Back in 1966, Kao and Hockham proposed the possibility of achieving low optical loss in high-purity glasses , which has no doubt led to a thriving research area in both fiber optics and fiber-optic technologies. In several decades since then, optical fibers with diameters larger than the wavelength of transmitted light had quickly found extensive applications including optical communication, sensing, power delivery and nonlinear optics. Recently, with the rapid progresses in nanotechnology, there is an increasing demand for faster response, smaller footprint, higher sensitivity, and lower power consumption, which spurred great efforts for miniaturization of fiber-optic components and devices. Although optical fibers with diameters close to the wavelength of propagating light had been investigated [2–9], they had not been paid much attentions. In 2003, Tong and Mazur demonstrated low-loss optical waveguiding in microfibers and nanofibers (MNFs) with diameters far below the wavelength of the guided light, which renewed research interests in MNFs . As potential building blocks for miniaturization optical components and devices, MNFs have been attracting intensive research interests regarding their fabrication, properties, and applications. Moreover, besides sub-wavelength optical waveguiding that enables miniaturized fiber-optic devices from optical cavities to lasers and sensors, the MNF has extended fiber optics to fields such as atom optics and optomechanics, which may add new possibilities to fiber optics on a lower spatial dimension.
Compared with a conventional optical fiber, a high index-contrast (Δn) MNF with wavelength (λ) or sub-wavelength (sub-λ) diameter offers a number of interesting properties and opportunities (Figure 1), including:
(1) Tight optical confinement
Tight optical confinement bestows the MNF with small allowable bending radius (i.e., low loss when passing through sharp bends) and small mode area, which makes MNFs highly potential for compact circuits and devices with smaller footprints, faster response, and lower power consumption [11–14]. Meanwhile, small mode area and field enhancement originated from the tight confinement allow the observation of spectacular nonlinear effects [15–18] with low thresholds and power-consumption, such as supercontinuum generation and nonlinear optical switching. Also, tight spatial confinement modifies vacuum states for radiation around the surface of the MNF, which, in turn, can significantly modify the emission of a nanoemitter or an atom nearby [19, 20].
(2) Strong evanescent field
Strong evanescent field offers strong near-field interaction between the MNF and its surroundings, making the MNF highly favorable for optical sensing [21–32] and evanescent coupling between the MNF and other waveguides (e.g., a semiconductor [33, 34], metal [35, 36] nanowire or planar waveguide ) or a substrate [30, 35, 38, 39]. Based on the high-efficiency evanescent coupling, a variety of optical components or devices (e.g., loop and knots resonators [40–51], lasers [52–58], and sensors [21–32]) have been demonstrated. Meanwhile, since the high fractional evanescent filed is tightly confined around the MNF, it can produce steep field gradient which provides large optical gradient force for manipulating cold atoms [19, 59–63] or micro-/nano-particles [64, 65], as well as large or manageable waveguide dispersion under single mode condition .
(3) Small mass/weight
Owing to its small mass or weight, an MNF can be highly sensitive to momentum change of photon guided through by mechanical vibration or displacement, making the MNF potential for realizing compact optomechanical components/devices, as well as triggering evident photon-phonon coupling or conversion in these tiny fibers [66–70]. For reference, the weight of a 200-nm-diameter 10-μm-length silica MNF is about 10-15 kg (equivalent to 10 pN), which is comparable to the pressure of light with power of 10 mW.
For optical waveguiding, excellent geometric uniformity and surface smoothness of the MNFs is critical for achieving low optical loss and high signal to noise ratio, and therefore the fabrication process of these tiny fibers is vitally important. Compared with many other techniques such as photo- or electron-beam lithography, chemical growth and nano-imprint, high-temperature taper-drawing method yield MNFs with lowest surface roughness (e.g., <0.5 nm ), largest length (e.g., >10 cm ) and excellent diameter uniformity. Also, the amorphous structure of the glass material bestows the MNF with circular cross-section, which is ideal for obtaining waveguiding modes by solving Maxwell’s Equations analytically. In this section, we briefly review taper-drawing techniques for fabricating MNFs from standard glass fibers or bulk glasses.
2.1 Flame-heated taper drawing of glass fibers
Flame-heated taper drawing is mostly used to draw MNFs from standard optical fibers. A typical illustration of flame-heated taper-drawing process is shown in Figure 2. A hydrogen flame is used for heating the fiber. Under a certain pulling force, the fiber is stretched and elongated gradually with reduced diameter until the desired length or diameter of the fiber taper is reached. Using this technique, the as-fabricated MNF is usually attached to the standard fiber through the tapering area at both ends, and is usually mentioned as a “biconical” fiber taper or MNF. In addition, by measuring optical transmission via standard fiber at both ends, it is possible to in-situ monitoring the waveguiding properties of the MNF during the pulling process in terms of propagation loss, multi-mode interference and group velocity delay [73, 74]. Based on the taper-drawing process mentioned above, in recent years, a number of improvements on this technique have been reported for fabricating MNFs with various parameters including ultra-small diameters , reduced propagation losses [15, 75], optimized tapering profiles and controllable cross-section geometries [76, 77].
