser output of 500 mW, the average velocity ofµm particles was 9 µm/s along the OFN, compared with the 2.6 µm/s

bserved along glass waveguides [95]. The larger velocity observed in Fig. 18ith respect to the glass planar waveguide can be explained in terms of aetter source or waveguide coupling and/or a larger evanescent field and highereld intensity at the interface between the optical guide and the water–article suspension.

igure 20 presents a comparison of the evanescent fields near the surface forhree waveguides used in propulsion experiments: an OFN, a Si3N4 ridgeaveguide [96], and a glass waveguide [95]. Simulations were carried out bysing the beam propagation method as before. The waveguide width andepth were taken to be 3 and 1 µm for the glass waveguide [95] and 1 and 0.2 µmor the Si3N4 waveguide [96]. The refractive indices of the glass substrate,lass waveguide, Si3N4 waveguide, and its substrate were taken to be 1.55, 1.58,.97, and 1.45 respectively. From Fig. 20 it is clear that the E field at thenterface of the OFN is several times larger than that experienced in the glasslanar waveguide, but about half of that calculated for the Si3N4 ridgeaveguide. This can be easily explained by the mode confinement geometry:hile in planar waveguides the mode can leak into the substrate (which

Figure 18

ingle-frame excerpt from the video recording (Media 1) of 3 µm polystyrenearticles propelled along an OFN with =0.95 µm.

Figure 19

ingle-frame excerpt from video (Media 2) of 10 µm polystyrene particlesropelled along an OFN with =0.95 µm.





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an host a large fraction of the power), in the OFN the mode can only extendnto the solution because of its cylindrical symmetry. Moreover, modeonfinement is related to the numerical aperture of the optical waveguide:ince the Si3N4 waveguide has an extremely high refractive index nSi3N4

1.97, the numerical aperture that the waveguide has with respect to waternH2O1.33 and to the substrate nSub1.45 is considerably larger than thatxperienced by the modes propagating in the glass waveguide and OFN.

owever, the evanescent field in the planar waveguides decreases more sharplyhan in the OFN; in fact, although the Si3N4 waveguide has a stronger fieldp to 250 nm from the interface, at distances longer than 250 nm the OFN E fields consistently larger and even extends beyond 2 µm above the surface. Inddition, the OFN exhibits the great advantage of manipulating particles in 3D.

.3. Sensors

he great majority of optical biochemical sensors can be classified accordingo two sensing approaches: homogeneous sensing and surface sensing97]. In homogeneous sensing, the device is typically surrounded by an analyteolution, and the homogeneously distributed analyte in the solution modifieshe bulk refractive index of the solution. In surface sensing, the optical device isretreated to have receptors or binding sites on the sensor surfaces, whichan selectively bind the specific analyte [97].

urface sensors based on OFNs have been predicted [67] and experimentallyealized for the detection of hydrogen [53] by coating an OFM withalladium. Because of the reduced sensor dimensions, the ultrathin palladiumlm allowed sensor response times of approximately 10 s, up to 15 timesaster than that of most optical and electrical hydrogen sensors reported so far.he detection range was 0.05%–5%, enough to detect hydrogen at the

ower explosion limit for gas mixtures. The sensor worked by checking the

Figure 20

0.0 0.5 1.0 1.5 2.0

0.01

0.1

1(b)

Nor

mal

ised

E-f

ield

Distance from surface (µm)

Si3N

4Waveguide

SMOWIon-exchanged Glass Waveguide

Si3N4 waveguideOFNIon-exchanged glass waveguide


Nor

mal

ised

E-f

ield

0.0 0.5 1.0 1.5 2.0

0.01

0.1

1(b)

Nor

mal

ised

E-f

ield


Si3N

4Waveguide

SMOWIon-exchanged Glass Waveguide

Si3N4 waveguideOFNIon-exchanged glass waveguide


Nor

mal

ised

E-f

ield

field distribution in an OFN and planar waveguides in the space adjacent theurface. The E field was normalized per unit power traveling in theaveguide.

bsorption changes with a simple transmission measurement setup that



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onsisted of a 1550 nm laser diode and a photodetector. OFNs can also beoated with bioreceptors or gelatin to detect biological components [67] andumidity [98], respectively. Polymers nanowires have also been bonded to silicaFNs and used as sensors for humidity, NO2, and NH3 [99]. In this case, these of a polymeric material allows the gas to diffuse in it and modify its opticalbsorption properties. By measuring the absorption changes it is possible toeasure changes in gas composition down to a sub-part-per-million level (to less

han 1 part in 106). Because of its large evanescent field, OFN sensors havelso found applications in the measurement of refractive index in microfluidichannels [100] and even as a tool for probing atomic fluorescence [101].owever, in all of these configurations the interaction length is limited by theFN’s physical length.

n contrast, resonant sensors allow an effective multiplication of the interactionength and thus allow incredibly compact devices to be manufactured. Smallize, high sensitivity, high selectivity, and low detection limits are the dominantequirements for evanescent field optical resonating sensors. To date, theesonators investigated include microspheres, photonic crystals, gratings, andicrorings [102–106]. Optical microresonators can provide large evanescentelds for high sensitivity, high Q factors for low detection limits, andorresponding small resonant bandwidths for good wavelength selectivity. Therawback of the vast majority of high-Q resonators relates to the difficultyf coupling light into and out of the resonator. Microcoil resonating sensors have

een manufactured by wrapping OFMs around copper wires [107]; althoughhey exhibit good sensitivities, they are prone to degradation. In Subsection 3.3bmbedding was examined and shown to preserve OFN from degradation;et the choice of the coating thickness is a challenge, because a thick coatingayer will limit the sensitive evanescent field, while a thin layer does notrovide appropriate protection to the device. In this Subsection, the possibilityf exploiting coated nanowire resonators for homogeneous [97] sensingpplications is investigated.

