1. Introduction

In the past decade nanowires have attracted much attention because of the unique properties that materials display on the nanoscale [1]. A vast variety of materials have been studied, including carbon nanotubes [2], single-element nanowires (Si, Ge, Cu, Au, and Ag [3, 4, 5, 6, 7]), multicomponent structures (GaAs, GaN, InP, CdS, SiC, ${\mathrm{Si}}_3{\mathrm{N}}_4$, $\mathrm{Si}{\mathrm{O}}_2$, ${\mathrm{Al}}_2{\mathrm{O}}_3$, ZnO, $\mathrm{Sn}{\mathrm{O}}_2$, ${\mathrm{In}}_2{\mathrm{O}}_3$ [8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18]), and even organic materials [19, 20]. Nanowires have been manufactured by using a wide range of techniques: electron beam lithography [21], laser ablation [22], template-based methods [23], bottom-up methods such as vapor–liquid–solid techniques [24], chemical and physical vapor deposition [8, 25], solgel methods [26], and top-down techniques such as fiber pulling [27, 28, 29, 30, 31] or direct draw from bulk materials [20, 32].

Prior to 2003 only two attempts to manufacture submicrometer wires by using a top-down process were reported in the literature [33, 34]. Interest in optical fiber nanowires (OFNs) has been limited mainly because of the perceived difficulties in manufacturing suitably low-loss structures. Although several OFNs were fabricated by using a variety of bottom-up methods [35, 36, 37, 38, 39, 40, 41, 42], all of them exhibited an irregular profile and a surface roughness that appear to have limited the loss levels that could be reliably achieved [43, 44]. In 2003 a two-step process to fabricate low-loss submicrometric silica wires was presented [27]; it involved wrapping and drawing a pretapered section of standard fiber around a heated sapphire tip. Although the measured loss was orders of magnitude higher than that achieved later with flame-brushing techniques [28, 29, 30, 31], it was low enough to allow the use of OFNs for optical devices and ignite interest in the technology. In the following years a spate of publications investigated novel properties and applications of OFNs. It has become commonly accepted to define optical fiber nanowires (or photonic nanowires) as fiber waveguides with a submicrometric diameter. In this paper wires with diameter bigger than $1\mu \mathrm{m}$ will be referred to as optical fiber microwires (OFMs)

OFNs and OFMs are of interest for a range of emerging fiber optic applications, since they offer a number of enabling optical and mechanical properties, including the following:

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

2. Manufacture of OFNs and OFMs

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

In the past few years, three different methodologies have been used to fabricate OFNs and OFMs from optical fibers:

The flame-brushing technique has been previously used for the manufacture of fiber tapers and couplers [68]. A small flame moves under an optical fiber that is being stretched: because of mass conservation, the heated area experiences a diameter decrease. Controlling the flame movement and the fiber stretching rate lets the taper shape be defined to an extremely high-degree of accuracy. This technique provides access to the OFN from both pigtailed ends. Moreover, it delivers OFNs with radii as small as $30\mathrm{nm}$ [31], the longest and most uniform OFNs–OFMs [28] and the lowest measured loss to date [29, 30, 31].

The third fabrication method is a modified version of the flame-brushing technique in which the flame is replaced by a different heat source. Two types of heat source have been used: a sapphire capillary tube hit by a $\mathrm{C}{\mathrm{O}}_2$ laser beam [59], and a microheater [69]. This method is not limited to silica but provides OFNs and OFMs from a range of glasses including lead silicates [69], bismuth silicate [69], and chalcogenides [48].

3. Properties of OFNs and OFMs

3.1. Loss

For diameters φ of the minimum waist region comparable with the wavelength λ of the radiation propagating in the OFNs, light is strongly guided. When $\phi \ll \lambda$, the mode is strongly affected by diameter fluctuations. It has been shown [70] that for very small φ the propagation loss α is related to the propagation constant k, the absolute value of the transversal component of the propagation constant γ and the characteristic length of diameter fluctuations $L_f$ by

3.2. Spot Size and Mode Confinement

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

A conventional optical fiber falls at the right in this figure. The label SMF in Fig. 3 represents the value of $V_{\mathrm{co}}$ for a telecom optical fiber at $1.55\mu \mathrm{m}$. When the optical fiber diameter decreases, V decreases and ω initially decreases until a minimum point (B) is reached. After that, the mode is no longer guided in the core, and ω suddenly increases to a maximum associated with cladding guiding. For even smaller diameters ω decreases with decreasing V until it reaches a minimum (A) for $V_{\mathrm{cl}}\sim 2$, and then it increases again. This region at $V_{\text{cl}}<2$ is typical of OFNs: the mode is only weakly guided by the waveguide, ω can be orders of magnitude bigger than the physical diameter of the OFN, and a larger fraction of the power resides in the evanescent field.

Figure 4 shows the evanescent field at the surface of an OFN with various waist diameters simulated by using the beam propagation method. Simulations were carried out by using a full 3D vectorial method, and the electric field E was normalized to unit power. The propagating mode of untapered optical fiber is completely confined within the physical boundary of the fiber, and when the fiber is tapered below a certain diameter a considerable fraction of the power propagates in the surrounding medium. The electric field at the interface shows a maximum around the waist diameter φ of about $0.7\mu \mathrm{m}$, below which it sharply decreases. This can be explained by the increased ω, which effectively decreases the power density in the OFN. The decrease at larger φ is ascribed to the increasing mode confinement into the core.

It is interesting to note that the minimum beam waist ω depends on the cladding material, and the minimum beam size is ultimately limited by diffraction. Figure 5 compares the dependence of ω on the cladding diameter for three different fiber glasses: silica, lead silicate (F2, Schott glass) and bismuth silicate (Asahi glass). ω in bismuth silicate is nearly 40% smaller than in silica, and the OFM diameter at which the minimum occurs is nearly 40% smaller.

In Fig. 5, it is possible to identify two regions: the high-confinement region (I) and the large-evanescent-field region (II). In the high-confinement region ω is comparable with φ, the beam has its minimum waist diameter, and the optical nonlinearity γ reaches its maximum. γ is a figure of merit that is related to the material nonlinear refractive index $n_2$ and the beam size $A_{\mathrm{eff}}$ $(=\pi {\omega }^2∕4)$ by the following equation:

By contrast, in the evanescent field region OFMs and OFNs have diameters smaller than the waist of the propagating modes. ω can be orders of magnitude bigger than φ, and a considerable fraction of the power propagates in the evanescent field outside the fiber physical boundary. OFMs and OFNs with diameters in this region can be used for high-Q resonators (knot, loop, and coil), particle manipulation, and sensing (Subsections 4.1, 4.2, 4.3).

3.3. Mechanical Strength

Although they have an extremely small diameter, OFNs can be handled relatively easily because of their exceptional mechanical strength. Their ultimate strength ${\sigma }_{\mathrm{fract}}$, defined as the maximum stress a material can withstand, can be measured in a simple static experiment by adding milligram masses at the lower extremity of the vertically held fiber pigtail until fracture occurs. The mass m can then be measured and ${\sigma }_{\mathrm{fract}}$ can be derived from the relation

Figure 6 shows a summary of the results carried out on OFNs with radii $r=\phi ∕2$ in the range from 60 to $300\mathrm{nm}$. The tapers were produced with the modified flame-brushing technique by scanning a microheater (NTT-AT, Japan) over $6\mathrm{mm}$ along the optical fiber. For OFNs with $r<200\mathrm{nm}$ ${\sigma }_{\mathrm{fract}}$ is in excess of $10\mathrm{GPa}$. Although this value is slightly smaller than that measured for carbon nanotubes (${\sigma }_{\mathrm{fract}}=21\text{–}63\mathrm{GPa}$ [72, 73]), it is still considerably larger than the values recorded for commercially available high-strength materials like Kevlar $({\sigma }_{\mathrm{fract}}=3.88\mathrm{GPa})$ [74] and the high-strength steel ASTM A514 $({\sigma }_{\mathrm{fract}}=0.76\mathrm{GPa})$.

${\sigma }_{\mathrm{fract}}$ for OFNs is also higher than the measured ${\sigma }_{\mathrm{fract}}\sim 5\mathrm{GPa}$ of bare telecom optical fibers, where the radius is up to 3 orders of magnitude larger $(r\sim 62.5\mu \mathrm{m})$ [75, 76]. It is interesting to note that OFNs fabricated by the modified flame-brushing technique seem to have a considerably better mechanical strength than those manufactured by the two-step technique, for which the reported tensile strength was $2.5\text{–}5\mathrm{GPa}$ [27]; this can be explained by the better surface quality. Nanowires manufactured by the modified flame-brushing technique also provide a better mechanical performance than those manufactured by the conventional flame-brushing technique because of the lower water content in the nanowires. The flame produces a considerable amount of OH groups that then diffuse in the nanowire at high temperatures, and it is known from experiments on optical fibers that the water content in silica reduces the overall mechanical strength.