2.2 Laser-heated taper drawing of glass fibers
In some situations, conventional flame-heated systems may present disadvantages such as the random turbulence of the flame and oxygen requirement in the burning process, leading to H2O/OH contamination in MNFs. To avoid these issues, a CO2 laser beam can be used as an alternative heating source. Usually, the direct laser heating tapering procedure shows a self-regulating effect , which automatically stops the stretching process when the fiber diameter goes down to a certain value (usually above 1 μm) . By drawing MNFs in a microfurnace comprising a sapphire tube heated with a CO2 laser, Sumetsky successfully fabricated sub-μm-diameter MNF with excellent surface smoothness and diameter uniformity . In addition, the laser-heating technique has been applied for fusion splicing of individual MNFs into functional optical components and devices [47, 56, 80, 81].
2.3 Electrically heated taper drawing of glass fibers
Besides the above-mentioned techniques, electrically heated taper drawing approach is another simple and effective technique for fabricating high-quality MNFs. Usually, the electrical heater can be shaped into various geometries to precisely generate required temperature and temperature distribution, which makes it possible to draw MNFs with more flexibilities. It is worth noting that, compared to flame-heated approach, the electrically heated technique is much convenient for drawing MNFs from soft glasses [30, 82, 83].
2.4 Flame-heated drawing of bulk glass
All the above fabrication techniques require an optical fiber as preform, which limits materials of MNFs to those used in traditional optical fibers. For materials not available in fiber forms, drawing directly from bulk glass is essential and can expand the MNF materials to a variety of glasses, especially for drawing active MNFs from glasses with functional dopants . Usually, a solid heating element (e.g., a flame-heated sapphire tip) is used to melt the glass and draw MNFs with high uniformity and repeatability.
2.5 Typical MNFs fabricated by physical drawing processes
Based on the fabrication techniques mentioned above, so far a variety of materials (including silicate, phosphate, tellurite, fluoride, bismuth oxide and chalcogenide glasses) have been drawn into optical-quality MNFs. Besides, to bestow the as-fabricated MNFs with greater versatilities, a number of post-fabrication techniques including micromanipulation [13, 85], plastic bend , coating [24, 29], embedding [44, 45, 86–90] and fusion splicing [47, 56, 80, 81] of MNFs have been investigated in the past years. Also, a variety of novel structures, such as MNFs with panda core to maintain polarization , elliptical cross-sections for high birefringence , or suspended cores to isolate surface contamination and contact leakage [92–94] have been also reported. For reference, Figure 3 shows typical micrographs of as-fabricated MNFs, in which MNFs of various materials and structures are investigated by either electron microscopes or optical microscopes.
3 Optical properties
3.1 Waveguiding modes in MNFs
For basic investigation, a straight MNF is assumed to have a circular cross-section, a smooth sidewall, a uniform diameter and an infinite cladding with a step-index profile. The fiber diameter (D) is not very small (e.g., D>10 nm) so that the statistic parameters permittivity (ε) and permeability (µ) can be used to describe the responses of a dielectric medium to an incident electromagnetic field. The length of the fiber is large enough (e.g., longer than 10 µm) to establish the spatial steady state.
With these assumptions, Figure 4 shows a mathematic model of an MNF for optical waveguiding, in which the refractive indices of the core and the cladding are n1 and n2, respectively. The index profile can be expressed as
where a is the radius of the MNF.
In the transparent spectral range of fiber material, MNFs can be treated as non-dissipative and source free waveguides. Therefore, Maxwell’s equations can be reduced to the following Helmholtz equations:
where k=2π/λ, λ is the wavelength of the light in vacuum, and β is the propagation constant.
Within cylindrical coordinate, Eq. (1) can be analytically solved  with eigenvalue equations
HEvm and EHvm modes
whereJv is the Bessel function of the first kind, and Kv is the modified Bessel function of the second kind, and
By numerically solving Eqs. (2–4), propagation constants (β) of guiding modes supported by the MNF can be obtained. For reference, Figure 5 gives diameter-dependent β of air-cladding silica MNFs guiding a 633-nm-wavelength light (D=2a, n1=1.46 at λ=633 nm, n2=1, and ). As one can see, when the fiber diameter is reduced to a certain value (denoted as dashed vertical line in Figure 5, at V=2.405, D=457 nm), only the HE11 mode exists, corresponding to the single mode operation. Generally, when its diameter goes close to or smaller than the wavelength of the guided light, a MNF with a low-index clad (e.g., vacuum, air or water) offers unusual properties such as tight optical confinement, high fractional evanescent fields and tailorable waveguide dispersion, which intrigue new opportunities for manipulating light on the micro-/nano-scale. Figure 6 shows power distribution (Z-direction Poynting vectors) of HE11 mode of silica MNFs with diameters of 800, 400, and 200 nm in 3-D and 2-D view, respectively. It is clear that, while a 800-nm-diameter MNF confines major energy inside the fiber, a 200-nm-diameter MNF leaves a large amount of light (>90%) guided outside as evanescent waves.
