Fig. 1. Overall description of optical MNFs in terms of characteristics and applications.

Fig. 2. (a) Structural diagram of a biconical optical MNF. SMF, single-mode fiber; $\mathrm{\Omega }$, tapering angle of the transition region; $D_{\mathrm{T}}$, fiber diameter in the transition region. (b) Tapering angle of a typical MNF (black squares) and calculated critical angle (red dots) as functions of local taper diameter at 1550-nm wavelength^[40].

Fig. 3. Typical flame-heated taper-drawing fabrication system. (a) Photograph of a flame-heated taper-drawing system for fabricating silica MNFs. Inset: close-up image of the flame nozzle. (b) Schematic (upper, not to scale) and experimentally measured (bottom) fiber diameter evolution of a biconical drawn silica MNF along the fiber length^[54]. The MNF has a diameter of about 930 nm and a uniform length of 9 cm. The diameter evolution of the tapering region (red circles) was measured by an optical microscope (upper insets), while that of the MNF (blue circles) was measured by a scanning electron microscope (bottom inset).

Fig. 4. Structural characterization of silica MNFs. (a) Optical microscope image of a 550-nm-diameter silica MNF. SEM images of (b) self-supporting bundle of MNFs assembled with silica MNFs with diameters of 140, 510, and 30 nm^[97], (c) 790-nm-diameter silica MNF with a smooth surface, (d) coiled 260-nm-diameter silica MNF with a total length of about 4 mm^[29], and (e) 360-nm-diameter silica MNF with a bending radius of 3 µm^[95]. (f) TEM image of the surface of a 330-nm-diameter silica MNF^[29]. Inset: electron diffraction pattern of the MNF.

Fig. 5. Typical electric heaters in fiber-drawing systems. Photographs of (a) a ceramic heater for drawing silica MNFs (NTT-AT, CMH-7022) and (b) a self-designed U-type copper heater for drawing soft-glass MNFs.

Fig. 6. Schematic diagram of the diameter-control technique in the fabrication of a silica MNF based on the mode-cutoff feedback^[39].

Fig. 7. Calculation of waveguiding modes in optical MNFs. (a) SEM image of a 400-nm-diameter tellurite glass MNF with a circular cross section^[56]. (b) Calculated propagation constant ($\beta$) of waveguiding modes in an air-clad silica MNF at a wavelength of 633 nm^[30]. Solid line: fundamental mode. Dotted lines: high-order modes. Dashed line: critical diameter for single-mode operation. (c) Electric fields of several waveguiding modes in a 600-nm-diameter silica MNF at 633-nm wavelength. (d) SEM image of a 900-nm-diameter CdS nanowire with a hexagonal cross section^[208]. $d_1$ and $d_2$ are the diagonal-circle approximation diameter and circular-area-equivalence diameter for nanowires with different cross sections, respectively.

Fig. 8. Optical waveguiding properties of silica MNFs. (a) $z$-direction Poynting vectors of the fundamental mode in silica MNFs with different diameters at 633-nm wavelength in 3D view (upper row) and 2D view (lower row)^[30,32]. (b) Diameter dependence of the waveguide dispersion of fundamental modes in silica MNFs at the wavelengths of 633 nm and 1.5 µm, respectively^[30]. (c) Calculated longitudinal electric-field intensity distribution of two evanescently coupled parallel 350-nm-diameter silica MNFs at 633-nm wavelength^[154]. The overlapping length between two MNFs is 4.8 µm. (d) Schematic diagram of two evanescently coupled identical parallel MNFs (upper row)^[190]. The lower row shows calculated cross-sectional electric-field intensity in the $x$- and $y$-polarizations of fundamental modes in the MNF $j$ ($j=1$ or 2). The radius $a$ of two identical MNFs is 200 nm, and the input light wavelength is 800 nm. (e) Schematic illustration of the crosstalk in two intersecting silica MNFs^[213]. (f) Calculated output patterns of 400-nm-diameter silica MNFs with flat, 30°-tapering-angled, and 60°-tapering-angled endfaces in air^[195]. The input light wavelength is set to be 633 nm. The white-line rectangles in (c) and (f) map the topography profile of the MNFs.