3.3a. The Big Issue

Surfaces degrade with time, and they need protection for long-term applications. Since OFNs have a large ratio between surface and volume, the effect of degradation is considerably more pronounced than in bigger specimens, i.e. optical fibers. Experiments have been conducted to quantify the long-term degradation of optical and mechanical properties of optical fiber nanowires and have shown a considerable difference between the nanowires preserved in a cleanroom environment and those kept in a conventional optics laboratory; in a conventional optics laboratory a group of OFNs manufactured by the flame-brushing technique with $r\sim 375\mathrm{nm}$ experienced a decay approximated by the relation [31]

The decrease in ${\sigma }_{\mathrm{fract}}$ has been related to optical properties, and it was found that an average decrease of $1.34\mathrm{GPa}$ in ${\sigma }_{\mathrm{fract}}$ was associated with an average induced loss of $1\mathrm{dB}∕\mathrm{mm}$. This connection was explained by the continuous formation of cracks, which simultaneously degrade the optical and the mechanical properties of the OFNs. This effect is well known to the optical fiber industry, where optical fibers are coated immediately after their fabrication to protect them from mechanical degradation. Some means to protect the surface of the nanowire is therefore required.

3.3b. Embedding

The acrylic coating used to protect optical fibers has a higher refractive index than silica because it has the additional purpose of stripping the modes propagating in the cladding. In OFNs the propagating mode has a significant intensity at the interface between silica and air, and the only approach to avoid confinement losses is to use low-refractive-index materials, such as silicone rubber [77], Efiron halogenated polymers, [78, 79] and Teflon [66, 80], which have refractive indices n of $\sim 1.4$, $\sim 1.373$ and $\sim 1.3$ at $\lambda =1.55\mu \mathrm{m}$, respectively. Silicone rubber is a thermocurable polymer that has been used to embed $8.5\mu \mathrm{m}$ OFMs and OFM resonators [77]. The Efiron UV37x family consists of UV-curable polymers manufactured by Luvantix (South Korea) [81] widely used to coat fibers used in optical fiber lasers. Teflon is a fluoropolymer with extremely low solubility in most chemicals. Still, a modified version exists that can be dissolved in fluorinated solvents [82]. This represents the best option to achieve high-confinement in embedded OFN or OFMs because of its low refractive index: the mode confinement is significantly higher than that achieved with other polymers because of the large refractive index difference between the OFN or OFM and the Teflon coating. The temporal stability of OFNs embedded in Teflon has also been studied over a period of time longer than $100\mathrm{h}$, and no change in transmitted power was observed [80]; for comparison, over the same time period a $20\mathrm{mm}$ long uncoated sample with the same φ experienced an induced loss in excess of $30\mathrm{dB}$. Similar experiments carried out on silicon rubber and Luvantix polymers showed that all the above-mentioned materials successfully protect OFNs and OFMs from degradation. For this reason, sensors and applications are based on embedded OFNs or OFMs.

4. Applications

Applications of OFMs and OFNs can be classified into three main groups according to what property they exploit:

Applications exploiting the confinement properties of OFMs correspond approximately to region I in Fig. 5 and include supercontinuum generation (Subsection 4.4), particle trapping (Subsection 4.5), and nonlinear switching or bistability [83, 84].

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

4.1. High-Q Resonators

High Q resonators have been widely studied because of their broad range of applications [85] ranging from optical communications to nonlinear optics, cavity QED, and sensing. If an OFN (or OFM) is coiled onto itself, the modes in the two different sections can overlap and couple, creating a resonator with an extremely compact geometry. A schematic of the transmission spectrum of a high-Q resonator is shown in Fig. 7.

Several resonator parameters can be easily estimated from the transmission spectra: quality factor (Q), free spectral range (FSR), and finesse (f) are the most important. Q is proportional to the confinement time in units of the optical period and can be expressed as [86]

The FSR is the inverse of the round-trip time (round-trip group delay) of an optical pulse. In the loop resonator spectrum, the FSR is the wavelength or frequency period of the peaks as shown in Fig. 7. It can be expressed as [86]

4.1a. Single-Loop Resonators

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

Loop resonators can be easily manufactured by coiling an OFN or OFM. The use of $XYZ$ stages to coil the OFM allows a great deal of control of the resonator geometry. Still, the geometry stability is based on surface forces; thus loop resonators are compromised in terms of long-term reliability. In contrast, knot resonators (like the one reported in Fig. 7) exhibit an enhanced temporal stability because of the friction that different sections of the OFM exert on one another. However, because the stiffness of the OFM is different than that of its pigtails, the bending curvatures needed to manufacture knot resonators induce an enormous stress in the OFM, which therefore breaks. The knot resonator can be easily manufactured if the fiber taper presented in Fig. 1 is broken; knotting is performed in the region of uniform waist (OFM), and no excess tension occurs. As a result, this type of resonator exhibits only one input–output fiberized pigtail.

The optical properties of single-loop resonators can easily be recorded by launching light from a broadband source into one of the OFM pigtails and analyzing the transmitted light with an optical spectrum analyzer. A typical transmission spectrum is shown in Fig. 9.

By using Eqs. (6, 7, 8, 9), ${\lambda }_{\mathrm{res}}\sim 1.55\mu \mathrm{m}$ and $\mathrm{FWHM}\sim 0.2\mathrm{nm}$, the FSR, f, and Q were estimated to be $4\mathrm{nm}$, 20, and $\sim 8\times {10}^3$, respectively.

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

Figure 10 shows the transmission spectra of a loop resonator sandwiched between two pieces of aerogel after $1\text{\hspace{0.17em}h}$, $2\text{\hspace{0.17em}h}$, and $1\text{\hspace{0.17em}day}$. Even after $1\text{\hspace{0.17em}day}$, there are no considerable changes in the spectral profile. This shows that aerogel is a very good substrate material on which to assemble optical nanowire loop resonators into functional microphotonics devices. However, aerogel is brittle and ultimately does not protect OFMs and OFNs from degradation in the same way as the polymers considered in Subsection 3.3b.

The loop resonator transmission coefficient can also be obtained analytically [60] by considering the output to be the sum of two interfering contributions: the first is represented by a fraction of the beam $a_1$, which is transmitted from input to output without entering the resonator, while the second consists of the remaining fraction of the beam $a_2$, which propagates through the coil. This leads to a simple relation for the transmitted power T as a function of the wavelength [60]:

4.1b. Coil Resonators

The flame-brushing or modified flame-brushing technique allows the fabrication of OFNs and OFMs with extremely long lengths. As a consequence, they can be coiled in more complicated resonant structures to form microcoil resonators. This potentially provides Q factors much higher (in excess of ${10}^9$ for losses approaching the material loss) and resonances much narrower than those presented in Figs. 9, 10. The OFN microcoil resonator (OMR) is a 3D resonator consisting of many self-coupling turns (Fig. 11), and it can be created by wrapping an optical fiber nanowire on a low-index dielectric rod.

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

The OMR spectral response can be derived analytically by solving the coupled wave equations for the amplitudes $A_m\left(\theta \right)$ of the light propagating in the mth turn of the OMR (Fig. 12).

If coupling between nonadjacent turns is ignored, the propagation of light along the coil in an M-turn OMR is described [60, 64, 65] by the coupled wave equations for slowly varying pitches:

Defining the average coil radius $R_0$ as

The OMR transmissivity coefficient T is defined as

The OMR spectrum is strongly dependent on its geometry; in particular, the resonance FWHM and FSR depend on the OMR geometry and the OFN size through K.

OMR Geometry and Coupling. The Q of the uniform OMR presented in Subsection 4.1b is extremely sensitive to the coupling strength. In theory, the highest Q can be achieved by selecting a K for which the FWHM is minimized, but in practice this is difficult to realize because the FWHM fluctuates considerably for small changes in K, and K has an exponential relation to the pitch [48, 49, 50, 54, 55, 56]. It is therefore desirable to find a geometry for which the FWHM is at its minimum and changes slowly with K.

Several different profiles have been studied in the literature [64, 65] to find the optimum resonator shape that allows the easiest realization of OMRs with high Q. Figure 13 presents some of the geometries considered.