.3a. Resonating Sensors: Schematic and Manufacture

o date, three resonating sensors based on OFNs–OFMs have been proposedr demonstrated: the coated microfiber coil resonator sensor (CMCRS)55,57], the embedded optical nanowire loop resonator refractometric sensorENLRS) [58], and the liquid ring resonator optical sensor (LRROS) [108].

hile the first two exploit the resonances created in an OFM resonator, anRROS effectively uses an OFM to excite a whispering gallery mode in aapillary, which acts as the real sensing device. In this subsection only the firstwo sensors will be discussed.

igure 21 shows a schematic of the CMCRS and the ENLRS. In Fig. 21(a) the

Because of their fiberized pigtails, OFN resonatorsuch as the ones presented in Subsection 4.1 doexhibit the input–output coupling problemsexperienced in other high-Q resonators.

snot

FM is shown in violet and blue, the analyte channel in brown, and Teflon in



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reen. The CMCRS is a compact and robust device with an intrinsic fluidichannel to deliver samples to the sensor. In Fig. 21(b) a very thin polymer layerovers the OFM loop of the ENLRS, while a thick coating deposit is used tox the two fiber pigtails. In the ENLRS two sides are exposed to the liquid to beensed. In both cases the embedded OFM has a considerable fraction of itsode propagating in the fluidic channel; thus any change in the analyte

roperties is reflected in a change of the mode properties at the sensor output.hen OFNs are used instead of OFMs, an even greater fraction of theode propagates in the evanescent field, thus increasing the overall sensitivity.ince OFMs–OFNs are fabricated from a single tapered optical fiber, lightan be coupled into the sensor with essentially no insertion loss, which is a hugedvantage over other types of resonator sensors.

he CMCRS can be fabricated from a microcoil resonator (Subsection 4.1b)y using an expendable rod, which is then removed. A candidate for the rodaterial is PMMA (polymethyl methacrylate), which is a polymer with an

morphous structure and which is soluble in acetone. In a similar way theNLRS can be made by using two substrates fabricated with disposableaterials such as PMMA coated with a thin layer of a low-loss,

ow-refractive-index polymer such as Teflon. Once the OFM loop resonatorSubsection 4.1b) is manufactured on one of the substrates, the other substrates placed on top of the nanowire resonator and glued with the same lowefractive-index polymer, and the expendable materials are removed, leaving ahin layer of low-refractive-index material on the nanowire. The use of a

Figure 21

chematics of (a) a coated microfiber coil resonator sensor (CMCRS) and (b)n embedded optical nanowire loop resonator refractometric sensorENLRS). Figures are not to scale.



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hick substrate allows easy handling of thin coating layers. A schematic crossection of the sensors as manufactured is presented in Fig. 22.

.3b. Resonating Sensors: Theory

ny change of the analyte refractive index na leads to a change in the effectivendex neff of the propagating mode; thus it shifts the mode relative to theesonance, which in turn modifies the transmissivity T, and it shifts the modeelative to the resonance. A two-turn CMCRS can be easily evaluated bysing the coupled mode equations presented in Subsection 4.1b; Eqs. (11)–(16)ive

T =expiL − L − i sin K

exp− iL + L + i sin K, 22

here is the real part of the propagation constant, the loss coefficient, and=L the coupling parameter for coupling coefficient and coil length L.esonances occur if K and satisfy

Km = arcsinexp− L + 2m , 23

n =2neff

res

=2p + 1

2L24

or integer m and p. For resonant coupling K=Km Eqs. (11)–(16) yield

Figure 22

chematic cross sections of (a) a coated microfiber coil resonator sensorCMCRS) and two embedded optical nanowire loop resonator refractometricensors (ENLRS) with (b) one and (c) two surfaces exposed to the analyte.



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FWHM =res

2

neffL

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2e2aL + e−2aL − 2

res

2

neffLe2aL + e−2aL − 2

e2aL + e−2aL − 1

res2

neff

, 25

hile for nonresonant coupling

FWHM + K − Km2. 26

he mode properties are particularly affected by the OFN radius r= /2 andhe distance d between the OFN and the analyte (coating thickness). The sensoresponse has been determined by calculating neff (using thenite-element-method software COMSOL3.3 with perfectly matched layers)nd the related shift of res as a function of the analyte concentration. neff haseen evaluated for a nanowire embedded in Teflon and coiled around aicrofluidic channel. The fundamental mode, which has the largest propagation

onstant, is the only mode that is well bounded in the vicinity of the fiberore [109,110]; thus it is the only mode considered here. Since neff is a functionf r and d, res also varies with r and d through Eq. (24). Figure 23 showshe intensity distribution of the fundamental mode for two different analyteefractive indices [Fig. 23(a)] na=1 and [Fig. 23(b)] na=1.37 when nOFN

1.451, nTeflon=1.311, d=100 nm, r=500 nm, =1550 nm. When na is smallFig. 23(a)] the field is still bound within the OFN physical boundary,hile it shifts into the coating and leaks into the analyte when na is large [Fig.3(b)].

igure 24 shows the dependence of neff on the analyte refractive index na. TheFN radius has been assumed constant at r=500 nm, while three values 10,00, and 500 nm have been considered for d. Generally, neff increases with na andncreases more quickly with smaller d, since in this case a larger fraction ofhe mode is propagating in the analyte, as shown in Fig. 23. If na=nTeflon, lightannot see the boundary between Teflon and the analyte solution; thus neff

s the same at any d, and in Figs. 24(a)–24(d) there is a crossing point forifferent diameters. It is interesting that this behavior is independent of

Figure 23

ntensity distribution of the fundamental mode at the sensor–analyte interfaceor nOFN=1.451, nTeflon=1.311, d=100 nm, r=500 nm. The analyteefractive index is (a) na=1 and (b) na=1.37, respectively. The OFN section isepresented by the white circle.



