Particle trapping with optical nanofibers: a review [Invited]

Optical trapping has proven to be an efficient method to control particles, including biological cells, single biological macromolecules, colloidal microparticles, and nanoparticles. Multiple types of particles have been successfully trapped, leading to various applications of optical tweezers ranging from biomedical through physics to material sciences. However, precise manipulation of particles with complex composition or of sizes down to nanometer-scales can be difficult with conventional optical tweezers, and an alternative manipulation tool is desirable. Optical nanofibers, that is, fibers with a waist diameter smaller than the propagating wavelength of light, are ideal candidates for optical manipulation due to their large evanescent field that extends beyond the fiber surface. They have the added advantages of being easily connected to a fibered experimental setup, being simple to fabricate, and providing strong electric field confinement and intense magnitude of evanescent fields at the nanofiber’s surface. Many different particles have been trapped, rotated, transported, and assembled with such a system. This article reviews particle trapping using optical nanofibers and highlights some challenges and future potentials of this developing topic.


Introduction
Trapping of particles using radiation pressure was first reported by Arthur Ashkin in 1970 [1] by using two counter-propagating laser beams.Subsequently, in 1986, Ashkin et al. invented a technique for trapping and manipulating particles using a single, tightly focused Gaussian beam, known as the 'optical tweezers (OT)' [2].Since then, this technique has spread to many interdisciplinary applications in micro-nanophotonics, biophotonics, biochemistry, and bio-medicine [3,4].The advantages of traps based on optical tweezers are that they are targeted, nondestructive, noninvasive, and allow for contactless manipulation of individual small particles.Hence, they have been used to trap a wide variety of materials, including viruses [5], DNA [6], aerosols [7], microbubbles [8], semiconductor nanowires [9], coral cells [10], marine microplastics [11], and cosmic dust particles [12].A recent roadmap on optical tweezers provides clear perspectives on the direction this field is likely to take in the coming years [13].
Although a very popular manipulation tool, conventional optical tweezers possess multiple disadvantages, including a bulky focusing objective and optical system, an inflexible micromanipulation process, diffraction limitations for trapping nanoparticles, and particle repulsion from the trap if the material has a refractive index lower than that of the environment or is strongly absorbing.Incorporating optical fibers into a conventional optical tweezers setup has allowed researchers to overcome many of these limitations and many reviews on the topic exist [14][15][16][17][18].The incorporation of optical fibers can be further enhanced due to the fact that their geometry can be changed to produce optical micro-or nanofibers (OMF or ONF) [19], fiber tips or tapered fiber tips [20][21][22], structured fiber tips [23,24], or optical fiber rings [25].These fiber-based structures enable the realization of optical traps with multiple functions and offer the user somewhat higher flexibility and precision.
Optical nanofibers (ONF), i.e., fibers with a diameter comparable to or smaller than the wavelength in vacuum of the guided light, are particularly interesting due to the nature of the evanescent field extending from the fiber's surface [26].As a result, ONFs have become a versatile tool for particle trapping and propulsion [27][28][29][30][31][32].Moreover, particle trapping, rotation, or manipulation can be achieved using structured light (using higher-order fiber modes [33,34] ) or even via (spin or orbital) angular momentum of light in the evanescent field [35].Most research related to this topic has focused on the fundamental guided mode within the ONF, but there are some exceptions as we will discuss in the following.Different methods of optical trapping, propulsion, and manipulation of particles using ONFs are depicted in Figure 1.In addition, due to the transfer of angular momentum of the evanescent field to the particle, spinning (around the particle axis) and rotation (around the fiber axis) of the particle may be observed under certain experimental conditions.While there are multiple fiber-based trapping methods, in this review, we focus on progress in optical trapping and manipulation using optical nanofibers due to the unique features of the evanescent field.This article is organized as follows: Firstly, we briefly introduce ONFs and discuss some of the advantages of using ONF-based trapping over conventional optical tweezers.This is followed by a discussion on how an ONF can be fabricated and a presentation of the optical forces and torques acting on a particle near an ONF's surface.The third section discusses the optical trapping of different particles and their potential applications.It begins with a review of single isotropic microparticles trapped and propelled along the ONF's surface.We also discuss the use of the angular momentum of the ONF's guided mode as an additional handle to precisely control and rotate particles around the nanofiber axis.Next, we discuss multiple particle trapping and optical binding effects using an ONF, followed by its applications to trapping and sorting of multiple cells and bacteria.Finally, we discuss the optical trapping of anisotropic and complex composition particles, such as NV-center diamonds and Janus particles, followed by the conclusion and future perspectives on this research topic.