The profiles have been described by the following mathematical formulas:

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

For this reason, a simpler way to tune the resonator properties has been investigated. Since the slow change in coupling properties has been shown to crucially affect Q, the possibility to easily achieve a high Q simply by tuning the input–output pigtails has been investigated. To this end coupling has been considered constant in the center [$K_n\left(\theta \right)=K_c$ for $2\pi <\theta <\theta (M-1)2\pi$)] and variable only at the ends, going to zero at the pigtail ends $(K_0=K_M=0)$.

Figure 14 shows five profiles of K for $M=4$. It was found [65] that sharp K profiles [such as Figs. 14(a), 14(e)] have a FWHM strongly dependent on $K_c$, while smoother profiles [Fig. 14(c)] can achieve flat FWHM profiles, i.e., high Q at nearly any $K_c$. Although the realization of an OMR with the exact profile of Fig. 14(c) is challenging, an OMR can be practically manufactured by wrapping the coils on a support rod and then tuning the input and output pigtails to achieve a slow decrease of coupling to zero.

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

OMR Internal Field Distribution. The field distribution inside an OMR has been found to depend strongly on the OMR geometry. Simulations were performed assuming an OFM with $r=1\mu \mathrm{m}$, $n=1.457$, the effective index $n_{\mathrm{eff}}=1.182$ at $1.55\mu \mathrm{m}$, coil radius $R_0=62.5\mu \mathrm{m}$, $dR=0.05\mu \mathrm{m}$, and K in the range 0–20. The field amplitudes $A_1\left(\theta \right)$, $A_2\left(\theta \right)$, and $A_3\left(\theta \right)$ were calculated for M for profiles H, V, and X in Fig. 13, choosing the wavelength and K that maximize the field amplitude. Figure 15 shows the dependence of the internal field distributions on the angle θ in three coils.

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

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

To test the resonator properties in real time during fabrication, the OFM had its pigtails connected to an erbium-doped fiber amplifier (EDFA) and an optical spectrum analyzer (OSA). Although early experiments were carried out by coiling the OFM on a low-refractive-index rod by hand with the aid of a microscope [Fig. 16(a)], the demands of continuous uniform coupling over the entire coil length necessitated the use of automated setups including a rotation stage (which controls the actual coiling) and a translation stage (which controls the coil pitch). It is clear from Fig. 16 that the coil uniformity is considerably better in the latter case. In the last stage of fabrication, the OFM pigtails were fixed to 3D stages and were tuned to find the optimum resonator spectrum.

If the coil was to be embedded, the fine tuning of the OFM pigtails was performed on uncured polymer, and the curing was carried out by checking the resonator properties in real time as the pigtails were adjusted. The polymer was then cured when the suitable adjustment had been completed. OMRs were wrapped on a low-refractive-index support rod to maximize the OMR temporal stability and robustness. Losses can be significant because of microbends and confinement losses. However, the loss can be minimized by increasing the microfiber thickness and the rod diameter, by using a low-refractive-index material for the rod, and by improving the smoothness of the rod surface. It was found [87] that using a rod coated with Teflon AF (DuPont, United States) or UV373 (Luvantix, Korea) provided good confinement because of the polymer’s low refractive index at the interface with the microfiber ($n\sim 1.3$ and $n\sim 1.37$ at $\sim 1.55\mu \mathrm{m}$, respectively). Support rods as small as $250\mu \mathrm{m}$ have been used without any significant observed loss. Most recent results seem to show that the particulate nature of the Teflon used in these experiments might induce higher losses than those observed for UV-curable fluoropolymers. Micrometer-size Teflon particles can in fact increase the Mie scattering and the overall OFM transmission loss [80].

4.2. Particle Manipulation

The radiation pressure exerted by light on matter was demonstrated by Lebedev more than a century ago [88]. However, until the laser was invented, light sources with high intensity were not readily available, and the radiation pressure was minute. Kawata and co-workers initially demonstrated the movement of dielectric microspheres initially by exploiting the evanescent field produced on the surface of a high-refractive-index prism [89] and subsequently by using the evanescent field of a single-mode channel waveguide [90]. Two effects take place: (1) the gradient force attracts and traps the particles laterally with an action similar to optical tweezers [91] while (2) the axial force due to absorption and scattering propels the microspheres along the direction of propagation of light in a waveguide [92]. The drag force opposes the propelling forces and acts to limit continuous acceleration, so that the particles ultimately reach a terminal velocity. This method may simultaneously manipulate several particles and provides a way to sort micrometer-size particles and biological cells. Driving microparticles by using the evanescent field produced by various types of planar waveguides has been investigated in more detail in the past two decades [93, 94, 95, 96]. Recently, the evanescent field of an OFN has also been exploited to propel $3\mu \mathrm{m}$ [51] and $10\mu \mathrm{m}$ [52] diameter polystyrene microspheres and microsphere clusters with diameters larger than $20\mu \mathrm{m}$. In Subsection 3.2 the beam size ω was shown to decrease for decreasing OFM–OFN diameters φ until a minimum for $V\sim 2$, after which it sharply increases. For small sizes, a considerable fraction of the power propagates outside the physical dimension of the OFN; the evanescent field can extend for several micrometers into the surrounding medium, and it can be exploited to propel particles.

The propulsion experiments were carried out by positioning OFNs on $\mathrm{Mg}{\mathrm{F}}_2$ substrates with their extremities fixed with adhesive tape. One of the pigtails was connected to a CW diode-pumped fiberized Nd:YLF laser. The power propagating in the fiber before the OFN was estimated to be $\sim 400\mathrm{mW}$ at $1047\mathrm{nm}$. While the power was completely confined within the fiber boundary in the fiber pigtails $(V_{\mathrm{cl}}\gg 2)$, in the liquid the OFN had $\phi <1\mu \mathrm{m}$ $(V_{\mathrm{cl}}<2)$; thus a considerable fraction of the power was propagating in the surrounding water. The water-based suspension containing polystyrene microspheres (refractive index $n_{\mathrm{PS}}=1.59$ and specific gravity ${\rho }_{\mathrm{PS}}\sim 1.05\mathrm{g}∕{\mathrm{cm}}^3$) was used to surround the OFN. Real-time monitoring was performed with a CCD camera mounted on top of the microscope with a $10\times$ objective and connected to a computer. A diagram of the experimental apparatus is given in Fig. 17.

Figures 18 (media 1) and 19 (media 2) show two movies taken by the CCD camera for suspensions of 3 and $10\mu \mathrm{m}$ spheres, respectively. Bright spots appear in Figs. 18, 19 because no filter was inserted into the microscope to reduce the collection of scattered laser light. The bright spots are explained as the excitation of whispering gallery modes in microspheres whose size is in resonance with the laser beam launched in the OFN. When the laser is switched on, the microspheres around the OFN were first attracted laterally to the OFN and then driven along it in the direction of light propagation. The particle velocities were evaluated from a measurement of the average displacement over a few seconds and were estimated to be of the order of $\sim 10\mu \mathrm{m}∕\mathrm{s}$. It is notable that even clusters of 6–7 particles with overall diameters larger than $20\mu \mathrm{m}$ can be propelled along the OFN (media 2).

The optical force experienced by particles is proportional to the optical intensity at their surface; in Subsection 3.2 the electric field (E field) at the surface of the OFN has been evaluated, and Fig. 4 shows how there is a maximum at $\phi =0.7\mathrm{mm}$. For a laser output of $500\mathrm{mW}$, the average velocity of $3\mu \mathrm{m}$ particles was $\sim 9\mu \mathrm{m}∕\mathrm{s}$ along the OFN, compared with the $\sim 2.6\mu \mathrm{m}∕\mathrm{s}$ observed along glass waveguides [95]. The larger velocity observed in Fig. 18 with respect to the glass planar waveguide can be explained in terms of a better source or waveguide coupling and/or a larger evanescent field and higher field intensity at the interface between the optical guide and the water–particle suspension.