Fig. 9. Optical losses and absorption of optical MNFs. (a) Roughness-induced radiation losses in air-clad MNFs versus the perturbation period^[223]. The amplitude of the surface roughness is assumed to be 0.2 nm and the wavelength of the input light is 1550 nm. (b) Mathematical simulation model of a circular 90° bent MNF^[188]. Inset: topography profile of the bent MNF. (c) Electric-field intensity distributions in the $x–z$ plane ($y=0$) of a 450-nm-diameter MNF at a wavelength of 633 nm, with bent radii of (I) 5 µm and (II) 1 µm. The output mode profiles of the 5-μm and 1-μm bent MNFs at the P1 transverse cross planes in (b) are shown in (III) and (IV), respectively. The black solid lines map the topography profiles of the MNFs. (d) Bending losses of a 350-nm-diameter silica MNF (I-line, squares), 350-nm-diameter PS MNF (II-line, circles), and 270-nm-diameter ZnO MNF (III-line, triangles) at 633-nm wavelength (quasi-$x$ and quasi-$y$ polarizations) as functions of the bending radius. (e) Schematic diagram of combined effects of the fiber heating, mechanically tapering, and pulsed laser guiding processes on the structural changes of siloxane rings^[234]. Heating and mechanical stretching processes break the six-membered rings into highly strained three-membered rings. Given the bandgap value of silica ($\sim 9\mathrm{eV}$), using a laser with photon energy in the range of $\sim 4–8\mathrm{eV}$ can break the highly strained three-membered rings and generate oxygen-dangling bonds. (f) Defect-absorption-induced temperature rise of a 1.2-μm-diameter silica MNF as a function of the waveguiding power around 1550-nm wavelength^[54].

Fig. 10. Optical losses of silica and ${\mathrm{As}}_2{\mathrm{Se}}_3$ MNFs over the last 20 years^{[29,31,33,37,41–43" target="_self" style="display: inline;">–43,53,143,211,235–237" target="_self" style="display: inline;">–237]}.

Fig. 11. Optical propagation losses of typical optical micro/nanowaveguides with corresponding effective mode areas^{[32,37,235,238–240" target="_self" style="display: inline;">–240]}.

Fig. 12. High-power CW optical waveguiding in subwavelength-diameter silica MNFs^[54]. (a) High-power optical transmittance of a 1.1-μm-diameter MNF around 1550-nm wavelength, with a CW waveguided power from 0 to 13 W. (b) Calculated diameter-dependent maximum power density in the MNFs at a waveguided power of 1 W. Insets: cross-sectional power density distribution of 0.5-μm-diameter and 1.1-μm-diameter silica MNFs.

Fig. 13. Encapsulation of optical MNFs. (a) Schematic of an MNF embedded in a PDMS film on a glass substrate^[247]. Inset: photograph of an MNF-embedded PDMS patch attached to a human hand. (b) Photograph of an optical MNF sealed in an airtight 3D-printed acrylic box, filled with high-purity nitrogen gas^[54]. (c) Long-term optical transmission of the MNF presented in (b) around 1550-nm wavelength. The waveguided power of the MNF is 12 W. (d) Photograph of an as-fabricated MNF mounted on a U-shaped bracket, with two standard fiber pigtails fixed on both sides of the bracket through the glue. (e) Photograph of an MNF sealed in an air-tight box.

Fig. 14. Nonlinear optical properties of optical MNFs. (a) Wavelength dependence of the GVD with different MNF diameters. (b) Nonlinear coefficient of silica MNFs versus the fiber diameter at 532-nm wavelength. Spectra of the (c) SHG and (d) THG in a silica MNF (779 nm in diameter, 7 cm in length) pumped by a 5-W-power CW light^[54]. The optimal phase matching of the SHG and THG is achieved at wavelengths of 1558.2 and 1572.5 nm, respectively. SH, second harmonic; TH, third harmonic. Insets of (c) and (d) show optical microscope images of output spots of the SH and TH signals at the output end of the standard fiber connected with the MNF, respectively. (e) Supercontinuum generation in a silica MNF pumped by 532-nm-wavelength ns pulses^[31], with output far-field patterns from the MNF at (I) low and (II) maximum powers. The pattern in (II) was passed through 10-nm bandpass filters at the center wavelengths of (III) 633, (IV) 589, and (V) 450 nm.

Fig. 15. Mechanical properties of optical MNFs. (a) Dependence of fracture strengths of silica MNFs on the MNF radius $r$^[61]. (b) SEM image of a plastically bent silica MNF (800 nm in MNF diameter)^[321]. The sharp bent radius is less than 1 µm. (c) SEM image of a 170-nm-diameter tellurite glass MNF with sharp plastic bends^[56]. (d) Maximum plastic elongation of silica MNFs. The horizontal dashed line (purple) indicates a reference line of 1%^[323].