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esesece

ss

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he sensor geometry, to the degree that the overlap between analyte and moderopagating in the OFN is the same: the CMCRS has the same overlapith the analyte as the ENLRS with one surface interface [Fig. 22(b)]; thus

hey have the same dependence of neff on na. The ENLRS with two interfaceurfaces [Fig. 22(c)] has an overlap that is twice as large, and thus theependence of neff on na is twice as strong.

.3c. Resonating Sensors: Sensitivity

he most important attribute of refractometric sensors is the homogeneousensitivity S, defined as the shift of the resonant wavelength res [correspondingo the solutions of Eq. (23)] with respect to the change in the analyte refractivendex na [97,111]:

S =res

na

=res

neff

neff

na

=2

n

neff

na

=res

neff

neff

na

. 27

ince most analytes are predominantly water and device performances areffected by high losses [Eqs. (21)–(25)], it is convenient to work in a wavelengthegion of low water absorption. Water absorption has a minimum at

Figure 24

1 1.1 1.2 1.3 1.41.4135

1.414

1.4145

1.415

na

nef

f

d=10nmd=100nmd=500nm

(a)

1 1.05 1.1 1.15 1.2 1.25 1.3 1.351.36

1.365

1.37

1.375

na

n eff


(b)

1 1.1 1.2 1.31.4

1.405

1.41

1.415

na

n eff

bare OFNd=10nm, 2 surfacd=100nm 2 surfacd=10nm, 1 surfacd=100nm, 1 surfa

(c)

1 1.1 1.2 1.31.4

1.405

1.41

1.415

na

n eff

bare OFNd=10nm, 2 surfacd=100nm 2 surfacd=10nm, 1 surfacd=100nm, 1 surfa

(c)

1 1.1 1.2 1.3

1.32

1.34

1.36

na

nef

f

Bare OFNd=10nm, 2 surfacesd=100nm, 2 surfaced=10nm, 1 surfaced=100nm, 1 surface

(d)

1 1.1 1.2 1.3

1.32

1.34

1.36

na

nef

f

Bare OFNd=10nm, 2 surfacesd=100nm, 2 surfaced=10nm, 1 surfaced=100nm, 1 surface

(d)

ependence of the effective index of a coated OFN neff on the index of thenalyte na for nTeflon=1.311, nOFN=1.451, r=500 nm, for several distancesetween OFN and analyte in a (a), (b) CMCRS and (c), (d) an ENLRS. Theavelength of the propagating mode is =600 nm in (a) and (c) and 970 nm in (b) and (d). A bare OFN is reported in (c) and (d) for reference.

500 nm, and it generally increases with wavelength up to 3000 nm [112–115];



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herefore, to limit its effect on device performance, it is beneficial to work atavelengths shorter than 1000 nm.

was calculated by using Eq. (27) near na=1.332 at operational wavelengthsf =600 nm and =970 nm. Figure 25 shows the dependence of S on ror different values of d. S increases when d decreases or increases becausef the increasing fraction of power in the evanescent field. Decreasing rlso increases S because this increases the fraction of the mode field inside theuidic channel. S reaches 500 nm/RIU (where RIU is refractive index unit)t r200 nm for =600 nm and 700 nm/RIU at r300 nm for =970 nm.his is higher than in most microresonator sensors [102,104,106,124,122,123].

or the same and OFN radius r, the sensitivity for the ENLRS with twoensing surfaces is larger than that with only one because of the larger overlapetween the evanescent field and the analyte (Subsection 4.3b). For verymall values of r the sensitivity reaches a plateau because the fundamental modes no longer well confined and most of the evanescent field is in the analyte.

Figure 25

200 600 1000 1400 180010

-6

10-4

10-2

100

102

104

r (nm)

S(n

m/R

IU)


(a)

200 600 1000 1400 180010

-6

10-4

10-2

100

102

104

r (nm)

S(n

m/R

IU)

d=10nmd=100nm

200 600 1000 1400 180010

-6

10-4

10-2

100

102

104

r (nm)

S(n

m/R

IU)


(a)

400 800 1200 1600 200010

-2

10-1

100

101

102

103

r (nm)

S(n

m/R

IU)


(b)

400 800 1200 1600 200010

-2

10-1

100

101

102

103

r (nm)

S(n

m/R

IU)


(b)

200 400 600 800 1000 1200 1400 1600 1800 210

-4

10-2

100

102

104

r (nm)

S(n

m/R

IU)

d=10nm , 2 surfacesd=100nm, 2 surfacesd=500nm , 2 surfacesd=10nm, 1 surface

d=100nm, 1 surfaced=500nm, 1 surface

(c)

200 400 600 800 1000 1200 1400 1600 1800 210

-4

10-2

100

102

104

r (nm)

S(n

m/R

IU)

d=10nm , 2 surfacesd=100nm, 2 surfacesd=500nm , 2 surfacesd=10nm, 1 surface

d=100nm, 1 surfaced=500nm, 1 surface

(c)

200 400 600 800 1000 1200 1400 1600 1800 2

10-1

100

101

102

103

104

r (nm)

S(n

m/R

IU)

d=10nm, 2 surfacesd=100nm, 2 surfaces

d=500nm, 2 surfacesd=10nm, 1 surfaced=100nm, 1 surfaced=500nm, 1 surface

(d)

200 400 600 800 1000 1200 1400 1600 1800 2

10-1

100

101

102

103

104

r (nm)

S(n

m/R

IU)

d=10nm, 2 surfacesd=100nm, 2 surfaces

d=500nm, 2 surfacesd=10nm, 1 surfaced=100nm, 1 surfaced=500nm, 1 surface

(d)

ependence of the sensitivity S on the OFN radius r for nTeflon=1.311, nOFN

1.451, and several coating thicknesses d in (a), (b) a CMCRS and (c), (d) anNLRS. The wavelength of the propagating mode is =600 nm in (a) and

c) and =970 nm in (b) and (d). Schematics of the ENLRS with one or twourfaces are shown in Figs. 22(b) and 22(c).