Optical forces near the surface of an optical nanofiber
Optical tweezers are generated by a tightly focused laser beam using a high numerical aperture (NA) objective, which allows one to hold and manipulate micrometer-or nanometer-sized particles.Conventional optical tweezers have fundamental operational constraints due to the diffraction-limited spot size of the trapping beam.Additionally, trapping of particles with nonuniform refractive indices, such as Janus particles, in a stable manner is nontrivial as the particles are rapidly repelled from the trap [36].To overcome such limitations, there is a clear need to look beyond conventional optical tweezers to improve the trapping efficiency.Photonic crystal cavities [37], plasmonic double nano-holes [38], slot waveguides [39,40], and micro/nanofibers [41] are some systems that can solve the diffraction limitation by confining light locally to regions smaller than the diffraction limit.Thus, in the following, we focus our discussion primarily on optical nanofibers, with some references to microfibers.
In general, evanescent fields have been used for a multitude of applications, including largescale organization [42,43], long-range delivery [44], particle propulsion [45], and particle sorting [46].Due to their ease of alignment and integration with existing optical setups, optical fibers are a popular choice for optical trapping and manipulation [47].Fibers can have different configurations or geometries, such as tapered optical fibers [48], structured optical fibers [49,50], single fiber tips [51], tapered fiber tips [52], and lensed fiber tips [53].One such form -the subwavelength diameter fiber or optical nanofiber - [54] is of particular interest.In an ONF, a significant fraction of the guided mode is outside the fiber as an evanescent field, as shown in Figure 2(a) and (c).Figure 2(a) depicts the intensity profile of a 200-nm diameter silica nanofiber with 633-nm wavelength light and Figure 2(c) shows the transverse intensity profile of a 700-nm diameter silica nanofiber with 1064-nm wavelength light.The large evanescent field suitable for particle manipulation is clearly seen in the plot.Any particle in this evanescent field may interact with it, leading to many interesting phenomena.Optical nanofibers can be fabricated by heating a section of commercial fiber to a temperature above the softening point of silica and simultaneously pulling the fiber to achieve the required subwavelength diameter [56].One of the most crucial points in the fabrication process is the need for adiabatic tapering, which ensures minimal coupling between a propagating mode and other modes throughout the length of the tapered optical fiber.For a nonadiabatic taper, coupling may occur to modes with a similar propagation constant.As a consequence, the beat length between the modes is larger than the length-scale of the taper region; hence, the tapered fiber becomes lossy [57].As the fiber diameter is reduced, it is no longer adiabatic for higher-order modes, and they are not efficiently guided.Therefore, below a particular diameter, only the fundamental mode propagates through the fiber.Figure 2(b) shows a schematic of optofluidic transport of a particle trapped in the evanescent field of a nanofiber.The forces, F scat , F abs , represent the radiation pressure force responsible for the transport (left to right), and F grad is the trapping force that holds the particle near the nanofiber's surface.Based on the ratio between particle size and wavelength of light, the theoretical calculation of the optical forces can be divided into the following three regimes.First is the geometric or ray optics regime, where the particle size is much larger than the wavelength of light (a>>λ) [58].Second is the Rayleigh regime, in which particle size is much smaller than the wavelength of light (a<<λ) [59].Finally, the generalized Lorentz-Mie regime describes the situation where the particle size is comparable to the wavelength of light (a ≈ λ) [60].Here, we will limit our discussions to the trapping of microand nanosized particles, briefly discussing the optical forces for the Rayleigh and generalized Lorentz-Mie regimes.
For the Rayleigh regime, the dipole approximation holds where the particles can be treated as dipoles [59].In this regime, the net force on the particle is given by where F grad , F rad , and F sc are the gradient, radiation pressure, and spin-curl forces, respectively, α is the polarizability of the particle, E is the electric field, σ ext = σ scat + σ abs is the extinction coefficient, σ scat (σ abs ) is the scattering (absorption) cross-section, S is the Poynting vector, s d is the spin density of the incoming wave, and c is the speed of light in vacuum.Of the three forces, F sc is generally minimal in magnitude compared to the other two.It is a nonconservative force that arises from the polarization gradient of the electromagnetic field and plays a significant role in inhomogeneous light fields, such as tightly focused beams or evanescent fields.Again, for the generalized Lorentz-Mie regime, the total optical force acting on the particle can be obtained by integrating the Maxwell stress tensor over the particle's surface where n is an outward normal unit vector and T M is the Maxwell stress tensor given by where ϵ and µ are the permittivity and the permeability of the medium surrounding the particle, respectively, T ij is the force per unit area in the i th direction on an element of surface oriented in the j th direction and δ ij is the Kronecker delta function.The torque acting on the particle due to the optical force is given by For an optical nanofiber, the gradient force, F grad , which is directed radially across the fiber (see Figure 2(b)), is generated due to the temporary polarization of the dielectric particle in a nonuniform field [61].For a particle of refractive index higher than the surrounding medium, F grad tends to attract the particle toward the highest intensity region of the evanescent field and is responsible for radial trapping.Next is the radiation pressure, which consists of both scattering, F scat , and absorption, F abs , forces.These are responsible for the movement of the particle along the optical axis of the nanofiber.Figure 2(d) shows simulation results of the gradient force, F grad , (red line) and scattering force, F scat , (blue line) acting on a 3.13-µm silica particle that is placed in the evanescent field of a nanofiber in water as a function of fiber diameter [28].We see that the gradient and scattering forces have the highest magnitudes for fiber diameters of 600-nm and 470-nm, respectively.The magnitudes of both forces decrease beyond these values.When the nanofiber diameter is smaller than the cut-off value (250 nm in water at 1064 nm wavelength light), the evanescent field spreads out into the surrounding medium, and the penetration depth of the evanescent field tends to infinity.Consequently, the field is no longer viewed as tightly confined.This leads to a decrease in the electric field amplitude at the fiber surface and a corresponding decrease in the scattering and gradient forces.In contrast, for relatively large diameters, the electric field at the fiber surface is small as the mode is almost fully confined within the fiber, also resulting in a decrease of the two forces.[33].Therefore, similar to optical tweezers, particles can be trapped and propelled along the nanofiber waist region by guided light or locally confined by counter-propagating guided beams.