Fig. 16. Near-field optical coupling with 1D micro/nanowaveguides using silica MNFs. (a) Optical microscope image of optical coupling of a 633-nm-wavelength light between two tellurite glass MNFs with diameters of 350 (top arm) and 450 nm (bottom arm), respectively^[56]. Optical microscope images of a silica fiber taper coupled with a (b) 200-nm-diameter silver nanowire^[324], (c) 450-nm-diameter polyacrylamide MNF doped with fluorescein sodium salt (FSS-PAM MNF)^[110], (d) 170-nm-diameter CdS nanowire^[330], and (e) 4.4-μm-diameter ice MNF^[126]. The wavelength of the light launched from the left side in (b)–(e) is 633, 355, 473, and 500 nm, respectively. In particular, an obvious PL signal around the 550-nm wavelength of the FSS-PAM MNF is observed in (d). (f) Schematic of an MNF-coupled SNSPD for NIR wavelengths^[332]. (g) Optical microscope image of an SU8 capped tapered fiber placed on the fork silicon-nitride-waveguide (SiN WG) coupler for low-loss, high-bandwidth fiber-to-chip coupling^[337]. (h) Optical microscope image of a fiber-nanowire-silicon-waveguide cascade structure for efficient fiber-to-chip coupling^[338]. The operation wavelength ranges from 1520 to 1640 nm.

Fig. 17. Near-field optical coupling with 2D materials using optical MNFs. Schematic diagrams of silica MNFs coated with (a) thin layer of graphene^[345], (b) few-layer GaSe^[349], (c) ${\mathrm{MoS}}_2$ nanosheets^[351], and (d) hBN flakes^[352].

Fig. 18. Optical MNF as an invaluable tool for evanescent-wave coupling with micro-cavities. Schematic diagrams of the optical MNF-coupled (a) rare-earth-doped microsphere^[359], (b) silica microcylinder^[360], (c) silicon microdisk^[361], and (d) rare-earth-doped microbottle resonators^[362].

Fig. 19. MNF-based photonic components. Optical microscopic images of MNF-based passive optical components including (a) loop^[366], (b) knot^[54], and (c) ring^[378] resonators. (d) Optical microscopic image of an MZI assembled with two 1-μm-diameter silica MNFs^[395]. (e) SEM image of a Bragg grating inscribed on a 1.8-μm-diameter silica MNF^[401]. (f) SEM image of a plasmonic-photonic cavity with several Au nanorods deposited on a 2.2-μm-diameter silica MNF^[413].

Fig. 20. Typical MNF-based photonic sensors. (a) Schematic illustration of a single NP detection system, where a pair of identical MNFs is used (upper panel)^[439]. A diode laser with a wavelength of 680 nm is employed as the probe light. The transmitted light is finally detected by a 125-MHz photodetector and monitored by an oscilloscope. Typical optical transmission of an MNF during a time interval of 10 s when the PS NPs are binding to the surface of the MNF one-by-one (lower panel). Each data point is the average of 250 values of measured transmitted power during 20 ms, and the red curve is for guiding the eyes. (b) Schematic illustration of a microchannel-supported polymer-MNF-based gas sensor^[112]. A laser with a wavelength of 532 nm is coupled into a 250-nm-diameter PANI/PS MNF with fiber tapers. The time-dependent absorbance of the sensor to cyclic ${\mathrm{NO}}_2/\text{nitrogen}$ exposure with ${\mathrm{NO}}_2$ concentration from 0.1 to 4 ppm is shown in the lower panel. Inset: dependence of the absorbance over the ${\mathrm{NO}}_2$ concentration ranging from 0.1 to 4 ppm. (c) Schematic illustration of a gelatin layer coated silica MNF for relative humidity sensing^[499]. The transmitted light intensity of the sensor at 1550 nm wavelength in the range of 9%–94% relative humidity, and the typical time-dependent transmittance of the sensor when relative humidity jumps from 75% to 88% are shown in the lower panel. (d) Plasmonic-nanostructure-activated MNF biosensor^[510]. Images in the lower panel demonstrate that the sensor can not only detect cancer cells, but also treat cells through cellular photothermal therapy. (e) Schematic illustration of a skin-like wearable MNF-based sensor^[247], constituting of an 80-μm-thickness PDMS film, a 980-nm-diameter MNF, and a glass slide. The response to the pressure of 2.1, 1.3, 0.2, and 0.1 Pa, and the temporary response to forced oscillation frequencies of 1, 4, and 20 kHz are shown in the lower panel. (f) Optical detection of cardiovascular vital signs (upper panel) based on the PDMS-packaged-MNF pulse-wave signal sensing principle shown in the lower panel^[517].