Figure 20 presents a comparison of the evanescent fields near the surface for three waveguides used in propulsion experiments: an OFN, a ${\mathrm{Si}}_3{\mathrm{N}}_4$ ridge waveguide [96], and a glass waveguide [95]. Simulations were carried out by using the beam propagation method as before. The waveguide width and depth were taken to be 3 and $1\mu \mathrm{m}$ for the glass waveguide [95] and 1 and $0.2\mu \mathrm{m}$ for the ${\mathrm{Si}}_3{\mathrm{N}}_4$ waveguide [96]. The refractive indices of the glass substrate, glass waveguide, ${\mathrm{Si}}_3{\mathrm{N}}_4$ waveguide, and its substrate were taken to be 1.55, 1.58, 1.97, and 1.45 respectively. From Fig. 20 it is clear that the E field at the interface of the OFN is several times larger than that experienced in the glass planar waveguide, but about half of that calculated for the ${\mathrm{Si}}_3{\mathrm{N}}_4$ ridge waveguide. This can be easily explained by the mode confinement geometry: while in planar waveguides the mode can leak into the substrate (which can host a large fraction of the power), in the OFN the mode can only extend into the solution because of its cylindrical symmetry. Moreover, mode confinement is related to the numerical aperture of the optical waveguide: since the ${\mathrm{Si}}_3{\mathrm{N}}_4$ waveguide has an extremely high refractive index $(n_{{\mathrm{Si}}_3{\mathrm{N}}_4}\sim 1.97)$, the numerical aperture that the waveguide has with respect to water $(n_{{\mathrm{H}}_2\mathrm{O}}\sim 1.33)$ and to the substrate $(n_{\mathrm{Sub}}\sim 1.45)$ is considerably larger than that experienced by the modes propagating in the glass waveguide and OFN.

However, the evanescent field in the planar waveguides decreases more sharply than in the OFN; in fact, although the ${\mathrm{Si}}_3{\mathrm{N}}_4$ waveguide has a stronger field up to $250\mathrm{nm}$ from the interface, at distances longer than $250\mathrm{nm}$ the OFN E field is consistently larger and even extends beyond $2\mu \mathrm{m}$ above the surface. In addition, the OFN exhibits the great advantage of manipulating particles in 3D.

4.3. Sensors

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

Surface sensors based on OFNs have been predicted [67] and experimentally realized for the detection of hydrogen [53] by coating an OFM with palladium. Because of the reduced sensor dimensions, the ultrathin palladium film allowed sensor response times of approximately $10\mathrm{s}$, up to 15 times faster than that of most optical and electrical hydrogen sensors reported so far. The detection range was 0.05%–5%, enough to detect hydrogen at the lower explosion limit for gas mixtures. The sensor worked by checking the absorption changes with a simple transmission measurement setup that consisted of a $1550\mathrm{nm}$ laser diode and a photodetector. OFNs can also be coated with bioreceptors or gelatin to detect biological components [67] and humidity [98], respectively. Polymers nanowires have also been bonded to silica OFNs and used as sensors for humidity, $\mathrm{N}{\mathrm{O}}_2$, and $\mathrm{N}{\mathrm{H}}_3$ [99]. In this case, the use of a polymeric material allows the gas to diffuse in it and modify its optical absorption properties. By measuring the absorption changes it is possible to measure changes in gas composition down to a sub-part-per-million level (to less than 1 part in ${10}^6$). Because of its large evanescent field, OFN sensors have also found applications in the measurement of refractive index in microfluidic channels [100] and even as a tool for probing atomic fluorescence [101]. However, in all of these configurations the interaction length is limited by the OFN’s physical length.

In contrast, resonant sensors allow an effective multiplication of the interaction length and thus allow incredibly compact devices to be manufactured. Small size, high sensitivity, high selectivity, and low detection limits are the dominant requirements for evanescent field optical resonating sensors. To date, the resonators investigated include microspheres, photonic crystals, gratings, and microrings [102, 103, 104, 105, 106]. Optical microresonators can provide large evanescent fields for high sensitivity, high Q factors for low detection limits, and corresponding small resonant bandwidths for good wavelength selectivity. The drawback of the vast majority of high-Q resonators relates to the difficulty of coupling light into and out of the resonator. Microcoil resonating sensors have been manufactured by wrapping OFMs around copper wires [107]; although they exhibit good sensitivities, they are prone to degradation. In Subsection 3.3b embedding was examined and shown to preserve OFN from degradation; yet the choice of the coating thickness is a challenge, because a thick coating layer will limit the sensitive evanescent field, while a thin layer does not provide appropriate protection to the device. In this Subsection, the possibility of exploiting coated nanowire resonators for homogeneous [97] sensing applications is investigated.

4.3a. Resonating Sensors: Schematic and Manufacture

To date, three resonating sensors based on OFNs–OFMs have been proposed or demonstrated: the coated microfiber coil resonator sensor (CMCRS) [55, 57], the embedded optical nanowire loop resonator refractometric sensor (ENLRS) [58], and the liquid ring resonator optical sensor (LRROS) [108]. While the first two exploit the resonances created in an OFM resonator, an LRROS effectively uses an OFM to excite a whispering gallery mode in a capillary, which acts as the real sensing device. In this subsection only the first two sensors will be discussed.

Figure 21 shows a schematic of the CMCRS and the ENLRS. In Fig. 21(a) the OFM is shown in violet and blue, the analyte channel in brown, and Teflon in green. The CMCRS is a compact and robust device with an intrinsic fluidic channel to deliver samples to the sensor. In Fig. 21(b) a very thin polymer layer covers the OFM loop of the ENLRS, while a thick coating deposit is used to fix the two fiber pigtails. In the ENLRS two sides are exposed to the liquid to be sensed. In both cases the embedded OFM has a considerable fraction of its mode propagating in the fluidic channel; thus any change in the analyte properties is reflected in a change of the mode properties at the sensor output. When OFNs are used instead of OFMs, an even greater fraction of the mode propagates in the evanescent field, thus increasing the overall sensitivity. Since OFMs–OFNs are fabricated from a single tapered optical fiber, light can be coupled into the sensor with essentially no insertion loss, which is a huge advantage over other types of resonator sensors.

The CMCRS can be fabricated from a microcoil resonator (Subsection 4.1b) by using an expendable rod, which is then removed. A candidate for the rod material is PMMA (polymethyl methacrylate), which is a polymer with an amorphous structure and which is soluble in acetone. In a similar way the ENLRS can be made by using two substrates fabricated with disposable materials such as PMMA coated with a thin layer of a low-loss, low-refractive-index polymer such as Teflon. Once the OFM loop resonator (Subsection 4.1b) is manufactured on one of the substrates, the other substrate is placed on top of the nanowire resonator and glued with the same low refractive-index polymer, and the expendable materials are removed, leaving a thin layer of low-refractive-index material on the nanowire. The use of a thick substrate allows easy handling of thin coating layers. A schematic cross section of the sensors as manufactured is presented in Fig. 22.

4.3b. Resonating Sensors: Theory

Any change of the analyte refractive index $n_a$ leads to a change in the effective index $n_{\mathrm{eff}}$ of the propagating mode; thus it shifts the mode relative to the resonance, which in turn modifies the transmissivity T, and it shifts the mode relative to the resonance. A two-turn CMCRS can be easily evaluated by using the coupled mode equations presented in Subsection 4.1b; Eqs. (11, 12, 13, 14, 15, 16) give

The mode properties are particularly affected by the OFN radius $r=\phi ∕2$ and the distance d between the OFN and the analyte (coating thickness). The sensor response has been determined by calculating $n_{\mathrm{eff}}$ (using the finite-element-method software COMSOL3.3 with perfectly matched layers) and the related shift of ${\lambda }_{\mathrm{res}}$ as a function of the analyte concentration. $n_{\mathrm{eff}}$ has been evaluated for a nanowire embedded in Teflon and coiled around a microfluidic channel. The fundamental mode, which has the largest propagation constant, is the only mode that is well bounded in the vicinity of the fiber core [109, 110]; thus it is the only mode considered here. Since $n_{\mathrm{eff}}$ is a function of r and d, ${\lambda }_{\mathrm{res}}$ also varies with r and d through Eq. (24). Figure 23 shows the intensity distribution of the fundamental mode for two different analyte refractive indices [Fig. 23(a)] $n_a=1$ and [Fig. 23(b)] $n_a=1.37$ when $n_{\mathrm{OFN}}=1.451$, $n_{\text{Teflon}}=1.311$, $d=100\mathrm{nm}$, $r=500\mathrm{nm}$, $\lambda =1550\mathrm{nm}$. When $n_a$ is small [Fig. 23(a)] the field is still bound within the OFN physical boundary, while it shifts into the coating and leaks into the analyte when $n_a$ is large [Fig. 23(b)].

Figure 24 shows the dependence of $n_{\mathrm{eff}}$ on the analyte refractive index $n_a$. The OFN radius has been assumed constant at $r=500\mathrm{nm}$, while three values 10, 100, and $500\mathrm{nm}$ have been considered for d. Generally, $n_{\mathrm{eff}}$ increases with $n_a$ and increases more quickly with smaller d, since in this case a larger fraction of the mode is propagating in the analyte, as shown in Fig. 23. If $n_a=n_{\text{Teflon}}$, light cannot see the boundary between Teflon and the analyte solution; thus $n_{\mathrm{eff}}$ is the same at any d, and in Figs. 24(a), 24(b), 24(c), 24(d) there is a crossing point for different diameters. It is interesting that this behavior is independent of the sensor geometry, to the degree that the overlap between analyte and mode propagating in the OFN is the same: the CMCRS has the same overlap with the analyte as the ENLRS with one surface interface [Fig. 22(b)]; thus they have the same dependence of $n_{\mathrm{eff}}$ on $n_a$. The ENLRS with two interface surfaces [Fig. 22(c)] has an overlap that is twice as large, and thus the dependence of $n_{\mathrm{eff}}$ on $n_a$ is twice as strong.