Particle manipulation with optical nanofibers
The idea of levitation, acceleration, and trapping of micron or nanometer-sized particles was originally presented by Ashkin et al. [1,2] in the context of an optical tweezers.Trapping using evanescent fields opens up several new possibilities.This section reviews particle trapping and propulsion using an evanescent field generated from an optical nanofiber (or microfiber).

Background
Kawata and Sugiura first demonstrated the movement of isotropic spherical polystyrene particles with diameters from 1 to 27-µm in the evanescent field of a high-refractive-index sapphire prism illuminated by a 1.06-µm YAG laser beam [62].Later, a polystyrene particle was trapped laterally in the vicinity of an evanescent field generated from a lithographically defined waveguide and then longitudinally moved along the direction of the waveguide channel [63,64].It was not until 2007 that polystyrene microspheres were trapped and manipulated in the evanescent field of a subwavelength waveguide [27,45], as shown in Figure 3(a).The authors justified shifting to the nanofiber system over the waveguide because the mode fraction of the field present as the evanescent field in an optical nanofiber is much larger than that of planar glass/Si 3 N 4 waveguides.In addition to lower insertion losses and flexibility in a 3D geometry, the evanescent field extends to longer distances than for the other two waveguides considered, as shown in Figure 3(b).

Isotropic particle trapping and propulsion
Optical nanofibers quickly became a new manipulation tool for particles [14,65].However, for any in-depth study on particle dynamics, it is important to precisely control the position of the particle relative to the ONF.Gusachenko et al. developed an integrated platform, combining an optical nanofiber and an optical tweezers system, to facilitate the controlled delivery of particles into the evanescent field region, thereby also enabling the trapping of particles in arrays [66].Trapping of spherical isotropic particles using the fundamental fiber mode depends on the particle size, as demonstrated by Xu et al. [67].The larger the particle, the larger the scattering and gradient forces acting on it, hence the faster and easier the trapping and delivery of such particles.Larger particles have a larger cross-section, thereby increasing their interaction with the evanescent field.In addition, the positioning of particles can be well-controlled if the environment (e.g., a fluid) flows in a direction opposite to that of the laser beam [68].In such a microfluidic system, the particles experience a viscous drag force exerted by the fluid flow, opposite to the scattering forces.When the scattering force equals the viscous drag force, particle motion is stopped, aiding in the realization of controlled positioning.
Maimaiti et al. showed that, if higher order fiber-guided modes (HOM) are used instead of the fundamental mode (FM), polystyrene particles were propelled up to eight times faster [61].HOMs have a larger evanescent field amplitude and longer field decay, increasing the sensitivity of the light-matter interaction and making it useful for applications requiring extreme sensitivities.On another note, conventional optical tweezers are restricted to the trapping of larger particles or higher refractive index particles due to the limits imposed by the diffraction of light.For stable trapping of lower index and/or diameter particles using such a diffraction-limited system, the power requirement would be very high, which can quickly denature the trapped particle.Daly et al. [40] developed a slotted micro-nanofiber (MNF) for evanescent field trapping and demonstrated confinement of 200-nm silica particles using 1.2 mW of power.The authors determined the trap stiffness by analyzing the transmitted signal through the fiber pigtails on either end of the tapered fiber.The electric field distribution at the center of the slotted fiber and either side of the fiber is shown in Figure 4