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S=

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n this case neff becomes linearly dependent on na, and the derivative in the lasterm of Eq. (27) reaches a uniform value, and so the sensitivity reaches alateau.

t is interesting to note that the sensor sensitivity is strongly dependent on thembedding material. Figure 26 shows S for a CMCRS embedded in UV375nUV3751.375 versus r at =600 nm [Fig. 26(a)] and =970 nm [Fig. 26(b)]or different values of d. As before, na=1.332 and nOFN=1.451.

in UV375 is smaller than that obtained in Teflon: S50 nm/RIU for r400 nm, d=10 nm and =970 nm, compared with S130 nm/RIU in Teflon

Figure 26

400 800 1200 1600 200010

-4

10 -3

10 -2

10-1

10 0

101

10 2

r (nm)

S(n

m/R

IU)

d=10 nmd=100 nmd=500 nm

(a)

400 800 1200 1600 200010

-2

10-1

100

101

102

r (nm)

S(n

m/R

IU)


(b)

400 800 1200 1600 200010

-2

10-1

100

101

102

r (nm)

S(n

m/R

IU)


(b)

ependence of the sensitivity S on the OFN radius r for nUV375=1.375, nOFN

1.451, and several coating thicknesses d in a CMCRS for (a) =600 nm andb) =970 nm.



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Fig. 25(b)]. Since the refractive index of UV375 is higher than that of Teflon,he overlap between the evanescent field and the analyte is smaller; thus theast expression of Eq. (27) for UV375-coated CMCRSs is smaller than that foreflon-coated CMCRSs.

.3d. Resonating Sensors: Detection Limit

nother important figure of merit of refractometric sensors is the detectionimit, defined as the smallest refractive index change that can be measured. If 0

s the smallest measurable wavelength shift, then the detection limit DL cane defined as [55,97,111]:

DL =0

S. 28

0 is generally limited by the instrument resolution and is empiricallyssumed to be 1/20 of the resonance FWHM [104]. The FWHM depends onhe resonator coupling and loss. Losses in the CMCRS and the ENLRS ariserom surface scattering, material (analyte, coating, and fiber) absorption,nd bending. The smallest reported OFN loss is about =0.001 dB/mm withadii in the range of hundreds of nanometers (Subsection 3.1). Waterbsorption can be reduced to levels well below 0.0001 dB/mm by operating athort wavelengths (Subsection 4.3c). Low-loss embedding materials (suchs Teflon or UV375) can be used: losses of 1 dB/m have been reported [116,117]or water-core Teflon waveguides. Bend losses can be estimated from [70]

bend =U2

2VclWK1W

rexp−

4W

3Vcl1 −

nOFN2

nTeflon2

r , 29

here is the bend curvature radius, r the OFN radius, and U, Vcl, and Wtheormalized modal parameters defined by Eqs. (2), (29), and (30):

U =2r

nOFN

2 − neff2 1/2, 30

W =2r

neff

2 − nTeflon2 1/2. 31

or r=200 nm and R=250 µm, bend0.0001 dB/mm at =600 nm, whichuickly decreases further with increasing coil size. Assuming =0.01 dB/mm,he other losses can be neglected, and for a CMCRS or an ENLRS with r200 nm at =600 nm, Eq. (22) gives FWHM410−4 nm and DL10−6

10−7 RIU, which is comparable with the best reported experimental results55,118–121]. Although these values of FWHM can be easily measuredith a high-resolution OSA, cost and practical considerations limit the

esolution to few picometers, leading to a practical detection limit of the orderf several 10−6 RIU (see Table 1).

n traditional microresonators input–output coupling occurs via a prism,ntiresonant reflecting waveguides, or a fiber taper [102–106]. With probablynly the exception of fiber taper coupling, which has been proved to beeasonably efficient [124], coupling to a microresonator has considerably
omplicated device design and/or has resulted in a significant increase in the


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verall loss. In contrast, CMCRSs and ENLRSs have an extremely lownsertion loss: the ease of mode size control and the lossless input–outputoupling via the fiber pigtails are unique features of devices based on OFNs.

.3e. Resonating Sensors: Experimental Demonstration

CMCRS was fabricated from an OFM with a length and diameter of theniform waist region of 50 mm and 2.5 µm. The OFM was then wrapped on1 mm diameter PMMA rod. The whole structure was repeatedly coatedith the Teflon solution 601S1-100-6. The dried embedded OMR was then left

n acetone to remove the support rod, which was completely dissolved in–2 days at room temperature. Thereby, a CMCRS with a 1 mm diametericrochannel and two input–output pigtails was obtained.A picture of the sensor

s shown in Fig. 27. The sensor consists of an OFM resonator with five turnsnd a microfluidic channel inside. The adjacent coils are very close, and theajor coupling area is on the left side of the picture. Although some bubbles are

eft inside the CMCRS during the drying process, these seem to be far fromhe OFM and did not affect overall sensor operation.

o simulate the sensor behavior in aqueous solutions, the sensor was connectedo an erbium-doped fiber amplifier and to an optical spectrum analyzer and

Table 1. Sensitivity S, FWHM, and Detection Limit DL for Evanescent FieldResonating Refractometric Sensorsa

Type of SensorS

(nm/RIU)res

(nm)FWHM

(nm)DL

(RIU) Ref

icrosphere 30 980 210−4 610−6 [104

hotonic crystal microresonator 228 1500 1 310−3 [102

icrocapillary 45 980 1.5510−4 310−6 [106

rating 1000 1550 0.1 10−5 [122

ollow-core ARROWbb 555 700 1 210−3 [123

RROS 800 1550 10−6 [108

MCRS or ENLRS 700 970 4 10−4 10−7 [55,5

ares represents the resonating working wavelength.bARROW, antiresonant reflective optical waveguide.