3.2 Evanescent coupling between two parrellel MNFs
Evanescent coupling between two adjacent MNFs is of special importance for designing nano fiber-optic devices such as couplers , modulators , resonators [81, 96, 97], lasers [34, 52–54, 56], and sensors [22, 28, 31], all of which involve the near-field coupling process (e.g., direct interconnection with external optical systems through fiber tapers, energy exchange between two MNFs, or recirculation of optical energy inside ring resonators).
Usually, evanescent coupling between adjacent weakly guiding waveguides (low-index-contrast waveguides) with a certain space (e.g., a few hundred nanometers) can be described by the perturbation theory . However, when two MNFs are brought in contact, they are no longer weak coupling system, in which perturbation theory cannot be applied. Thus, we need to investigate the mode coupling by numerical calculations. Using the finite-difference time-domain (FDTD) method, Huang et al. calculated the evanescent-coupling efficiency between two air-clad parallel MNFs  (Figure 7A). For reference, Figure 7B gives a simulation result of two parallel 350-nm-diameter silica MNFs. As one can see, the minimum transfer length (2.4 μm) for energy exchange is much shorter than that in weakly coupled waveguides . Also, the coupling efficiency shows an oscillating behavior depending on the overlapping length (Figure 7B and C), with a minimum considerably higher than zero (e.g., 34% for two 350-nm-diameter silica MNFs) owing to the strong coupling and a maximum lower than 100% (e.g., 96% for 350-nm-diameter silica MNFs). Moreover, for two MNFs with different diameter, the coupling efficiency is direction dependent: coupling light from a thinner MNF to a thicker one (e.g., 350→400 or 350→450) shows higher efficiency (e.g., 91% for 350→400 or 82% for 350→450) than in the opposite direction (e.g., 88% for 400→350 or 71% for 450→350), which may be explained as thinner MNF have stronger evanescent field (as depicted in Figure 6).
3.3 Bending loss
Bent MNFs are important building blocks that can be readily assembled into highly compact photonic integrated circuits (PICs) or devices such as couplers [13, 84], interferometers , resonators [81, 96, 97], and lasers [34, 52–54, 56]. Usually, bending losses of conventional fibers can be calculated using weakly guiding or adiabatic approximation. However, these approximation are not valid for sharply bent (a few micrometers) MNFs, which are usually high-index-contrast waveguides. Based on FDTD method, Yu et al. investigated the bending losses of MNFs with circular 90° bends, with an acceptable value of 1 dB/90° for bending radii down to micrometer level (e.g., with a minimum allowable bending radius of 5 μm for a 350-nm-diameter silica MNF) . For reference, based on the mathematical model shown in Figure 8A, numerical simulations of a 450-nm-diameter silica MNF with a bending radius of 5 μm and 1 μm are shown in Figure 8B–E. As one can see, there is virtually no power leakage (with calculated bending loss of 0.14 dB/90°) for the 5 μm bent silica MNF, owing to its strong optical confinement ability. When the bending radius decreases to 1 μm, obvious energy leakage occurs around the bending region (Figure 8D), with evident lateral shift of the modal field (Figure 8E) and a calculated bending loss of about 4.8 dB/90°. Bending-radius-dependent bending losses in MNFs of some typical materials at 633-nm wavelength are also investigated (Figure 8F). As one can see, with increasing bending radius or index of the MNF (from silica, to PS or ZnO wire), the bending loss reduces as a result of the enhanced optical confinement.
Owing to the sub-wavelength cross-section, MNFs exhibit many novel properties, such as tight optical confinement, high fractional evanescent fields, and large manageable waveguide dispersion, which are highly desirable for functionalizing fiber-optic circuits with great versatility on a micro/nano scale. In the last 10 years, the research on MNFs has brought numerous opportunities in renewing and expanding the fiber optics and technology on micro/nano scale, as summarized in the “MNF tree” in Figure 9. Based on the optics behind, these recent advances are categorized into 5 areas: waveguide and near-field optics, nonlinear optics, quantum and atom optics, plasmonics, and optomechanics. In each branch, some typical examples with citations are provided. In this review, based on our recent progresses in MNFs, we mainly focus on waveguide and near-field optics, and go details into typical linear MNF-based photonic components and devices including couplers, Mach–Zehnder interferometers (MZI), gratings, resonators, lasers and sensors. In addition, applications of MNFs in fields of quantum and atom optics, and nonlinear optics are briefly introduced.
4.1 MNF couplers
Owing to the strong evanescent field, a MNF can be efficiently coupled to photonic or plasmonic nanowires within a short interaction length when they are brought in close proximity, which can be used for deriving a variety of MNF-based couplers with high compactness.