Isotropic particle spinning and rotation
Light can carry angular momentum, which, in general, is viewed as one of two types: spin angular momentum (SAM), possessed by light with circular polarization, and orbital angular momentum (OAM), manifested by light beams with a helical wavefront [69].When a circularly polarized, paraxial, free-space beam of light containing SAM interacts with a material object (absorbing or anisotropic), the object may spin around its own axis due to the transfer of angular momentum [70].In contrast, isotropic and non-absorbing particles may display orbital rotations when interacting with a beam containing OAM [71].In other words, the angular momentum of light can exert mechanical forces and associated torques on a material object.Conventionally, SAM is directed along the propagation direction (z) of a light field for a circularly polarized plane wave due to the rotation of the electric field components along the transverse plane (x, y).
In 2012, Banzer et al. experimentally demonstrated the transverse component of angular momentum by converting tightly focused, linearly polarized light into laterally segmented left and right circular polarization beams by using a segmented quarter-wave plate and a high NA objective.As a result, the longitudinal components of angular momentum canceled each other, while the transverse components were added, thereby generating a purely transverse angular momentum at the focal plane of the objective [72].Such a state of light was termed a 'photonic wheel.' In an evanescent field, generated using a Kretschmann configuration, if the electric field decays along x and propagates along z, the situation is quite different.For this scenario, Bliokh et al. explained the components of transverse SAM generated from an evanescent field for different states of polarization [73].First, one should consider that the imaginary part of the longitudinal and transverse components, (E z , E x ) and (H z , H x ), of a complex electromagnetic field are 90 • out-of-phase, respectively.This results in a cycloid-like projection of the electric and magnetic field distributions in the (x, z) plane.Second, due to the exponential decay of the evanescent field along the x-direction, the spin momentum rotations do not cancel each other.Therefore, multiple loops of the spin produce a transverse momentum and SAM in the xz-plane.The transverse momentum is proportional to the helicity of the incident field, while the SAM turns out to be helicity polarization-independent.Consequently, even supposedly linearly polarized evanescent wave can carry transverse SAM, whilst circularly polarized evanescent light can carry the above-mentioned polarization-independent transverse spin, the usual longitudinal spin, and the radial helicity spin polarization-dependent component that is perpendicular to the propagation direction, z [73].Hence, if we probe a material object in a linearly polarized evanescent field, the particle may experience radiation pressure and a polarization-independent transverse torque.Moreover, if we apply a circularly polarized evanescent field, the particle experiences the above-mentioned force and torque, together with a polarization-dependent transverse force and longitudinal torque [73].The effect of the spin and orbital angular momenta of light and their corresponding forces and torques acting on a particle in an evanescent field can, in principle, be studied [74], though the literature regarding this is not very rich.Here, we focus on the effects observed when using the evanescent field from a tapered optical fiber.
In 2016, Antognozzi et al. directly observed transverse spin-dependent angular momenta and their associated forces via a fN-resolution nanocantilever, immersed in the evanescent field above a total internal reflecting glass surface [75].Unlike the conventional scattering force, the transverse spin-dependent force is relatively weak.The authors used a planar dielectric nanocantilever and measured the force component normal to its plane, which was neither the scattering nor the gradient force.Henceforth, it was understood that material objects placed in such an evanescent field can experience both polarization-dependent and polarization-independent transverse spin forces.
For an optical nanofiber, the guided light is a vector beam, and its polarization is not uniform over the cross-sectional xy-plane.To get insight into the relationship between the linear and angular momenta of light, Le Kien et al. [76,77] decomposed the Poynting vector of the evanescent field into the spin, orbital, and surface parts, and, subsequently, calculated the angular momentum of the axial and azimuthal components of guided light in an ONF.The authors found that a substantial orbital component appears and reaches its maximum value of approximately 0.25 ℏ when the fiber radius is about one-fourth of the light wavelength for a quasi-circularly polarized fundamental mode.This OAM can be transferred to particles trapped in the nanofiber's evanescent field.The theoretical axial and azimuthal optical forces acting on a dielectric spherical microparticle near the nanofiber's surface were proposed by Le Kien and Rauschenbeutel in 2013 [78].In addition, the universal spin-momentum locking of evanescent waves was demonstrated [79].This spin-polarization dependence of optical azimuthal force and torque was experimentally demonstrated in 2020 [35], where the total angular momentum of a guided fundamental light mode induced rotation of dielectric microspheres around an ONF.The experimental setup is shown in Figure 5(a).A 660-nm diameter ONF was immersed in deionized water containing 3-µm polystyrene spheres.This was integrated into a conventional optical tweezers setup.A 1064-nm laser beam was coupled into both pigtails of the nanofiber and, using free-space polarization compensators [PC in Figure 5(a)], the polarization state was controlled at the nanofiber waist.A 3-µm polystyrene particle was trapped using the tweezers and placed near the waist of the nanofiber, see inset to Figure 5(a).The orbital motion of the particle was observed for quasi-circularly polarized light (σ = +1), see Figure 5(b, upper).When the sign of σ was reversed, the particle rotated in the opposite direction, see Figure 5(b, lower).Interestingly, for elliptical polarization with |σ|<1, the trajectory of the particle was changed and acquired a figure-of-eight shape [35].Later, Tkachenko et al. experimentally demonstrated the transverse spin of light of the evanescent field by its contribution to the motion of a probe anisotropic particle, which was held and spun by optical tweezers near the surface of the nanofiber [80].There are two types of circular motion of the particle: one is the rotation of the particle around the fiber axis, and the other is the spinning of the particle around its own axis.The former (particle rotation) appears due to the extrinsic torque acting on the particle, created from the transfer of total (spin and orbital) angular momentum of the evanescent field to the particle.The latter (particle spinning) arises due to the intrinsic torque generated from the spin angular momentum.These observations open up a new direction toward optical micromanipulation and circular motion of material objects using the transverse spin-dependent radiation force in the evanescent field of an ONF.Such a microparticle-nanofiber system could be implemented in microfluidics or nanophotonics-based applications.