4.3c. Resonating Sensors: Sensitivity

The most important attribute of refractometric sensors is the homogeneous sensitivity S, defined as the shift of the resonant wavelength ${\lambda }_{\mathrm{res}}$ [corresponding to the solutions of Eq. (23)] with respect to the change in the analyte refractive index $n_a$ [97, 111]:

S was calculated by using Eq. (27) near $n_a=1.332$ at operational wavelengths of $\lambda =600\mathrm{nm}$ and $\lambda =970\mathrm{nm}$. Figure 25 shows the dependence of S on r for different values of d. S increases when d decreases or λ increases because of the increasing fraction of power in the evanescent field. Decreasing r also increases S because this increases the fraction of the mode field inside the fluidic channel. S reaches $500\mathrm{nm}∕\mathrm{RIU}$ (where RIU is refractive index unit) at $r\approx 200\mathrm{nm}$ for $\lambda =600\mathrm{nm}$ and $700\mathrm{nm}∕\mathrm{RIU}$ at $r\approx 300\mathrm{nm}$ for $\lambda =970\mathrm{nm}$. This is higher than in most microresonator sensors [102, 104, 106, 124, 122, 123].

For the same λ and OFN radius r, the sensitivity for the ENLRS with two sensing surfaces is larger than that with only one because of the larger overlap between the evanescent field and the analyte (Subsection 4.3b). For very small values of r the sensitivity reaches a plateau because the fundamental mode is no longer well confined and most of the evanescent field is in the analyte. In this case $n_{\mathrm{eff}}$ becomes linearly dependent on $n_a$, and the derivative in the last term of Eq. (27) reaches a uniform value, and so the sensitivity reaches a plateau.

It is interesting to note that the sensor sensitivity is strongly dependent on the embedding material. Figure 26 shows S for a CMCRS embedded in UV375 $(n_{\mathrm{UV}375}\sim 1.375)$ versus r at $\lambda =600\mathrm{nm}$ [Fig. 26(a)] and $\lambda =970\mathrm{nm}$ [Fig. 26(b)] for different values of d. As before, $n_a=1.332$ and $n_{\mathrm{OFN}}=1.451$.

S in UV375 is smaller than that obtained in Teflon: $S\sim 50\mathrm{nm}/\mathrm{RIU}$ for $r=400\mathrm{nm}$, $d=10\mathrm{nm}$ and $\lambda =970\mathrm{nm}$, compared with $S\sim 130\mathrm{nm}/\mathrm{RIU}$ in Teflon [Fig. 25(b)]. Since the refractive index of UV375 is higher than that of Teflon, the overlap between the evanescent field and the analyte is smaller; thus the last expression of Eq. (27) for UV375-coated CMCRSs is smaller than that for Teflon-coated CMCRSs.

4.3d. Resonating Sensors: Detection Limit

Another important figure of merit of refractometric sensors is the detection limit, defined as the smallest refractive index change that can be measured. If $\delta {\lambda }_0$ is the smallest measurable wavelength shift, then the detection limit DL can be defined as [55, 97, 111]:

In traditional microresonators input–output coupling occurs via a prism, antiresonant reflecting waveguides, or a fiber taper [102, 103, 104, 105, 106]. With probably only the exception of fiber taper coupling, which has been proved to be reasonably efficient [124], coupling to a microresonator has considerably complicated device design and/or has resulted in a significant increase in the overall loss. In contrast, CMCRSs and ENLRSs have an extremely low insertion loss: the ease of mode size control and the lossless input–output coupling via the fiber pigtails are unique features of devices based on OFNs.

4.3e. Resonating Sensors: Experimental Demonstration

A CMCRS was fabricated from an OFM with a length and diameter of the uniform waist region of $50\mathrm{mm}$ and $\sim 2.5\mu \mathrm{m}$. The OFM was then wrapped on a $1\mathrm{mm}$ diameter PMMA rod. The whole structure was repeatedly coated with the Teflon solution 601S1-100-6. The dried embedded OMR was then left in acetone to remove the support rod, which was completely dissolved in $1–2\text{\hspace{0.17em}days}$ at room temperature. Thereby, a CMCRS with a $\sim 1\mathrm{mm}$ diameter microchannel and two input–output pigtails was obtained. A picture of the sensor is shown in Fig. 27. The sensor consists of an OFM resonator with five turns and a microfluidic channel inside. The adjacent coils are very close, and the major coupling area is on the left side of the picture. Although some bubbles are left inside the CMCRS during the drying process, these seem to be far from the OFM and did not affect overall sensor operation.

To simulate the sensor behavior in aqueous solutions, the sensor was connected to an erbium-doped fiber amplifier and to an optical spectrum analyzer and then inserted into a beaker containing mixtures of isopropanol and methanol. The isopropanol ratios were (1) 60%, (2) 61.5%, (3) 63%, (4) 64.3%, (5) 65.5%, (6) 66.7%, and (7) 67.7%. The refractive indices of isopropanol and methanol at $1.5\mu \mathrm{m}$ are reported to be 1.364 and 1.317, respectively [125]. The sensor was then immersed into the mixtures, and spectra were recorded at $1530\mathrm{nm}$. Figure 28 shows that for increasing isopropyl concentrations the resonator peak shifts to longer wavelengths. The extinction ratio increases, achieves a maximum, and then decreases: this can be explained by a change in the coupling coefficient due to the change in the mixture’s refractive index.

The transmission properties of a multiturn microfiber coil resonator depend on the resonator coupling and loss and can be simulated by solving Eqs. (11, 12, 13, 14, 15, 16). The FWHM (and therefore the Q factor) in the traditional microsphere and microring resonators is controlled primarily by modifying the input–output coupling by means of prism coupling, antiresonant reflecting waveguide coupling, and fiber taper coupling [102, 103, 104, 105, 106].

There is only one primary resonance, which can be easily evaluated in a way analogous to that for a single-loop resonator. $n_{\mathrm{eff}}$ of the fundamental mode was calculated for several values of d by using Eqs. (22, 23, 24, 25, 26). Figure 29 shows the measured wavelength shift (dashed curve) and calculated (solid lines) wavelength shift as a function of the analyte refractive index $n_a$ and polymer thicknesses d for $r=1250\mathrm{nm}$.

The best fit occurs for $d\sim 0$, showing that the average coating thickness is small, possibly because the tight wrapping of the OFM on the support rod left little space for the coating to fill. The small difference observed in Fig. 29 has been attributed to the unevenness in the OFM diameter profile, to the imprecision in the coil winding, to the channel roughness, and to the uneven coating thickness (OFM distance from the microfluidic channel). S was obtained from the line slope as $\sim 40\mathrm{nm}/\mathrm{RIU}$. This value is comparable with those reported previously for microsphere, microring, and liquid-core resonators [103, 104, 108], but smaller than recently reported values for a slot waveguide ($212.13\mathrm{nm}/\mathrm{RIU}$) [126]. The relatively low value of S can be attributed to the small overlap between the mode propagating in the OFM and the analyte. In fact, S has been shown to increase by orders of magnitude for increasing $n_a$ [108]. Another factor that has probably contributed to the degraded S is the surface roughness of the device in contact with the analyte, possibly caused by the PMMA support rod. This roughness might also be responsible for the moderately low Q factor $(Q\sim {10}^4)$ observed.