Figure 27

icroscope picture of a CMCRS. The yellow dashed lines and red arrowshow the fluidic channel and input–output pigtails, respectively.



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hen inserted into a beaker containing mixtures of isopropanol and methanol.he isopropanol ratios were (1) 60%, (2) 61.5%, (3) 63%, (4) 64.3%, (5)5.5%, (6) 66.7%, and (7) 67.7%. The refractive indices of isopropanol andethanol at 1.5 µm are reported to be 1.364 and 1.317, respectively [125]. The

ensor was then immersed into the mixtures, and spectra were recorded at530 nm. Figure 28 shows that for increasing isopropyl concentrations theesonator peak shifts to longer wavelengths. The extinction ratio increases,chieves a maximum, and then decreases: this can be explained by a change inhe coupling coefficient due to the change in the mixture’s refractive index.

he transmission properties of a multiturn microfiber coil resonator depend onhe resonator coupling and loss and can be simulated by solving Eqs.11)–(16). The FWHM (and therefore the Q factor) in the traditionalicrosphere and microring resonators is controlled primarily by modifying the

nput–output coupling by means of prism coupling, antiresonant reflectingaveguide coupling, and fiber taper coupling [102–106].

here is only one primary resonance, which can be easily evaluated in a waynalogous to that for a single-loop resonator. neff of the fundamental mode wasalculated for several values of d by using Eqs. (22)–(26). Figure 29 showshe measured wavelength shift (dashed curve) and calculated (solid lines)avelength shift as a function of the analyte refractive index na and polymer

hicknesses d for r=1250 nm.

he best fit occurs for d0, showing that the average coating thickness ismall, possibly because the tight wrapping of the OFM on the support rod left

Figure 28

ependence of the OMCRS spectrum on the analyte refractive index forifferent mixtures of isopropanol and methanol. The isopropyl fractions in (1),2), (3), (4), (5), (6), and (7) are 60%, 61.5%, 63%, 64.3%, 65.5%, 66.7%,nd 67.7%, respectively.



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ittle space for the coating to fill. The small difference observed in Fig. 29 haseen attributed to the unevenness in the OFM diameter profile, to themprecision in the coil winding, to the channel roughness, and to the unevenoating thickness (OFM distance from the microfluidic channel). S was obtainedrom the line slope as 40 nm/RIU. This value is comparable with thoseeported previously for microsphere, microring, and liquid-core resonators103,104,108], but smaller than recently reported values for a slot waveguide212.13 nm/RIU) [126]. The relatively low value of S can be attributed tohe small overlap between the mode propagating in the OFM and the analyte.n fact, S has been shown to increase by orders of magnitude for increasing

a [108]. Another factor that has probably contributed to the degraded S is theurface roughness of the device in contact with the analyte, possibly causedy the PMMA support rod. This roughness might also be responsible for theoderately low Q factor Q104 observed.

.4. Supercontinuum Generation

ince its first observation in 1970 [127], supercontinuum generation hasttracted much attention owing to the large range of applications associatedith ultrabroadband light sources. As a physical phenomenon, supercontinuumeneration involves a number of nonlinear optical effects, including self-nd cross-phase modulation, four-wave mixing, soliton effects, and stimulatedaman scattering, combined with appropriate dispersion properties. High

ntensity is a fundamental requirement for the observation of the phenomenon.his can be achieved either by using high-energy ultrashort pulses or, moreractically, by using tight spatial confinement within a suitably nonlinearaveguide. The higher the nonlinearity of the material, the lower the requiredower levels. Silica holey fiber and tapers have previously been usedxtensively [128–131]; however the intrinsic nonlinearity of silica is relativelyow (Subsection 3.2), and there has therefore been growing interest insing optical fibers and microstructured optical fibers fabricated from highlyonlinear glasses [132–135]. Most recently, OFMs have attracted an increasing

Figure 29

Analyte refractive index na

1.345 1.346 1.347 1.348 1.349

Wav

elen

gth

Shif

t(nm

)

0.30

0.35

0.40

0.45

0.50MeasurementSimulations

d=500nmd=100 nm

d=0 nm

ependence of the measured (dashed) and calculated (solid) wavelength shiftsn the analyte refractive index na for r=1250 nm and different polymerhicknesses d.

nterest for continuum generation because of the high nonlinearity associated



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ith their tight confinement (Subsection 3.2), easy connectivity to fiberizedomponents, and extreme flexibility in tailoring the zero dispersion wavelength.n particular, OFMs provide higher confinement than untapered fibers andower input–output coupling losses than small-core microstructured fibers ofimilar minimum core dimensions. If the bandwidth is measured at −20 dB fromhe peak, supercontinuum generation over a width of 1000 nm has beenbserved [45–47]. The use of highly nonlinear materials for OFMs has beentudied to increase the optical nonlinearity even further (Subsection 3.2):ismuth silicate [136] and chalcogenide [48] OFMs have been successfully usedo generate supercontinua over a broad range of wavelengths. In particular,ismuth silicate can be considered a promising material because of a much widerransmission window in the IR than silica, the lack of Raman peaks, and thextremely smooth spectral profiles of the generated supercontinua. In fact, whilepectra generated in silica OFMs have spectral oscillations in excess of0 dB, an extremely smooth spectrum has been obtained for a bismuth silicateFM over 1000 nm.