Multiparticle trapping and optical binding
Aside from single-particle trapping, multiple particles are also of interest due to various phenomena that can be revealed [81].In 1989, Burns et al. first demonstrated optical binding of multiple particles using an intense laser beam [82].Optical binding is a phenomenon that arises due to the modification of the incident light field in the presence of multiple, simultaneously illuminated objects.As a result, the objects mutually optically interact and self-arrange into an ordered configuration.Optical binding can also be studied using the evanescent field from an ONF.This was first reported on by Frawley et al. when they observed optical binding in a chain of dielectric microbeads trapped near an optical nanofiber [28].They demonstrated optical propulsion and self-arrangement of chains of one to seven silica particles of diameter 3.13-µm, with the interparticle distance decreasing as the number of beads in the chain increased.Later, Maimaiti et al. studied one-dimensional longitudinal optical binding interactions of chains of 3-µm polystyrene particles in the evanescent field when using both fundamental and higher order guided modes (LP 11 mode family) of a 2-µm diameter tapered fiber with a propagating wavelength of 1064-nm [29].They experimentally observed the self-ordering, speed variation, and long-range interactions of particles in the chain, thereby revealing the strong optical binding effect between the particles.The authors simulated the effect using a tritter scattering-matrix approach, and the results for a one-dimensional array of N particles scattering light when in the evanescent field from HOMs for a 2-µm fiber are shown in Figure 6(a).The forces, F n (white arrow) and F p (red arrow) represent the attractive and repulsive binding forces, respectively.Micrographs of the particle speed are shown in Figures 6(b) and (c), for fundamental and HOM propagation, respectively, with particles in the chain labeled from p 1 to p 5 .The authors demonstrated experimentally and numerically that a higher-order mode in the microfiber was more efficient regarding multiple particle trapping, faster particle propulsion, and stability.Also, it provided better control over each trapped particle, all of which could prove promising for biological applications.
Nanoparticle trapping has also received significant attention.For example, the optical identification and characterization of nanoparticles to provide information on particle type, composition, etc., is of general interest.However, the optical detection of nanoparticles is challenging due to the diffraction limit, but it can be overcome using waveguide technology.Moreover, various applications, like artificial quantum emitter fabrication, biological particle detection and separation, and gas separation, require filtering of the particles by size.Optical filtering methods [83] have gained popularity due to their inherent flexibility.Sadgrove et al. demonstrated an optically induced sieve effect for filtering nanoparticles near a tapered optical fiber [84].The filtering was performed using the difference in the variation of radiation pressure force as a function of wavelength for the evanescent field of the fiber.Using gold nanospheres (GNSs) with significant size differences ensured that trapping occurred at different laser powers.This result is somewhat analogous to an optical sieve effect, where particles of one size are trapped while the others are transported.Subsequently, Watanabe et al. [85] incorporated a two-color tapered optical fiber trap, similar to that for cold atoms [86][87][88][89], where the evanescent field creates a three-dimensional trapping potential.Using this method, they confined colloidal nanoparticles and adjusted their positions by controlling the relative powers of the two light fields.They also trapped quantum dots together with gold nanoparticles so that the trapping fields doubled the excitation field for the quantum dots [85].