Fig. 21. Optical MNF optomechanical systems. (a) Schematic illustration of the light-control-light process in an MNF nano-optomechanical system^[91]. The evanescent-field coupling of the pump light (at a wavelength of ${\lambda }_{\mathrm{p}}$) to the substrate generates a repulsive optical force to push the MNF far away from the substrate, allowing the signal light (at a wavelength of ${\lambda }_{\mathrm{s}}$) to pass through with less loss. (b) Time-sequential optical microscope images of 3-μm-diameter PS particles propelled along a 950-nm-diameter MNF in the deionized water at 1-s intervals^[532]. The wavelength of the input light from the left side is 1047 nm. (c) Schematic illustration and time-lapse-compilation images of light-induced rotation of 3-μm-diameter PS particles around a 700-nm-diameter MNF in the deionized water^[540]. The counter-propagating lights from both sides come from the same source at 1064-nm wavelength, with a helicity parameter $\sigma =+1$. (d) Sequencing optical microscope images showing optical propelling of an oil droplet ($11\mathrm{\mu m}\times 10\mathrm{\mu m}$ ellipsoid) along a silica MNF (1 µm in diameter) at an interval of 1.2 s^[54]. The input CW light (0.7 W in power) is coupled and waveguided along the MNF from left to right. (e) Schematic of pulling a hexagonal gold plate (5.4 µm in side length and 30 nm in thickness) up on a tapering-profile silica MNF (6° in cone angle) near the tapered end^[541]. The photophoretic pulling force originates from the light-induced thermal effect. (f) Schematic of optical selection and sorting of single nanodiamonds along an optical MNF in pure water^[546]. When two different-wavelength lasers counter-propagate along the MNF, a nanodiamond can be trapped by the gradient force and transported by the absorption and scattering forces. The scattering forces can be cancelled out by choosing applicable laser power and in this case, the movement of the nanodiamond depends on the absorption cross section.

Fig. 22. Optical MNF-based fiber lasers. (a) Single-longitudinal-mode laser emission in an ${\mathrm{Er}}^{3+}/{\mathrm{Yb}}^{3+}$-doped phosphate glass MNF knot^[391]. Inset: optical microscope image of the MNF knot. Clear green upconverted photoluminescence is excited by a 975-nm-wavelength light. (b) Output spectrum of the hybrid photon-plasmon lasing emission in a Au-nanorod-coupled dye-doped polymer MNF structure^[417]. The insets show the optical microscope image (left) and SEM image (right) of the lasing structure (2 µm in MNF diameter). (c) Schematic of a mode-locked ${\mathrm{Yb}}^{3+}$-doped ultrafast fiber laser integrated with silica MNFs inside and outside the laser cavity (upper panel)^[83]. WDM, wavelength division multiplex; ISO, isolator; PBS, polarization beam splitter; $\lambda /4$ ($\lambda /2$), quarter-(half)-wave plate. The middle panel shows the output spectra of fiber lasers with (red solid line) and without (blue solid line) the dechirping MNF outside the cavity. For reference, the output spectrum of the fiber laser without the intracavity MNF is shown in the black dashed line. The bottom panel shows interferometric autocorrelation signals of fiber lasers with (red) and without (blue) the dechirping optical MNF. (d) Schematic of a high-repetition-rate ultrafast mode-locked laser based on a hybrid plasmonic MNF resonator (upper panel)^[374]. Insets: optical microscope image of the employed MNF knot resonator and SEM image of the MNF. The output spectrum of the fiber laser in the middle panel manifests that the generated pulses have a high repetition rate of 144.3 GHz around 1550-nm wavelength. The bottom panel shows the corresponding autocorrelation trace.

Fig. 23. MNF-based atom optics. (a) Schematic of the MNF-based atom trapping in the evanescent field (upper panel)^[559]. Fluorescence image of a trapped ensemble of cesium atoms (lower panel). (b) Transmission spectrum of a probe beam waveguided along the MNF after loading the trap (black squares)^[559]. Green line: the measured spectrum of a magneto-optical trap (MOT) cloud. Red line: theoretical fit. (c) Schematic of storage of MNF-guided light based on the EIT in an evanescent-field configuration^[573]. An ensemble of cold cesium atoms is spatially overlapped with a silica MNF (400 nm in diameter). The signal pulse to be stored is waveguided inside the MNF while the control light propagates outside the MNF with an angle of $\sim 13°$. (d) Transmitted pulses with different control powers in (I). The reference is measured in the absence of atoms. (II) Storage and retrieval processes. In the absence of the control field, the blue and purple points give the transmitted pulses without and with atoms. The red data indicate the memory sequence, showing leakage and retrieval. The black line represents the control timing. After the end of the input pulse, the reference and absorption curves are superimposed and correspond to the background noise level. (III) Normalized efficiency versus the control linear polarization angle. The zero-angle corresponds to a vertical polarization. (e) Schematic of a fiber ring cavity containing an MNF section for collective strong coupling of cold atoms with a cavity mode^[576]. DM, dichroic mirror; APD, avalanche photo diode. (f) Normalized transmission of the cavity as the probe laser frequency is scanned across the atomic resonance with input powers of 30 pW and 2.3 nW. The blue circles show data for a cavity in the absence of atoms with a Lorentzian fit. The red crosses correspond to an ensemble of atoms interacting with the cavity mode, with the theoretical fit shown as a red solid line.