he OFM used for supercontinuum generation was manufactured by using theodified flame-brushing technique (Section 2) on a highly nonlinear fiber

n23.210−19 m2/W [137]) fabricated by Asahi Glass Ltd. (Japan). Theptical fiber had core and cladding diameters and refractive indices at 1.55 µm of

core6.9 mm and cladding125.6 mm, ncore2.02 and ncladding2.01,espectively. The total loss of the taper (fiber input facet to fiber output facet)as monitored continuously during the fabrication process by injecting

ight at 1.55 µm from a fiberized laser source and measuring the total throughputower with a powermeter. The total loss of the taper at the end of theabrication process was approximately 13 dB. The material group-velocityispersion of the OFM is given by the dispersion of the cladding material of theriginal untapered fiber, as shown in Fig. 30(a), with a zero-dispersionavelength at 2.6 µm. The total group-velocity dispersion D of the guidedode has a strong contribution from the waveguide design [138]:

D =1

c

dng

d−

2

2 ng2Vcl

n

2Vclb

dVcl2

+dng

d

Vclb

dVcl , 32

here Vcl is defined by Eq. (2) and is dependent on the OFM radius r. Figure0(b) shows the dependence of the (first) zero-dispersion wavelength on r.o generate a supercontinuum, the OFM radius was chosen as r1.6 µm so that

ts zero-dispersion wavelength coincided with the pump central wavelengtht 1.63 µm [Fig. 30(b)]. Femtosecond laser pulses at this wavelength from anptical parametric amplifier (Coherent Opera pumped by Coherent Legend)ere injected into the OFM by using a 10 microscope objective NA0.2.he pulse duration and repetition rate were 120 fs and 1 kHz, respectively.he output spectra were measured by using an OSA for the wavelength range.85–1.75 µm and an extended InGaAs detector with a monochromator forhe range 1.55–2.4 µm.

igure 31 compares the spectra of laser pulses at the laser output and at theFM output for pumping at 1.63 µm. With a laser output pulse energy of Ep

5 nJ, a supercontinuum spectrum has been generated extending from 1 to2.3 µm, with a 3 dB spectral width of 700 nm. It is interesting to note that the

upercontinuum profile is remarkably flat with 5 dB variation over the
pectral range 1.2–2 µm. Moreover, the spectrum is more than 1000 nm broad


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t the 10 dB level. The observed decrease in the output power at longavelengths is probably, at least in part, due to the roll-off in our detection

ystem’s sensitivity.

.5. Particle Trapping

hile tight confinement in an OFM is associated with large nonlinearity, at aleaved fiber end tight mode confinement results in high beam divergence.ecause of the large numerical aperture of the OFM, the intensity profile at theber output experiences large gradients within very short distancesFig. 32).

his characteristic can be exploited to trap particles with the so-called opticalweezers [139,140], which use forces exerted by a strongly focused beam

Figure 30

a) Dependence of the dispersion of the cladding material on the wavelength.b) Correlation between diameter and zero-dispersion wavelength in OFMsanufactured from the Asahi bismuth silicate fiber: simulations were performed

sing the exact solution of Maxwell’s equations for an air-suspended rodaving the dispersion characteristics of the fiber cladding glass [128].

f light to trap small objects. Small particles develop electric dipole moments



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s a consequence of the optical field; thus they are shifted toward the focus byntensity gradients in the electric field [140]. In contrast, large objects areepicted as acting as lenses, refracting the rays of light and redirecting theomentum of their photons; this reaction moves them toward a focus, where the

ntensity peaks [139]. In free space, beam focusing is limited by diffraction:he minimum focal spot size is typically half of the wavelength (of the order offraction of a micrometer, typically). Metallic probes have also beenroposed to trap small particles [141,142], where strong field enhancementrom light scattering at a metallic tip could generate a trapping potential deepnough to overcome Brownian motion and to capture a nanometric particle141]. Alternatively, a combination of evanescent illumination from a substratend light scattering at a tungsten probe apex is used to shape the opticaleld into a localized, 3D optical trap [142]. All these approaches require highowers for the illumination (well above 1 W) and are difficult to integraten conventional microscopy instruments. Lensed optical fibers haveeen demonstrated to be highly efficient optical traps [143–145] and can easilye integrated with microscope technology but have the drawback of a largeize, difficult end face processing, and large mode field diameter (typically of therder of 10 µm).

hort adiabatic tips can be manufactured by breaking an OFN at its minimumaist region. These tips can be used to trap 1 µm polystyrene particles inater with low powers 10 mW. The use of an OFN allows for small probe

ize and optimal confinement (submicrometer spots) and potentially reduceshe trapping power by orders of magnitude. Trapping experiments were carriedut at 1.5 µm by connecting an OFN to an EDFA capable of delivering.2 W of maximum power. The OFN tip was immersed in a solution containingilica microspheres with 1 µm diameter and was analyzed by using anptical microscope. The EDFA power was increased in steps of 0.1 mW, andictures were taken every 1 s. At low powers, because of Brownian motion andther environmental factors, the microparticles move quickly, and no trappingas observed. With powers of 10 mW, single particles were trapped at

Figure 31

omparison of output spectra from the laser source and the OFN for pulsenergies of 5 and 3 nJ. The spectra have been shifted vertically for clarity.



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he OFN tip. Figures 33(a) and 33(b) present photos taken at an 1 s intervalhere one particle is clearly trapped at the fiber tip while the others moveithin the liquid. When the power was reduced [Fig. 33(c)], the particle was

eleased from the optical trap at the OFN tip. When the power was increasedgain, other particles were trapped at the fiber tip when the EDFA poweras of the order of 10 mW.

his experiment demonstrated that optical trapping with OFN and adiabaticapers uses lower intensities 10 mW than that used in free space 1 W146] or with lensed fibers 22 mW [145]).