Bioparticle trapping and sorting
Confining individual living micro-organisms, and manipulating and delivering them to a certain location is of significant interest in studying their biochemical processes, such as metabolism or the response of a cell to external stimuli.Ashkin and Dziedzic extended the first optical tweezers setup to trap individual tobacco mosaic viruses and bacteria [5].Furthermore, Ashkin et al. observed the reproduction of Escherichia coli (E.coli) bacteria and yeast cells within the optical traps [90].Lei et al. demonstrated photophoretic assembly and propulsion of E. coli bacteria along the light propagation direction [19], whereas Rong et al. took this one step further by rotating the bacteria using higher order modes [91] and a seven-core tapered fiber.Most optical manipulation of biological samples has been done with conventional optical tweezers or using fiber tips.One of the first reported trappings of biological samples in the evanescent field of a nanofiber was by Xin et al. [92], as shown in Figure 6(d)-(f).They immersed the nanofiber of diameter 600-nm in a microfluidic channel for controlled positioning of E. coli bacteria by sending laser light of wavelength 980-nm with a power of 25 mW into the nanofiber.Another important biosample is liposomes.Lipid vesicles or liposomes are artificial spherical particles primarily used for drug delivery due to their many advantages.However, their trapping and manipulation are challenging, as the contrast in the refractive index of the liposome is confined to its membrane, limiting the region that experiences an optical force to a minimum.This limitation was overcome by reducing the diameter of an optical nanofiber to provide a stronger evanescent field, leading to better trapping and propulsion [93].
An interesting study by Liu et al. demonstrated how E. coli bacteria could be used to form an optical conveyor belt between dual fiber tips [30].The authors trapped and propelled polystyrene particles and a human red blood cell, as shown in Figure 6(g).Such a method may allow for in-vivo transportation of drugs if extended to mammalian cells.Optical tweezers have helped scientists understand many biological processes at the cellular level [94,95].This research field is quite vast and rapidly growing; incorporating an optical nanofiber into the optical tweezers provides an additional degree of manipulation for studying particle dynamics and transporting particles over larger distances.