When integrated with a low-index substrate, optical couplers can be assembled with silica MNFs. For example, using a silica aerogel as the substrate, Tong et al. reported an X-shape structure assembled from two 420-nm-diameter MNFs. With an overlap <5 μm, the structure working as a 3-dB splitter with an excess loss of <0.5 dB . For high-index MNFs (e.g., tellurite glass MNFs), the light can be well confined and guided along the MNFs even supported by common substrates such as silicate glass or MgF2 crystal, which offers enhanced mechanical robustness and great convenience for handling compared to silica aerogel substrate . Figure 10A1, A2 shows an optical coupler assembled using two tellurite glass MNFs (with diameters of 350 and 450 nm, respectively) supported by a silica substrate with a refractive index of 1.46. When 633-nm-wavelength light is launched into the bottom left arm, the coupler splits the flow of light in two, with an interaction length of <4 μm and virtually no excess loss (no scattering is observed around the coupling area). Also, the MNFs can be integrated with semiconductor or metal nanowires through near-field coupling, to fabricate various hybrid nanophotonic components [35, 126], as shown in Figure 10B1–D2.
4.2 MNF MZIs
The MNF MZI is of particular interest owing to its compact-size and high-sensitivity, which may find applications in nanophotonic circuits and devices including sensors, modulators and filters. In 2008, Li et al. reported a MNF MZI assembled from two silica/tellurite glass MNFs, with footprints down to tens of micrometers (Figure 11A) . As-assembled MNF MZI showed good interference fringes with extinction ratios of 10 dB, and the path-length difference could be tuned by micromanipulation. Instead of using straight MNF as one arm of the MZI, Chen et al. proposed a novel hybrid MNF MZI using a knot resonator as an alternative, achieving a higher Q-factor of ~15,000 and extinction ratio of ~15 dB compared to the single knot resonator and single MZI . To enhance the device stability and robustness, embedding the MNF MZI in low index polymer is also investigated, which exhibit a larger FSR and a slight degradation in transmission loss and extinction ratio . Meanwhile, splicing microfibers via polymer nanowires in the contact regions was also proposed to enhance robustness and as-processed MNF MZI was also evaluated in air and water, both showing good performance . By integrating Ag nanowires with MNFs (Figure 11B, C), Li et al. demonstrated a hybrid photon-plasmon Mach-Zehnder interferometer (MZI) with Q-factor of 6×106 and extinction ratio up to 30 dB . Using this MZI, fiber-compatible plasmonic sensing was also demonstrated with high sensitivity and low optical power. Owing to the strong evanescent field of MNFs, a slight change of the ambient refractive index (RI) changes the microfiber propagation constant, which further changes the optical length, resulting in significant change in the transmission spectrum. In 2012, Wo et al. reported a RI sensor based on the MNF MZI with a RI sensitivity of about 7159 μm/refractive index unit (RIU) using 2-μm-diameter MNFs .
4.3 MNF gratings
MNF gratings have attracted wide attention owing to high-compactness, strong near-field interaction with surrounding materials, and high-resistance to mechanical and thermal shocks. Several fabrication techniques such as CO2 laser irradiation , excimer laser irradiation [149, 150], femtosecond laser exposure , etched corrugations , and focused ion beam milling [134–136, 152, 153], have been demonstrated to write gratings directly on as-drawn MNFs. Here we categorize typical MNF gratings into three types:
(1) Bragg gratings
MNF Bragg gratings (MNFBG) employ the similar mechanism of standard fiber Bragg gratings (FBG) that spectrally manipulate waveguided light by periodically modified refractive index along the length of the fiber. However, due to the much lower diameter, the index-contrast of the MNF grating is usually much higher. In 2005, relying on a wet chemical etch-erosion procedure, Liang et al. fabricated an MNFBG out of a 6-μm-diameter silica MNF, and used the MNFBG for index measurement in liquids . Later in 2010, using femtosecond laser pulse irradiation, Fang et al. reported an MNFBG based on a 2-μm-diameter MNF, which was used for RI measurements with a maximum sensitivity of 231.4 nm/RIU at a RI value of 1.44 . Around the same time, Zhang et al. reported a MNFBG written in a photosensitive microfiber using KrF excimer laser, and demonstrated a sensitivity of 102 nm/RIU at a RI value of 1.378 in a 6-μm-diameter MNF . In 2011, Liu et al. demonstrated a 518-μm-length 1.8-μm-diameter MFBG with evident transmission dip up to 15 dB and a high sensitivity of 660 nm/RIU (Figure 12) . Similarly, Kou et al. reported an all-silica first-order fiber Bragg grating fabricated by FIB milling, and demonstrated temperature sensing from room temperature to around 500°C with a sensitivity of nearly 20 pm/°C near the resonant wavelength of 1550 nm . More specifically, Y. Ran fabricated MNFBGs with diameters ranging from 3 μm to tens of μm, and found that the grating resonant wavelength dramatically blueshifts with diameter only when the microfiber diameter is below 10 µm . In addition, thinner fiber and higher order mode can result in higher RI sensitivity. For example, the RI sensitivity of the LP01 peak and LP21 peak of the MFBGs with diameter of 3.3 µm was ~165 and ~600 nm/RIU, respectively, at RI of 1.42. MFBG can be also used as wavelength-specific reflector and two MFBGs can form a high-Q Fabry-Perot (F-P) cavity [21, 136].