Figure 32

lectric field profile at an OFM cleaved end (a). Cross sections at differentistances along the z direction. (b) The OFN cleaved end is positionedt 3.2 µm. Simulations were carried out using a beam propagation method.



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.6. Mode Filtering

n addition to allowing efficient focusing of light (Subsection 4.5), OFNransition regions can act as an efficient tool for higher-order mode filtering inultimode waveguides [147]. A conventional telecom fiber with a 1 µmFM shows broadband single-mode operation with minimal optical loss

0.1 dB for the fundamental mode. Figures 34 and 35 represent a schematicf the device: if the conical transition regions are adiabatic (Fig. 34), guidedodes in the core of the multimode fiber are continuously mode converted to

uided cladding modes in the OFN on a one-to-one basis by the downtapernd are then coupled back into guided modes in the multimode fiber by theptaper; however, when the transition regions are not adiabatic (Fig. 35),igh-order modes are converted in even higher-order modes, which can beffectively suppressed by controlling the OFN diameter [148].

he single-mode operation range is determined by the mode cutoff conditions148] and the OFN small cladding V number Vcl [Eq. (2)] limits the numberf propagating modes without the use of additional index matching oil to stripway the high-order modes [149,150]. The different mode evolutionadiabatic for fundamental mode and nonadiabatic for higher-order modes)llows only the transverse single mode to propagate along the waveguide, which

Figure 33

icroscope pictures of an OFM tip in a solution of 1 µm silica spheres. (a),b) At laser outputs of 10 mW a particle (indicated by an arrow) is trapped athe OFN tip. (c) The particle is released when the laser is switched off.



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ermits single-mode operation for a conventional fiber over an extremely wideange of wavelengths.

he experimental demonstration was carried out by manufacturing low-lossFMs by the modified flame-brushing technique (Section 2). A telecom opticalber (Corning SMF-28) was selected as a simple example of a fiber providingultimode operation at short wavelengths; in fact, while above 1250 nm

nly the LP01 mode propagates, at shorter wavelengths the SMF-28 supportsn increasing number of modes: this is clearly seen by the increased fiber outputn the wavelength range 850–1250 (where two modes are supported) withespect to the single-mode operation range above 1250 nm (Fig. 36).

he profile of the transition regions was approximated by a decreasingxponential function, achieved by an appropriate control of the translationtage movement during fabrication [151]. Transmission spectra were recorded

Figure 34

+

P01+LP11

AdiabaticTransition

(LP01, LP11)

UniformWaist

LP01

in core

LP11

in core

LP01

in clad

LP11

In clad

LP01+LP

AdiabaticTransition

chematic of an OFN with adiabatic transition regions: all modes continuouslyvolve from core modes to cladding modes and are collected at the fiberutput. The evolution of the spatial profile of the first two guided modes alonghe transition tapers is also shown.

Figure 35

chematic of an OFN with nonadiabatic transition regions: higher-order coreodes are converted to even higher-order cladding modes or radiationodes that are not guided by the OFN because of its low cladding V number

cl.



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or various outer diameters during fabrication. Figure 37 shows the spectralutput of an SMF28 for different radii r in the uniform waist region.

s r decreases from 62.5 to 35 µm, intermodal interference appears in theultimode spectral region, while no change is observed above 1250 nm

single-mode operation region). This can be explained by the interference and

Figure 36

omparison between the transmission spectra of a standard telecom opticalber (SMF-28) without (black) and with (red) a 1 µm OFN. c_LP11, c_LP21,nd c_LP02 represent the cutoff wavelengths for the LP11, LP21 and LP02

odes.

Figure 37

ransmission spectra of a SMF-28 telecom fiber with an OFM for differentinimum waist radii r. When r=500 nm, single-mode operation is observed for

he whole range of wavelengths.



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eat of high-order modes that have been excited by a nonadiabatic transitionegion. When r2 µm, the higher-order mode cutoff shifts to shorteravelengths, enlarging the single-mode operation region. For r=500 nm there

s no higher-order mode cutoff, and the optical loss is negligible (0.1 dBt =1.55 µm). For even smaller r, propagation [Eq. (1)] and bending [Eq. (28)]osses pose limitations at long wavelengths. Therefore, r500 nm appearso be the optimal size for efficient single-mode operation. Usually, theingle-mode operation bandwidth is limited at short wavelengths by aigher-order mode cutoff. However, Fig. 37 shows that a very broad range400–1700 nm of single-mode operation was successfully realized by applyinghe efficient mode filtering scheme based on an OFM and a nonadiabaticransition region.

igure 38 shows far-field images taken with a 50 lens and a CCD camerahen laser light at =633 nm was launched into one of the fiber pigtails. In

he multimode fiber, interference between guided modes produces degradationf the laser beam quality at the fiber output [Fig. 38(a)]. Moreover, theutput pattern is extremely sensitive to external perturbations such as bending:evere modal interference occurs when bending is applied [Fig. 38(b)].owever, when a mode filter is inserted, the fiber output shows a single-modeeam [Fig. 38(c)] that is unperturbed by external bends [Figs. 38(d)]. Noptical degradation was detected in the mode profile or in the transmissionpectrum even after several bends and multipoint splices were applied to theMF with the mode filter.

.6a. Mode Filtering: Theory

n explanation of the mode filtering effect has been provided by the study ofhe mode propagation in the transition regions: the adiabaticity criterion

Figure 38

straight

straight

bending1

bending1

(a) (b)

(d)(c)

ar-field image of a beam propagating at =633 nm in a SMF (a), (b) withoutnd (c), (d) with ) the mode filter based on OFM and nonadiabatic tapers.n (a) and (c) the fiber was kept straight; in (b) and (d) it was bent.