Composite and anisotropic particle trapping
Inhomogeneous or anisotropic particles possess one or multiple anisotropies in the morphology, composition, interfacial or physical, and optical properties.Examples of such anisotropic particles include nonspherical particles, patchy particles [96], colloidal crystals with various shapes, Janus particles [32], and so on, with diameters ranging from hundreds of nanometers to a few micrometers.In optical nanofiber trapping, the size of the particles being trapped is determined by the penetration depth and amplitude of the evanescent field available for interaction.Therefore, optical trapping and manipulation of such anisotropic micro-and nanoparticles using ultrathin fibers have attracted significant interest [97,98], as the particles may prove suitable for manipulating and drug delivery, self-assembly, and to predict applications of biological particles, which may have an arbitrarily complex refractive index.Aside from applications, these complex particles can also be used to gain fundamental insight into the interaction between matter and the evanescent field.Combining nanocrystals and nanoparticles with waveguide technology has led to a versatile tool in nanophotonics research [99][100][101].In 2018, Leménager et al. used single and dual fiber tip optical tweezers to trap spherical YAG:Ce 3+ particles of 300-nm and 60-nm diameter and lanthanide-doped NaYF 4 nanorods with dimensions 640-nm to 1.9-µm [52].With a similar setup, Minz et al. demonstrated that using a quasi-Bessel beam in a dual fiber tip optical tweezers, long-range manipulation of nanorods could be obtained [24].In general, nanorods are of interest because they could be used to realize single photon sources, in bio-imaging, or in single-molecule spectroscopy.
Nitrogen vacancy centers (NVCs) in nanodiamonds (NDs) have properties such as high sensitivity and no photobleaching.A nondestructive method to sort NDs with and without NVCs is important.NDs exhibit quantum resonances of point defects.In addition to the gradient and scattering forces exerted by an optical tweezers setup, a third force -the quantum resonant absorption force -is exerted on such nanomaterials.Fujiwara et al. demonstrated selective transportation of NDs along an optical nanofiber and they were able to sort the particles according to whether they had NVCs or not, as shown in Figure 7(a) and (b) [31].Using a 400-nm ONF and two counter-propagating beams (one at 532-nm and one at 1064-nm), the resonant absorption and scattering forces were balanced.The NDs with NVCs moved in one direction, while those without NVCs moved in the opposite direction.
We now move our discussion to another important anisotropic particle, the Janus particle [102][103][104], that is a unique composite, anisotropic particle composed of two or more parts with distinct chemical and physical characteristics.The broken symmetry aids in the emergence of properties inconceivable for symmetric and/or homogeneous particles [105].The term was first coined by Casagrande et al. in 1989 when they fabricated particles whose surface was half hydrophilic and half hydrophobic [102].The term gained popularity when, in 1991, de Gennes described particles called Janus grains in his Nobel lecture [106].Janus particles possess unique properties and can be fabricated in many ways [103,[107][108][109] and, depending on the fabrication method, they can come in different structures, e.g.dimers, nanotrees, and nanocorals [110,111].Since its first introduction, the Janus particle has driven research interests due to its versatility, size-wise compatibility with living tissue [112,113], and eco-friendliness [114].Due to this, Janus particles have found numerous applications in sensing, biological motors, and cellular imaging [115].The multitude of applications implies the need for efficient manipulation of such particles.
Wang et al. were amongst the first to optically trap Janus particles in an optical tweezers [116].They used spherical Janus particles consisting of two different hemispheres of slightly different refractive indices.However, conventional optical tweezers are not the best option for trapping Janus particles with metallic parts due to the high absorbance by the metal, causing the particle to be pushed from the trap.This absorption causes a local temperature gradient around the particle, known as thermophoresis [117].This phenomenon can be exploited to form a microscale elevator, as shown by Nedev et al. [118].In 2020, Gao et al. demonstrated a novel angular trapping method for spherical Janus particles consisting of two hemispheres made of polystyrene (PS) and polymethyl-methacrylate (PMMA) [119].They observed that the hemispherical interface of the particle aligned itself parallel to the laser propagation direction and polarization direction.Recently, Erez et al. demonstrated the trapping and propulsion of a bowl-shaped Janus particle [120].Due to its unique shape, it was also used to demonstrate cargo loading and transport.
Unrestricted Janus particles assume a random orientation in the host environment.One method to make the induced propulsion directional is to use confined environments like polarization gradients, elastic forces, and gravity.As metallo-dielectric Janus particles move toward highergradient electric field regions, using evanescent fields should aid in manipulating Janus particles.Such trapping was demonstrated recently by Tkachenko et al., where they showed the manipulation of Janus particles by optical forces in the evanescent field of an optical nanofiber [32].The authors prepared the silica-gold Janus particles by using the evaporation coating method, where, initially, a loosely packed monolayer of silica microspheres was formed on a glass substrate by drop-casting them in an ethanol suspension and drying them under ambient conditions.Then, it was coated with a 5-nm-thick adhesion layer of titanium, followed by a few nanometer-thick ( 10or 20-nm) layer of gold.Finally, the authors detached the Janus particles from the substrate by sonication in Milli-Q-water.The authors demonstrated that the particles exhibit strong transverse localization on the nanofiber and a faster speed than all-dielectric particles of the same size.A schematic of the experimental setup is shown in Figure 7(c).A single-mode nanofiber of diameter 700-nm was immersed in a water suspension with a mixture of 3-µm silica and Janus particles, which were then separately trapped and placed the ONF via optical tweezers (beam 3 in Figure 7(c)).Two polarization compensators (PC), consisting of two quarter-wave plates, were used for maintaining the polarization along the ONF.A CMOS video camera was used for imaging the ONF and particles.Comparison of propulsion speeds between silica and Janus particles as a function of laser power are shown in Figure 7(d) and (e).The propulsion speed for Janus particles was always higher than for silica particles and both were proportional to laser power.More recently, Ciriza et al. demonstrated a highly-controllable micro-engine using a similar Janus particle (here, a gold-capped silica bead) by trapping it using circularly polarized light [121].This induced a moon-like rotation on the particle, causing it to rotate around the beam axis with the gold cap facing the center.The speed and orientation of this motion can be controlled by changing the ellipticity of the incoming beam.Extending this to optical nanofiber manipulation should provide an effective means for precise optical manipulation of Janus particles and a promising tool for future applications such as micro-or nanoscale actuators or transporters.