(2) Long period gratings
MNF long period grating (LPG) is also of interest in microfiber-based devices, circuits, and sensors. Using a femtosecond IR laser to periodically modify the surface of wavelength-diameter (1.5~3 μm) MNF, Xuan et al. reported a MNF LPG with periods of 10–20 μm, which exhibited strong resonant dip as high as 22 dB around 1330 nm with only 10 periods . Later in 2010, a 20-period LPG with a 27 dB attenuation dip was further demonstrated in a MNF with a diameter of about 6.3 μm. Also, the sensitivity for temperature and refractive index was also investigated, with sensitivity of -130 pm/°C and 1900 nm/RIU, respectively .
(3) Evanescently coupled gratings
Evanescently coupled gratings are manufactured by wrapping a microfiber on a micro-structured rod . The rod is designed with an inner hollow channel for microfluidic sensing and some air-holes arranged in the outer circle. By exploiting the large evanescent field in an inner channel, microfluidic refractometric sensors based on the evanescently coupled gratings can be achieved  with a sensitivity higher than 103 nm/RIU.
MNF-based resonators have attracted wide interest recently in a variety of applications ranging from optical filters, sensors to lasers. Recent progress in the fabrication of low-loss MNFs, as well as high-efficiency evanescent coupling between MNFs, has led to high quality factor (Q) resonators in various structures. Figure 13 shows typical MNF-based resonators, which are categorized into 4 types structures (loop, knot, ring and coil), as introduced below.
(1) Loop/knot/ring resonators
Loop/knot/ring structures are most commonly used in MNF resonators. By coiling or tying a MNF into a loop or knot, the light guided by the MNF can recirculate inside the closed-loop circular cavity through evanescent coupling at the joint area. The Q factor (the ratio of the wavelength to the full width at half-maximum (FWHM) ) of this kind of resonators can go beyond 100,000 in loop  ring  and coil  structures, with highest finesses (the ratio of the free spectral range (FSR) to the FWHM and relates to losses per resonator round trip rather than per optical cycle ) up to 100 in a knot structure resonator with double-ended taper fibers .
Typically, a loop cavity can be assembled by using micro-positioners to coil a MNF into a self-touching loop, as shown in Figure 13A1, A2. The loop resonator was first demonstrated by Caspar et al. in 1989 . By coiling an 8.5-μm-diameter biconical tapered fiber into a 2-mm-diameter loop and embedding the resonator in a silicone rubber, they obtained a resonance Q of 27,000 at wavelength of ~1.5 μm. In 2005, Sumetsky et al. reported a loop resonator assembled with a biconical MNF with minimum diameter down to 0.66 μm. With a loop length of 2 mm, a Q factor exceeding 15,000 and a finesse of 42 was demonstrated at the optical communication wavelength near 1.5 μm, which was soon improved to a loaded Q of 95,000 by the same group . In 2006, relying on extremely high coupling efficiency achieved through an adiabatically slow variation of the MNF diameter in the coupling region , Sumetsky et al. reported a Q of 120,000 in a MNF resonator with loop length of about 2 mm. In 2007, Guo et al. reported an copper-rod-supported loop resonator assembled by wrapping a 2.8-μm-diameter MNF around a 460-μm-diameter copper rod . With the copper-rod supporting, such structure exhibits high stability and flexibility of achieving critical coupling within a broad spectral range, with a maximum extinction of 30 dB and a Q of about 4000 around 1.53-μm wavelength (Figure 13A3). Meanwhile, the resonance wavelength can be tuned by applying an electric current through the copper rod. In 2010, Wang et al. theoretically investigated the polarization effect of loop resonators and found that the coupling at the joint regions was highly polarization-dependent due to lack of circular symmetry . In 2012, Ismaael et al. demonstrated resonantly enhanced third harmonic generation in a MNF loop resonator with an enhanced conversion efficiency of 1.8×10-5 compared to that of straight MNFs (3×10-6) . In 2012, Hu et al. demonstrated an approach of splicing the contact region of the loop resonator via fused polymer nanowires for enhanced robustness and stability .
Compared with the loop structure that is usually maintained by the Van der Waals or electrostatic forces in the contact region, a knot structure (Figure 13B1, B2) shows higher robustness and flexibility to change the knot diameter. In 2003, Tong et al. reported the first MNF knot resonator by coiling a 950-nm-diameter MNF to a 150-μm-diameter knot, with a Q-factor of 1500 around 1.5 μm wavelength . In 2006, Jiang et al. demonstrated a MNF knot resonator with Q factor as high as 57,000 and finesse of 22 (Figure 13B3) in free space . The possibility of supporting the knot resonator with a low-index MgF2 substrate was also investigated. To avoid perturbations such as vibrations or dust in the air, in 2007, Vienne et al. embedded MNF knot structures in low refractive index polymer, and investigated effect of host polymer on the resonators . Usually, knot resonator exhibit only one input/output end with untapered fiber, and the other end relying on evanescent coupling to the output/input port (Figure 13B1). In 2011, Xiao et al. demonstrated an optical microfiber knot resonators from thin tapered fibers (diameter down to 1 μm) linked to untapered fiber at both ends, which is highly favorable for achieving efficient light in/out coupling, resulting in a high-quality resonator with finesse up to 104 .