4.4. Supercontinuum Generation

Since its first observation in 1970 [127], supercontinuum generation has attracted much attention owing to the large range of applications associated with ultrabroadband light sources. As a physical phenomenon, supercontinuum generation involves a number of nonlinear optical effects, including self- and cross-phase modulation, four-wave mixing, soliton effects, and stimulated Raman scattering, combined with appropriate dispersion properties. High intensity is a fundamental requirement for the observation of the phenomenon. This can be achieved either by using high-energy ultrashort pulses or, more practically, by using tight spatial confinement within a suitably nonlinear waveguide. The higher the nonlinearity of the material, the lower the required power levels. Silica holey fiber and tapers have previously been used extensively [128, 129, 130, 131]; however the intrinsic nonlinearity of silica is relatively low (Subsection 3.2), and there has therefore been growing interest in using optical fibers and microstructured optical fibers fabricated from highly nonlinear glasses [132, 133, 134, 135]. Most recently, OFMs have attracted an increasing interest for continuum generation because of the high nonlinearity associated with their tight confinement (Subsection 3.2), easy connectivity to fiberized components, and extreme flexibility in tailoring the zero dispersion wavelength. In particular, OFMs provide higher confinement than untapered fibers and lower input–output coupling losses than small-core microstructured fibers of similar minimum core dimensions. If the bandwidth is measured at $-20\mathrm{dB}$ from the peak, supercontinuum generation over a width of $1000\mathrm{nm}$ has been observed [45, 46, 47]. The use of highly nonlinear materials for OFMs has been studied to increase the optical nonlinearity even further (Subsection 3.2): bismuth silicate [136] and chalcogenide [48] OFMs have been successfully used to generate supercontinua over a broad range of wavelengths. In particular, bismuth silicate can be considered a promising material because of a much wider transmission window in the IR than silica, the lack of Raman peaks, and the extremely smooth spectral profiles of the generated supercontinua. In fact, while spectra generated in silica OFMs have spectral oscillations in excess of $10\mathrm{dB}$, an extremely smooth spectrum has been obtained for a bismuth silicate OFM over $1000\mathrm{nm}$.

The OFM used for supercontinuum generation was manufactured by using the modified flame-brushing technique (Section 2) on a highly nonlinear fiber ($n_2\sim 3.2\times {10}^{-19}{\mathrm{m}}^2∕\mathrm{W}$ [137]) fabricated by Asahi Glass Ltd. (Japan). The optical fiber had core and cladding diameters and refractive indices at $1.55\mu \mathrm{m}$ of ${\phi }_{\mathrm{\text{core}}}\sim 6.9\mathrm{mm}$ and ${\phi }_{\mathrm{\text{cladding}}}\sim 125.6\mathrm{mm}$, $n_{\mathrm{\text{core}}}\sim 2.02$ and $n_{\mathrm{\text{cladding}}}\sim 2.01$, respectively. The total loss of the taper (fiber input facet to fiber output facet) was monitored continuously during the fabrication process by injecting light at $1.55\mu \mathrm{m}$ from a fiberized laser source and measuring the total throughput power with a powermeter. The total loss of the taper at the end of the fabrication process was approximately $13\mathrm{dB}$. The material group-velocity dispersion of the OFM is given by the dispersion of the cladding material of the original untapered fiber, as shown in Fig. 30(a), with a zero-dispersion wavelength at $\sim 2.6\mu \mathrm{m}$. The total group-velocity dispersion D of the guided mode has a strong contribution from the waveguide design [138]:

Figure 31 compares the spectra of laser pulses at the laser output and at the OFM output for pumping at $\sim 1.63\mu \mathrm{m}$. With a laser output pulse energy of $E_p\sim 5\mathrm{nJ}$, a supercontinuum spectrum has been generated extending from 1 to $>2.3\mu \mathrm{m}$, with a $3\mathrm{dB}$ spectral width of $700\mathrm{nm}$. It is interesting to note that the supercontinuum profile is remarkably flat with $<5\mathrm{dB}$ variation over the spectral range $1.2–2\mu \mathrm{m}$. Moreover, the spectrum is more than $1000\mathrm{nm}$ broad at the $10\mathrm{dB}$ level. The observed decrease in the output power at long wavelengths is probably, at least in part, due to the roll-off in our detection system’s sensitivity.

4.5. Particle Trapping

While tight confinement in an OFM is associated with large nonlinearity, at a cleaved fiber end tight mode confinement results in high beam divergence. Because of the large numerical aperture of the OFM, the intensity profile at the fiber output experiences large gradients within very short distances (Fig. 32).

This characteristic can be exploited to trap particles with the so-called optical tweezers [139, 140], which use forces exerted by a strongly focused beam of light to trap small objects. Small particles develop electric dipole moments as a consequence of the optical field; thus they are shifted toward the focus by intensity gradients in the electric field [140]. In contrast, large objects are depicted as acting as lenses, refracting the rays of light and redirecting the momentum of their photons; this reaction moves them toward a focus, where the intensity peaks [139]. In free space, beam focusing is limited by diffraction: the minimum focal spot size is typically half of the wavelength (of the order of a fraction of a micrometer, typically). Metallic probes have also been proposed to trap small particles [141, 142], where strong field enhancement from light scattering at a metallic tip could generate a trapping potential deep enough to overcome Brownian motion and to capture a nanometric particle [141]. Alternatively, a combination of evanescent illumination from a substrate and light scattering at a tungsten probe apex is used to shape the optical field into a localized, 3D optical trap [142]. All these approaches require high powers for the illumination (well above $1\mathrm{W}$) and are difficult to integrate in conventional microscopy instruments. Lensed optical fibers have been demonstrated to be highly efficient optical traps [143, 144, 145] and can easily be integrated with microscope technology but have the drawback of a large size, difficult end face processing, and large mode field diameter (typically of the order of $10\mu \mathrm{m}$).

Short adiabatic tips can be manufactured by breaking an OFN at its minimum waist region. These tips can be used to trap $1\mu \mathrm{m}$ polystyrene particles in water with low powers $(\sim 10\mathrm{mW})$. The use of an OFN allows for small probe size and optimal confinement (submicrometer spots) and potentially reduces the trapping power by orders of magnitude. Trapping experiments were carried out at $\sim 1.5\mu \mathrm{m}$ by connecting an OFN to an EDFA capable of delivering $0.2\mathrm{W}$ of maximum power. The OFN tip was immersed in a solution containing silica microspheres with $1\mu \mathrm{m}$ diameter and was analyzed by using an optical microscope. The EDFA power was increased in steps of $0.1\mathrm{mW}$, and pictures were taken every $\sim 1\mathrm{s}$. At low powers, because of Brownian motion and other environmental factors, the microparticles move quickly, and no trapping was observed. With powers of $\sim 10\mathrm{mW}$, single particles were trapped at the OFN tip. Figures 33(a), 33(b) present photos taken at an $\sim 1\mathrm{s}$ interval where one particle is clearly trapped at the fiber tip while the others move within the liquid. When the power was reduced [Fig. 33(c)], the particle was released from the optical trap at the OFN tip. When the power was increased again, other particles were trapped at the fiber tip when the EDFA power was of the order of $10\mathrm{mW}$.

This experiment demonstrated that optical trapping with OFN and adiabatic tapers uses lower intensities $(\sim 10\mathrm{mW})$ than that used in free space $(\sim 1\mathrm{W})$ [146] or with lensed fibers $\left(22\mathrm{mW}\right)$ [145]).

4.6. Mode Filtering

In addition to allowing efficient focusing of light (Subsection 4.5), OFN transition regions can act as an efficient tool for higher-order mode filtering in multimode waveguides [147]. A conventional telecom fiber with a $1\mu \mathrm{m}$ OFM shows broadband single-mode operation with minimal optical loss $(<0.1\mathrm{dB})$ for the fundamental mode. Figures 34, 35 represent a schematic of the device: if the conical transition regions are adiabatic (Fig. 34), guided modes in the core of the multimode fiber are continuously mode converted to guided cladding modes in the OFN on a one-to-one basis by the downtaper and are then coupled back into guided modes in the multimode fiber by the uptaper; however, when the transition regions are not adiabatic (Fig. 35), high-order modes are converted in even higher-order modes, which can be effectively suppressed by controlling the OFN diameter [148].

The single-mode operation range is determined by the mode cutoff conditions [148] and the OFN small cladding V number $V_{\mathrm{cl}}$ [Eq. (2)] limits the number of propagating modes without the use of additional index matching oil to strip away the high-order modes [149, 150]. The different mode evolution (adiabatic for fundamental mode and nonadiabatic for higher-order modes) allows only the transverse single mode to propagate along the waveguide, which permits single-mode operation for a conventional fiber over an extremely wide range of wavelengths.

The experimental demonstration was carried out by manufacturing low-loss OFMs by the modified flame-brushing technique (Section 2). A telecom optical fiber (Corning SMF-28) was selected as a simple example of a fiber providing multimode operation at short wavelengths; in fact, while above $1250\mathrm{nm}$ only the ${\mathrm{LP}}_{01}$ mode propagates, at shorter wavelengths the SMF-28 supports an increasing number of modes: this is clearly seen by the increased fiber output in the wavelength range $850–1250$ (where two modes are supported) with respect to the single-mode operation range above $1250\mathrm{nm}$ (Fig. 36).