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152,153] has been examined by calculating the beat length and taper angleecessary to ensure adiabatic behavior between points B and C of Fig. 3. Arofile is called adiabatic for a mode when there is no power transfer betweenodes. In an ideal adiabatic transition taper, the taper angle is small enough that

he core modes can be considered unperturbed on transition from being coreuided to being cladding guided. In particular, the beat length zb between twoodes having propagation constants 1 and 2 in a fiber with radius r has

een assumed to be the defining factor for the manufacture of lossless tapers152]. For distances larger than zb the two modes do not exchange power and theaper is adiabatic: this yields the critical angle to be defined as

=r

zb

=r1 − 2

2. 33

or nonadiabatic tapers, core modes couple to higher-order cladding modes ofhe same symmetry [152]. Coupling to the next high-order mode (LP01

LP02, LP11→LP12, LP21→LP22) is dominant with respect to the coupling tother higher-order modes (LP01→LP03, LP11→LP13, LP21→LP23); thus itepresents the limiting factor for an adiabatic transition. Figure 39 shows thealculated effective indices of the first three LP0m modes as a function of theore V number [Eq. (2)] at the wavelength =1 µm.

imilarly, Fig. 40 shows the calculated effective indices of the first three LP1m

odes as a function of the core V number at the wavelength =1 µm.

igure 41 shows for LP01 and LP11 modes evaluated by applying Eq. (33) tohe curves in Figs. 39 and 40. It is notable that the LP11 adiabatic curve isocated at smaller tapering angles than the LP01 one; this implies that for a wideange of tapering angles the LP01 mode converts adiabatically into a LP01

ode guided by the cladding–air interface, while the LP11 mode experiences

Figure 39

0.0 0.5 1.0 1.5 2.0 2.5 3.0

1.448

1.450

1.452

1.454

Eff

ectiv

ein

dex,

n eff

Core guidance parameter, V(z)

LP01

LP02

LP03

nclad

0.83

ode effective index versus core V number [Vco, Eq. (2)] for the first threeP0m modes. nclad and neff represent the cladding and the mode effective indices,

espectively. V=0.83 corresponds to point C in Fig. 3.



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onadiabatic conversion into higher-order modes. Smaller taper angles andelatively longer taper transition lengths are needed for the adiabatic conversionf LP11.

he dashed blue curve in Fig. 41 also represents the exponential taper profilesed in this set of experiments. The taper lies in the lossy region of the

Figure 40

0.0 0.5 1.0 1.5 2.0 2.5 3.0

1.448

1.450

1.452

1.454

Eff

ectiv

ein

dex,

n eff

Core guidance parameter, V(z)

LP11

LP12

LP13

nclad

2.405

ode effective index versus core V number [Vco, Eq. (2)] for the first threeP1m modes. nclad and neff represent the cladding and the mode effective indices,

espectively. V=2.405 corresponds to the LP11 cutoff.

Figure 41

0.0 0.2 0.4 0.6 0.8 1.010-4

10-3

10-2

LP11

Cor

eta

per

angl

e,Ω

Inverse taper ratio, ρ(z)/ρ0

LP01

Taper profile

Lossless

Lossless

Lossy

Lossy

LP11

LP01

diabatic profiles for LP01 and LP11 modes obtained from Eq. (33) and Figs.9 and 40. The dashed blue curve represents the profile of the transition region.ince between inverse taper ratios rz /r0=0.65 and rz /r0=0.8 it is above

he LP11 adiabatic curve, the LP11 mode will not experience adiabatic conversionor rz /r00.8 and will be converted in LP1m m1 modes.



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diabatic curve for the LP11 mode for inverse tapering ratios between 0.65 and.8, meaning that the LP11 mode is coupled into LP1m modes m1. Thiseems in good agreement with the results of Fig. 37: at r50 µm Fig. 41 predictsonversion of the LP11 mode into higher-order cladding modes that interferend produce oscillations at 1250 nm. Figure 41 can also be used to design anptimal adiabatic taper profile: the LP01 curve provides a solution for optimaldiabatic tapers (less than a few millimeters) that convert all modes apartrom the LP01 into unguided higher-order modes.

inally, as was shown in Subsections 3.3a and 3.3b, embedding is necessaryor long-term device reliability. In addition to protection, embedding providesode filters with a high-refractive-index surrounding medium; because of

his, the diameter of the uniform waist region necessary to strip the higher modesff is larger than that used in the experiments in air, allowing for increasedevice robustness.

. Conclusions

n summary, nanowires manufactured from optical fibers have been shown torovide outstanding optical and mechanical properties. Among theanufacturing methods, the flame-brushing and modified flame-brushing

echniques provide optical fiber microwires and nanowires with minimumptical losses and maximal robustness. Ultimate strength similar to that achievedn carbon nanotubes has been shown. The issue of device degradation overime and its solution by embedding has been proposed and demonstrated. Threeroups of optical applications have been explained: (1) applications basedn evanescent fields, which take advantage of the power propagating outside thehysical boundary of the wire and include high-Q knot, loop, and coilesonators, particle manipulation, and sensors; (2) applications exploiting theonfinement properties, which include supercontinuum generators andarticle trapping (Subsection 4.5); and (3) applications exploiting transitionegions to convert and filter modes.

lthough still in its early development, the use of nanowires for opticalevices opens the way to a host of new optical applications for communications,ensing, lasers, biology, and chemistry.

cknowledgments

he authors acknowledge financial support from the Engineering and Physicalciences Research Council (UK, EPSRC). G. Brambilla gratefullycknowledges the Royal Society (London, UK) for his research fellowship.

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