Benefitting from the high flexibility of the knot structure, a variety of MNF-based functional components or devices, including lasers [34, 52, 54], filters , and sensors [157, 208] have been reported. Using MNFs drawn from or integrated with gain media, a variety of active knot laser can be fabricated [34, 52, 54], as will discussed in Section 4.5 in details.
Besides the above-mentioned resonator structures with MNFs connected to the standard fibers, a free-standing ring resonator can be made by fusing and splicing two ends of MNFs into a closed ring (Figure 13C1, C2), which exhibits enhanced mechanical robustness and overall stability of the device [47, 56, 80, 81]. In 2008, Pal and Knox reported a technique of splicing microfibers using a CO2 laser with splice losses lower than 0.3% , and then further demonstrated a microfiber ring resonator with a Q-factor of about 25,000 by fusion splicing of the coupling region of a microfiber knot . In 2009, Wang et al. demonstrated a free-standing microfiber ring resonator with a Q-factor of 110,500 and a finesse of 15.3, by fusion splicing two ends of a 3.8-μm-diameter MNF into a 2.4-mm-diameter ring . In 2010, Li et al. reported a technique for fusion splicing nonsilica soft glass MNFs, and demonstrated a 1.34-mm-diameter phosphate glass MNF ring cavity with a factor of about 25,000 (Figure 13C3) .
(2) Multicoil resonators
Multicoil resonators are usually made by wrapping a microfiber around a low-index rod in several turns, as shown in Figure 13D1, D2. As three-dimensional (3D) resonators, multicoil resonators exhibit a number of novel properties, including high flexibility, mechanical robustness, great convenience in light in/out coupling, and easy handling with two ends naturally connected to standard glass fiber. The multicoil resonator was first proposed by Sumetsky in 2004  and experimentally realized in 2007 . Using the coupled wave equations, the analytical transmission properties of multicoil resonators can be predicted [138, 140–142]. In 2007, Xu et al. demonstrated a multicoil resonator by wrapping a 1.5-μm-diameter MNF on a low refractive index rod with diameter of ~560 μm in 2~4 turns . As-fabricated resonator exhibits a transmission spectrum with an extinction ratio of 10 dB and a FSR of 1 nm. To optimize the resonator and achieve higher Q, several options of geometry modification were theoretically investigated [142, 144], including wrapping the MNF around nonuniform rods (e.g., conical or biconical rods), varying the pitch of each turn or the coupling distance between adjacent turns. In 2010, Jung et al. demonstrated a uniform cylindrical MNF multicoil resonator with an improved Q factor up to 220,000 and an extinction ratio of 11.5 dB (Figure 13D3) . Applications of multicoil resonators to sensors will be discussed in Section 4.6.
(3) Resonators based on other strutures
Besides the above-mentioned ring-type structures, resonators based on several other structures have also been reported in recent years. In 2009, Wang et al. demonstrated all fiber F–P resonators based on Sagnac loop mirrors assembled with 1.42-μm-diameter tellurite microfibers, as shown in Figure 14A, B . As-assembled F–P resonators, with dimensions of hundreds of micrometers, show clear resonant responses with typical quality factor of about 5700, free spectral range (FSR) of about 1 nm, and a maximum extinction ratio of 18 dB (Figure 14C). The reflectivity of the loop mirror and the effective cavity length of the F–P resonator can be tuned by micromanipulation under an optical microscope. As shown in Figure 14D, the resonance peaks of transmission spectra of the F-P resonator shift before (a) and after (b) tuning the overlapping length of one of the Sagnac loop mirrors. Around the same time, Vienne et al. proposed a novel reef knot microfiber resonator using two MNFs, which possess 4 ports and can serve as an add-drop filter as well . Recently, Jung et al. demonstrated a MNF racetrack loop-resonator using two U-bent microfibers with diameter down to 2 μm. As-assembled racetrack resonator, with dimensions of several millimeters, exhibits a Q of 2.21×104 and a FSR of 0.11 nm .
4.5 MNF lasers
To construct a MNF laser, the typical approach is to incorporate active materials (e.g., rare-earth ions or laser dyes) into a MNF cavity structure, such as loop, knot, ring and F-P (FBG-FBG) cavities as discussed in Section 4.3 and 4.4.
In 2006, Jiang et al. reported active MNF knot lasers assembled using Er:Yb-doped phosphate glass MNFs (Figure 15A) . With a doping concentration of 1.25 mol % in Er3+ ions, single-longitudinal mode emission around 1.5 μm wavelength was obtained in a 2-mm-diameter knot, with a threshold of about 5 mW (for pumping light of CW 975-nm light) and a maximum output of 8 μW. Using numerical simulations, Li et al. showed that, by resonating of pump light, as well as the signal light along the MNF knot, it was possible to significantly reduce the threshold of the rare-earth-doped MNF laser to μW level, and subsequently increase the external quantum efficiency . Similarly, Song et al. reported a knot laser assembled using dye-doped polymer MNF. When optically pumped by pulsed 532-nm-wavelength light, lasing emission around 625-nm wavelength was obtained with a linewidth of 0.07 nm . More recently, by fusion splicing a rare-earth-ion-doped phosphate glass MNFs into a 3.5-mm-diameter closed-ring, lasing emission around 1.5-μm wavelength was observed with a linewidth of about 0.05 nm .