The profile of the transition regions was approximated by a decreasing exponential function, achieved by an appropriate control of the translation stage movement during fabrication [151]. Transmission spectra were recorded for various outer diameters during fabrication. Figure 37 shows the spectral output of an SMF28 for different radii r in the uniform waist region.

As r decreases from $62.5\text{\hspace{0.17em}to}35\mu \mathrm{m}$, intermodal interference appears in the multimode spectral region, while no change is observed above $1250\mathrm{nm}$ (single-mode operation region). This can be explained by the interference and beat of high-order modes that have been excited by a nonadiabatic transition region. When $r\sim 2\mu \mathrm{m}$, the higher-order mode cutoff shifts to shorter wavelengths, enlarging the single-mode operation region. For $r=500\mathrm{nm}$ there is no higher-order mode cutoff, and the optical loss is negligible ($<0.1\mathrm{dB}$ at $\lambda =1.55\mu \mathrm{m}$). For even smaller r, propagation [Eq. (1)] and bending [Eq. (28)] losses pose limitations at long wavelengths. Therefore, $r\sim 500\mathrm{nm}$ appears to be the optimal size for efficient single-mode operation. Usually, the single-mode operation bandwidth is limited at short wavelengths by a higher-order mode cutoff. However, Fig. 37 shows that a very broad range $(400–1700\mathrm{nm})$ of single-mode operation was successfully realized by applying the efficient mode filtering scheme based on an OFM and a nonadiabatic transition region.

Figure 38 shows far-field images taken with a $50\times$ lens and a CCD camera when laser light at $\lambda =633\mathrm{nm}$ was launched into one of the fiber pigtails. In the multimode fiber, interference between guided modes produces degradation of the laser beam quality at the fiber output [Fig. 38(a)]. Moreover, the output pattern is extremely sensitive to external perturbations such as bending: severe modal interference occurs when bending is applied [Fig. 38(b)]. However, when a mode filter is inserted, the fiber output shows a single-mode beam [Fig. 38(c)] that is unperturbed by external bends [Figs. 38(d)]. No optical degradation was detected in the mode profile or in the transmission spectrum even after several bends and multipoint splices were applied to the SMF with the mode filter.

4.6a. Mode Filtering: Theory

An explanation of the mode filtering effect has been provided by the study of the mode propagation in the transition regions: the adiabaticity criterion [152, 153] has been examined by calculating the beat length and taper angle necessary to ensure adiabatic behavior between points B and C of Fig. 3. A profile is called adiabatic for a mode when there is no power transfer between modes. In an ideal adiabatic transition taper, the taper angle is small enough that the core modes can be considered unperturbed on transition from being core guided to being cladding guided. In particular, the beat length $z_b$ between two modes having propagation constants ${\beta }_1$ and ${\beta }_2$ in a fiber with radius r has been assumed to be the defining factor for the manufacture of lossless tapers [152]. For distances larger than $z_b$ the two modes do not exchange power and the taper is adiabatic: this yields the critical angle Ω to be defined as

Similarly, Fig. 40 shows the calculated effective indices of the first three ${\mathrm{LP}}_{1m}$ modes as a function of the core V number at the wavelength $\lambda =1\mu \mathrm{m}$.

Figure 41 shows Ω for ${\mathrm{LP}}_{01}$ and ${\mathrm{LP}}_{11}$ modes evaluated by applying Eq. (33) to the curves in Figs. 39, 40. It is notable that the ${\mathrm{LP}}_{11}$ adiabatic curve is located at smaller tapering angles than the ${\mathrm{LP}}_{01}$ one; this implies that for a wide range of tapering angles the ${\mathrm{LP}}_{01}$ mode converts adiabatically into a ${\mathrm{LP}}_{01}$ mode guided by the cladding–air interface, while the ${\mathrm{LP}}_{11}$ mode experiences nonadiabatic conversion into higher-order modes. Smaller taper angles and relatively longer taper transition lengths are needed for the adiabatic conversion of ${\mathrm{LP}}_{11}$.

The dashed blue curve in Fig. 41 also represents the exponential taper profile used in this set of experiments. The taper lies in the lossy region of the adiabatic curve for the ${\mathrm{LP}}_{11}$ mode for inverse tapering ratios between 0.65 and 0.8, meaning that the ${\mathrm{LP}}_{11}$ mode is coupled into ${\mathrm{LP}}_{1m}$ modes $m>1)$. This seems in good agreement with the results of Fig. 37: at $r<50\mu \mathrm{m}$ Fig. 41 predicts conversion of the ${\mathrm{LP}}_{11}$ mode into higher-order cladding modes that interfere and produce oscillations at $\lambda <1250\mathrm{nm}$. Figure 41 can also be used to design an optimal adiabatic taper profile: the ${\mathrm{LP}}_{01}$ curve provides a solution for optimal adiabatic tapers (less than a few millimeters) that convert all modes apart from the ${\mathrm{LP}}_{01}$ into unguided higher-order modes.

Finally, as was shown in Subsections 3.3a, 3.3b, embedding is necessary for long-term device reliability. In addition to protection, embedding provides mode filters with a high-refractive-index surrounding medium; because of this, the diameter of the uniform waist region necessary to strip the higher modes off is larger than that used in the experiments in air, allowing for increased device robustness.

5. Conclusions

In summary, nanowires manufactured from optical fibers have been shown to provide outstanding optical and mechanical properties. Among the manufacturing methods, the flame-brushing and modified flame-brushing techniques provide optical fiber microwires and nanowires with minimum optical losses and maximal robustness. Ultimate strength similar to that achieved in carbon nanotubes has been shown. The issue of device degradation over time and its solution by embedding has been proposed and demonstrated. Three groups of optical applications have been explained: (1) applications based on evanescent fields, which take advantage of the power propagating outside the physical boundary of the wire and include high-Q knot, loop, and coil resonators, particle manipulation, and sensors; (2) applications exploiting the confinement properties, which include supercontinuum generators and particle trapping (Subsection 4.5); and (3) applications exploiting transition regions to convert and filter modes.

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

Acknowledgments

The authors acknowledge financial support from the Engineering and Physical Sciences Research Council (UK, EPSRC). G. Brambilla gratefully acknowledges the Royal Society (London, UK) for his research fellowship.

Tables and Figures

Table 1. Sensitivity S, FWHM, and Detection Limit DL for Evanescent Field Resonating Refractometric Sensors^a

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Fig. 1 Optical fiber taper.

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Fig. 2 Summary of optical loss α achieved in OFNs and OFMs for the three manufacturing techniques presented in Section 2: 1, the two stage process involving a sapphire rod heated by a flame [27]; 2, the flame-brushing technique [28, 29, 30, 31]; 3, the modified flame-brushing technique [this work, 30, 71].

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Fig. 3 Relationship between the spot size ω (defined as the radius where the intensity has dropped to $1∕e^2$ [71]), the cladding $\left(V_{\mathrm{cl}}\right)$ and core $\left(V_{\mathrm{co}}\right)$ V numbers of a tapered telecom fiber. Labeled points are the points of maximum confinement, A, in the cladding and, B, in the core and, C, the beginning of cladding guiding. $V_{\mathrm{cl}}$ and $V_{\mathrm{co}}$ are related to the cladding φ and core ${\phi }_{\mathrm{co}}$ diameters by Eq. (2). SMF and OFN represent the V numbers of a common telecom optical fiber and an optical fiber nanowire with $r=500\mathrm{nm}$ in air at $1.55\mu \mathrm{m}$.

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Fig. 4 Relationship between the electric field at the OFN surface and the OFN diameter φ. The wavelength and the refractive indices of the silica OFN were taken to be $1.047\mu \mathrm{m}$ and 1.45, respectively. Water was taken as the surrounding medium with a refractive index of 1.33.

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Fig. 5 Relationship between the spot size ω and the OFM–OFN diameter φ for three different fiber materials: silica (refractive index at $\lambda =1.55$, $n_{\mathrm{Si}{\mathrm{O}}_2}=1.444$), a lead silicate glass $(n_{{\mathrm{F}}_2}=1.597)$, and a bismuth silicate glass $(n_{\mathrm{BS}}=2.02)$. For increasing refractive indexes, the minimum ω becomes smaller and occurs at smaller diameters φ.

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Fig. 6 Dependence of the ultimate strength of silica OFN on the radius r.

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Fig. 7 Schematic of a spectrum with the related notation for FWHM, free spectral range (FSR), and resonant wavelength $\left({\lambda }_{\mathrm{res}}\right)$.

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Fig. 8 Knot resonator with radius $R\sim 45\mu \mathrm{m}$ manufactured from an OFM with $r\sim 1\mu \mathrm{m}$.

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Fig. 9 Transmission spectrum of a loop resonator as recorded from an optical spectrum analyzer (OSA).

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Fig. 10 Transmission spectra of a loop resonator sandwiched between aerogels recorded 1, 2, and $12\mathrm{h}$ after fabrication. The OFN radius is $r=400\mathrm{nm}$.

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Fig. 11 Optical fiber nanowire microcoil resonator (OMR). Light can both propagate along the OFN (red arrow) or be coupled into an adjacent coil (green arrow).

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Fig. 12 Cylindrical coordinates system used for the analytical description of the OMR. The angle θ continuously increases along the coil.

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Fig. 13 Schematic of various OMR geometries. H represents the OMR with a constant coil radius (along Z) and coil pitch (along R). V and X have a constant coil pitch and a variable coil radius; I and T a constant coil radius and a changing coil pitch.

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Fig. 14 Schematic of pigtail geometries in four-turn OMRs.

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Fig. 15 Internal field amplitude in three-turn OMRs for profiles H, V, and X (Fig. 13).

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Fig. 16 OMRs manufactured (a) by hand and (b) by an automated stage. The number of turns is three in (a) and two in (b).

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Fig. 17 Schematic of the experimental apparatus used to demonstrate optical propulsion of polystyrene microparticles.

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Fig. 18 Single-frame excerpt from the video recording (Media 1) of $3\mu \mathrm{m}$ polystyrene particles propelled along an OFN with $\phi =0.95\mu \mathrm{m}$.

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Fig. 19 Single-frame excerpt from video (Media 2) of $10\mu \mathrm{m}$ polystyrene particles propelled along an OFN with $\phi =0.95\mu \mathrm{m}$.

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Fig. 20 E field distribution in an OFN and planar waveguides in the space adjacent the surface. The E field was normalized per unit power traveling in the waveguide.

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Fig. 21 Schematics of (a) a coated microfiber coil resonator sensor (CMCRS) and (b) an embedded optical nanowire loop resonator refractometric sensor (ENLRS). Figures are not to scale.

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Fig. 22 Schematic cross sections of (a) a coated microfiber coil resonator sensor (CMCRS) and two embedded optical nanowire loop resonator refractometric sensors (ENLRS) with (b) one and (c) two surfaces exposed to the analyte.

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Fig. 23 Intensity distribution of the fundamental mode at the sensor–analyte interface for $n_{\mathrm{OFN}}=1.451$, $n_{\mathrm{\text{Teflon}}}=1.311$, $d=100\mathrm{nm}$, $r=500\mathrm{nm}$. The analyte refractive index is (a) $n_a=1$ and (b) $n_a=1.37$, respectively. The OFN section is represented by the white circle.

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Fig. 24 Dependence of the effective index of a coated OFN $n_{\mathrm{eff}}$ on the index of the analyte $n_a$ for $n_{\mathrm{\text{Teflon}}}=1.311$, $n_{\mathrm{OFN}}=1.451$, $r=500\mathrm{nm}$, for several distances between OFN and analyte in a (a), (b) CMCRS and (c), (d) an ENLRS. The wavelength of the propagating mode is $\lambda =600\mathrm{nm}$ in (a) and (c) and $\lambda =970\mathrm{nm}$ in (b) and (d). A bare OFN is reported in (c) and (d) for reference.

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Fig. 25 Dependence of the sensitivity S on the OFN radius r for $n_{\mathrm{\text{Teflon}}}=1.311$, $n_{\mathrm{OFN}}=1.451$, and several coating thicknesses d in (a), (b) a CMCRS and (c), (d) an ENLRS. The wavelength of the propagating mode is $\lambda =600\mathrm{nm}$ in (a) and (c) and $\lambda =970\mathrm{nm}$ in (b) and (d). Schematics of the ENLRS with one or two surfaces are shown in Figs. 22(b), 22(c).

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Fig. 26 Dependence of the sensitivity S on the OFN radius r for $n_{\mathrm{UV}375}=1.375$, $n_{\mathrm{OFN}}=1.451$, and several coating thicknesses d in a CMCRS for (a) $\lambda =600\mathrm{nm}$ and (b) $\lambda =970\mathrm{nm}$.

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Fig. 27 Microscope picture of a CMCRS. The yellow dashed lines and red arrows show the fluidic channel and input–output pigtails, respectively.

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Fig. 28 Dependence of the OMCRS spectrum on the analyte refractive index for different 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%, and 67.7%, respectively.

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Fig. 29 Dependence of the measured (dashed) and calculated (solid) wavelength shifts on the analyte refractive index $n_a$ for $r=1250\mathrm{nm}$ and different polymer thicknesses d.

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Fig. 30 (a) Dependence of the dispersion of the cladding material on the wavelength. (b) Correlation between diameter and zero-dispersion wavelength in OFMs manufactured from the Asahi bismuth silicate fiber: simulations were performed using the exact solution of Maxwell’s equations for an air-suspended rod having the dispersion characteristics of the fiber cladding glass [128].

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Fig. 31 Comparison of output spectra from the laser source and the OFN for pulse energies of 5 and $3\mathrm{nJ}$. The spectra have been shifted vertically for clarity.

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Fig. 32 Electric field profile at an OFM cleaved end (a). Cross sections at different distances along the z direction. (b) The OFN cleaved end is positioned at $\sim 3.2\mu \mathrm{m}$. Simulations were carried out using a beam propagation method.

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Fig. 33 Microscope pictures of an OFM tip in a solution of $1\mu \mathrm{m}$ silica spheres. (a), (b) At laser outputs of $\sim 10\mathrm{mW}$ a particle (indicated by an arrow) is trapped at the OFN tip. (c) The particle is released when the laser is switched off.

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Fig. 34 Schematic of an OFN with adiabatic transition regions: all modes continuously evolve from core modes to cladding modes and are collected at the fiber output. The evolution of the spatial profile of the first two guided modes along the transition tapers is also shown.

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Fig. 35 Schematic of an OFN with nonadiabatic transition regions: higher-order core modes are converted to even higher-order cladding modes or radiation modes that are not guided by the OFN because of its low cladding V number $V_{\mathrm{cl}}$.

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Fig. 36 Comparison between the transmission spectra of a standard telecom optical fiber (SMF-28) without (black) and with (red) a $1\mu \mathrm{m}$ OFN. ${\lambda }_c\_{\mathrm{LP}}_{11}$, ${\lambda }_c\_{\mathrm{LP}}_{21}$, and ${\lambda }_c\_{\mathrm{LP}}_{02}$ represent the cutoff wavelengths for the ${\mathrm{LP}}_{11}$, ${\mathrm{LP}}_{21}$ and ${\mathrm{LP}}_{02}$ modes.

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Fig. 37 Transmission spectra of a SMF-28 telecom fiber with an OFM for different minimum waist radii r. When $r=500\mathrm{nm}$, single-mode operation is observed for the whole range of wavelengths.

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Fig. 38 Far-field image of a beam propagating at $\lambda =633\mathrm{nm}$ in a SMF (a), (b) without and (c), (d) with ) the mode filter based on OFM and nonadiabatic tapers. In (a) and (c) the fiber was kept straight; in (b) and (d) it was bent.

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Fig. 39 Mode effective index versus core V number [$V_{\mathrm{co}}$, Eq. (2)] for the first three ${\mathrm{LP}}_{0m}$ modes. $n_{\mathrm{clad}}$ and $n_{\mathrm{eff}}$ represent the cladding and the mode effective indices, respectively. $V=0.83$ corresponds to point C in Fig. 3.

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Fig. 40 Mode effective index versus core V number [$V_{\mathrm{co}}$, Eq. (2)] for the first three ${\mathrm{LP}}_{1m}$ modes. $n_{\mathrm{clad}}$ and $n_{\mathrm{eff}}$ represent the cladding and the mode effective indices, respectively. $V=2.405$ corresponds to the ${\mathrm{LP}}_{11}$ cutoff.

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Fig. 41 Adiabatic profiles for ${\mathrm{LP}}_{01}$ and ${\mathrm{LP}}_{11}$ modes obtained from Eq. (33) and Figs. 39, 40. The dashed blue curve represents the profile of the transition region. Since between inverse taper ratios $r\left(z\right)∕r_0=0.65$ and $r\left(z\right)∕r_0=0.8$ it is above the ${\mathrm{LP}}_{11}$ adiabatic curve, the ${\mathrm{LP}}_{11}$ mode will not experience adiabatic conversion for $r\left(z\right)∕r_0<0.8$ and will be converted in ${\mathrm{LP}}_{1m}$ $(m>1)$ modes.

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