Besides doping gain materials inside the fiber, the strong evanescent field waveguided outside the MNF provides an alternative approach to dope active materials outside but in the optical near fields of the MNF. In 2007, by immersing a pure silica MNF knot into a rhodamine 6G dye solution, Jiang et al. realized a miniaturized MNF knot dye laser via evanescent-wave coupled gain (Figure 15B) . Under optical pumping (532-nm wavelength laser pulses), the 350-μm-diameter knot offered lasing emission around 570 and 580 nm wavelength, providing possibilities for integrating MNF lasers with optofluidic systems. Similarly, in 2009, by attaching zinc oxide (ZnO) nanowires to a silica MNF knot cavity, Yang et al. reported a hybrid structure laser with ZnO-nanowire serving as gain (Figure 15C) . Benefitting from the high-quality cavity of the MNF knot, the lasing threshold of the ZnO nanowire was as low as 0.2 μJ/pulse, which is much lower than that of a freestanding ZnO nanowire. It is also noticeable that, by attaching three distinct semiconductor nanowires (CdSe, CdS and ZnO) to a silica MNF, Ding et al. demonstrated a compact hybrid-structure red-green-ultraviolet three-color laser in a single MNF .
Recently, by incorporating carbon nanotubes or graphene as saturable absorber, a variety of mode-locked MNF laser were reported, providing an opportunity to generating femosecond or picosecond pulses from MNF lasers [57, 166–170].
4.6 MNF sensors
Owing to the large fractional evanescent fields guided outside the fiber core, light guided along an MNF can be very sensitive to environmental changes, leading to instant changes in optical intensity, phase or spectral components for optical sensing. According to the sensing mechanisms, MNF sensors can be summarized into two categories spectral/intensity detection, and phase sensitive detection.
(1) Spectral/intensity detection
Intensity detection is one of the simplest and mostly employed schemes in MNF optical sensors. By measuring the output intensity of a sensitive MNF with respect to the input intensity, the measurand can be retrieved. Benefitting from the large fractional evanescent fields of a waveguiding MNF, the intensity-dependent MNF sensor usually offers high sensitivity in either air or liquid solutions. In 2005, Polynkin et al. reported a MNF optical sensor for measuring the refractive index of liquids in microfluidic channels . By measuring the refractive-index-dependent leakage loss of 1.5-μm-wavelength light guided in a 700-nm-diameter silica MNF, they realized an accuracy of refractive-index measurement of 5.3×10-4. Around the same time, Villatoro et al. demonstrated a miniature hydrogen sensor that consists of a 1.3-μm-diameter silica MNF coated with an ultra-thin palladium film . Relying on the hydrogen-concentration-dependent transmission intensity of the MNF at 1550-nm wavelength, they successfully achieved a fast-response (~10 s) hydrogen sensor with low detection limit. In 2007, based on nanoparticle-induced Rayleigh–Gans scattering in a waveguiding MNF, Wang et al. calculated the possibility of detection single nanoparticles adsorbed on the surface of an MNF, and showed that, by optimizing the wavelength of the probing light and the diameter of the MNF, nanoparticle-induced scattering intensity can reach detectable level with possibilities for single-molecule detection . In 2007, relying on absorption of molecules adsorbed on the surface of a 500-nm-diameter MNF, Warken et al. reported an ultra-sensitive molecular sensor that was possible to detect sub-monolayers of 3,4,9,10-perylene-tetracarboxylic dianhydride (PTCDA) molecules at ambient conditions . In 2011, by integrating a 900-nm-diameter MNF into a 125-μm-wide microfluidic channel, Zhang et al. demonstrated a MNF sensor for chemical and biological applications (Figure 16A–E) . As shown in Figure 16F, using a broadband white light as probing light with power of about 150 nW, the absorbance of bovine serum albumin (BSA) was clearly observed with a detection limit down to 10 fgml-1. In addition, Figure 16F provides transmission intensity of the MNF response to analytes cycled with 500 pm methylene blue (MB) solution and ultrapure water, showing good absorbance reversibility of the sensor.
(2) Phase sensitive detection
Compared to intensity detection whose detection limit is usually determined by the instability of the transmission system (e.g., power fluctuation of the probing light and drifting of the propagation properties of the fibers), phase sensitive detection measures the wavelength shift (rather than the intensity) of the spectral response, and thus offer much better stability of the sensing system. In 2005, Lou et al. proposed a Mach-Zehnder-based sensor assembled using two single-mode sub-wavelength-diameter silica MNFs, with one MNF serving as sensitive arm with a certain length of sensitive area exposed to the measurand. By calculating the refractive-index-dependent phase shift of 325-nm-wavelength light guided in a 200-nm-diameter silica MNF, they predicted a refractive-index detection limit of 6×10-4 within a sensitive length of 245 μm . In 2007, Shi et al. proposed using optical MNF loop resonators for ambient refractive index sensing, with optimized structural parameters, they predicted a detection limit down to 10-5 RIU . In 2008, Guo et al. demonstrated a copper-rod-supported MNF loop resonator for refractive-index sensing using a 2.1-μm-diameter MNF wrapping around a 480-μm-diameter copper rod . By measuring the resonance dip wavelength shift induced by the concentration change of the immersing liquid, sensitivity of refractive-index measurement of 1.1×10-4 and 1.8×10-5 were obtained in a low-concentration ethanol solution and high-concentration glycerol solution, respectively. Around the same time, Xu et al. reported a loop resonator refractometric sensor embedded in polymer and studied the dependency of sensitivity on the MNF diameter and coating thickness . Later, the same group demonstrated a refractometric sensor based on optical microfiber coil resonator and achieved a sensitivity of about 40 nm/RIU by using a 2.5-μm-diameter MNF wrapping around a 1-mm-diameter rod with a total sensing length of about 50 mm . In 2009, Scheuer proposed an optical rotation sensor based on a fiber microcoil resonator. Based on the combination of slow-light and conventional propagation effects, an enhancement of the rotation-detection sensitivity by orders of magnitudes (up to 4) was obtained theoretically . In 2011, Wu et al. reported two fiber-optic interferometric humidity sensors based on silica/polymer microfiber knot resonators using silica/polymer MNFs without any humidity-sensitive coating . The silica microfiber knot resonator sensor has a humidity sensitivity of ~12 pm/10%-RH within a linearity range from 15%-RH to 60%-RH, while the polymer microfiber knot resonators sensor has a humidity sensitivity of ~88 pm/10%-RH, with a linearity range from 17%-RH to 95%-RH. In 2012, Li et al. demonstrated an all-fiber magnetic-field sensor based on a device consisting of a microfiber knot resonator and magnetic fluid . By measuring the change of the resonance wavelength in sensor transmission spectra, they realized a minimal detectable magnetic-field strength of 10 Oe. Recently in 2013, Muhammad et al. proposed using non-adiabatic silica microfibers for displacement or strain and temperature sensing. By measuring the resonant wavelength shift, they achieved a displacement sensitivity of 4.2 pm/μm and a temperature sensitivity of 12.1 pm/°C with an excellent linearity for temperature measurement up to 800°C. Around the same time, Bo et al. demonstrated an optical microfiber coupler-based refractive index sensor using two 2.5-μm-diamter MNFs to assemble an X-shape coupler with a coupling length of 2 mm . As-assembled MNF coupler can achieve an average sensitivity of 2723 nm/RIU over the entire refractive index range from 1.3340 to 1.3800 and a highest sensitivity of 4155 nm/RIU over the range from 1.3340 to 1.3515.
4.7 More applications
Besides the microphotonic components and devices introduced above, more applications of MNFs, including optical nonlinear effects and atom manipulation, have been extensively explored in recent years. Owing to the miniaturized mode area [11, 18] and engineerable dispersion [11, 16, 211], MNFs exhibit enhanced nonlinear effects such as supercontinuum generation [9, 15, 17, 112, 113, 118, 119, 182], third-harmonic generation [183–188], bistability [46, 160], two-photon absorption [189, 190] with relatively low optical power. To obtain higher optical nonlinearity, many other materials with high nonlinearities (e.g., lead-silicate, bismuth-silicate, As2Se3 chalcogenide) have been drawn into MNFs for various purposes [82, 191]. In addition, sub-wavelength-diameter MNFs offer tightly confined evanescent field with high spatial gradients, which can be used to efficiently trap and guide atoms near the surface of the MNF [20, 59, 60, 63, 175, 176] and couple radiation atoms to the guided modes of the MNF [61, 62, 177]. Based on the full quantization of both the radiation and guided modes of the MNF, new possibilities for quantum optics have also been proposed [20, 62, 178].
So far, optical MNFs have been extensively investigated regarding their fabrication technique, optical properties, and photonic applications. By reducing the transverse dimensions of an optical fiber to the wavelength or sub-wavelength scale, these tiny fibers have offered a number of favorable properties for manipulating light on the micro or nanoscale, and served as a new platform for both scientific research and technological applications in nanophotonics. Based on their capability of waveguiding tightly confined evanescent fields with low losses, strong near-field interaction and miniaturized sizes, several new applications of optical MNFs in atom optics, plasmonics and optomechanics have recently been proposed and/or demonstrated, which may bring new opportunities for utilizing light beyond optics and photonics, and lead to a great future of fiber optics and technology.
The authors thank Yaoguang Ma for helps in numerical simulations. This work was supported by the National Basic Research Program of China under Contract No 2013CB328703, and the National Natural Science Foundation of China under Contract Nos 61036012 and 61108048.
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