Conclusion and Perspectives
This article comprehensively reviews the progression of scientific and technical developments in the optical trapping and manipulation of particles using ultrathin, tapered optical fibers, with an emphasis on optical nanofibers.The integration of an optical tweezers with an ONF facilitates long-range, stable trapping and delivery of different targets to the trapping region.The trapping stability of dielectric microparticles could be improved by using structured guided light fields through the propagation of higher-order fiber modes in an OMF system.This has been exploited to explore optical binding for a number of dielectric microparticles.Such knowledge of interparticle binding and the associated chain-related multiparticle trapping can lead to a better understanding of large-scale particle conveyance as well as optical sorting.Moreover, an ultrathin fiber system can provide light confined in a circularly polarized fundamental mode, which carries both finite spin and orbital angular momentum.This provides us with extra degrees of freedom for particle spinning, rotation, and manipulation in the evanescent field of the ultrathin fiber.
In addition, ONF trapping has seen significant progress in biophysics, where trapping and propulsion of E. coli bacteria, lipid vesicles, or liposomes have been achieved.Although it is challenging to manipulate these living organisms in-vivo, ONFs can no doubt provide an opportunity for characterizing the dynamics of various living systems.Recently, optical trapping and manipulation of anisotropic and composite particles have also gained attention.In particular, Janus particles with different optical properties are ideal candidates for general applications in nano-and microdevices, such as micromachines, microvalves, and micropumps.The ONF could become an essential tool for optical trapping and propulsion of composite particles such as Janus particles and NV diamonds.
Optical nanofiber-based trapping provides a novel level of performance as it easily connects free-space beams with the tightly confined evanescent field.Despite the substantial applications of optical nanofibers for particle manipulation, there are some drawbacks.The evanescent field penetration depth limits the trapping and manipulation of particles to a particular size distribution.Moreover, photothermal effects may cause damage to the particle and/or to the nanofiber, which could be a problem if trapping absorbing materials.Trapping multiple particles leads to a substantial power drop along the fiber, making it difficult to estimate the actual optical force acting on each particle.In addition, nanofibers are very thin and fragile, making them difficult to handle or do any post-processing on them for more advanced photonic tools.However, recent experimental developments could overcome this difficulty.For instance, the integrated platform of optical tweezers and nanofibers is a powerful asset for trapping multiple particles and for spectroscopic studies where the ONF can be used both as an active or a passive excitation probe.In addition, this combined system can be used for controlled optomechanical experiments to study the spin-orbit interaction of light by measuring the optical force and torque experienced by probe particles in the evanescent field.This can disclose the fundamental concept of the spin structure of the guided light in ONFs and, consequently, could impact the physics of momentum and spin in classical and quantum fields.One recent area of progress for optical nanofibers is the possibility of structuring the fiber itself by nanomachining, thereby incorporating cavities or metastructures within the fiber.This can increase the evanescent field at the waist region and allows for the possibility of generating a structured evanescent field that could significantly impact optical trapping and manipulation.Structured ultrathin fibers could become an essential tool for studying optical binding effects and make many exciting applications, such as migration, assembly, and separation of different particles, feasible.Many aspects of ONF-based trapping are still under development, but it clearly has a promising application potential for providing a versatile system that could help us to better understand both physical and biological phenomena in addition to revealing some underlying fundamental physics about tightly confined light.

Fig. 1 .
Fig. 1.The evanescent field in an optical nanofiber (ONF) can be used to trap and manipulate particles, including living cells.

Fig. 2 .
Fig. 2. (a) Intensity profile of a 200-nm diameter silica nanofiber guiding 633-nm wavelength light; reprinted with permission from [55] © Elsevier.(b) Schematic of the forces acting on a particle trapped in the evanescent field of a nanofiber.The directions of the forces are indicated by the arrows.(c) Transverse intensity profile of a silica 700-nm diameter nanofiber guiding 1064-nm wavelength light.(d) Gradient and scattering forces acting on a single 3.13-µm particle as a function of fiber diameter; (d) reprinted with permission from [28] © Optica.
(a).An SEM image of the slotted MNF and a representative image of a trapped fluorescent silica nanoparticle inside the slot are shown in Figure4(b) and (c), respectively.This geometry could be a promising device for spectroscopy measurements by passing probe beams of different wavelengths through the fiber and simultaneously capturing the transmission signal at the output pigtail.

Fig. 4 .
Fig. 4. (a) Schematic of a slotted micro-nanofiber (MNF), showing the field distribution of the fundamental mode (i) observed at either end of the fiber and (ii) at the center.(b) SEM image of a slotted MNF.(c) Image of a trapped red fluorescent silica nanoparticle with an outline of the slot for better visualization.All figures reprinted with permission from [40] © Optica.

Fig. 5 .
Fig. 5. (a) Schematic of the experimental setup with polarization compensators (PC) and quarter-wave plates (QWP) to control the polarization.Inset: A 3-µm polystyrene particle trapped near an optical nanofiber.(b) Time-lapse compilation of images showing the orbital motion of the particle in (a) around the optical nanofiber for left circular polarization σ = +1 (upper) and right circular polarization σ = −1 (lower).All figures reprinted with permission from [35] © Optica.

Fig. 6 .
Fig. 6.(a) 1D array of N particles scattering light under the influence of the higher order mode evanescent fields of a 2-µm fiber.1064-nm laser light, with input power, P in = 30 mW, is coupled into the microfiber.F n (white arrow) and F p (red arrow) indicate the attractive and repulsive binding forces; A j (orange sinusoidal arrow) and B j (pink sinusoidal arrow) represent the amplitudes of the incoming and outgoing light fields from the particles; d is the relative distance between the particles.Micrograph of inter-particle distance for particles 1-5 in particle chains using (b) fundamental mode (FM) propagation and (c) higher order mode (HOM) propagation; (a), (b), (c) reproduced with permission from [29] © Springer Nature.(d) Schematic of the trapping and delivery of E. coli bacteria.SEM images of (e) a nanofiber and (f) the E. coli bacteria; (d), (e), (f) reprinted with permission from [92] © RSC Pub.(g) Schematic of red blood cell (RBC) transport along the bio-conveyor belt; reproduced with permission from [30] © John Wiley and Sons.

Fig. 7 .
Fig. 7. (a) Experimental setup for sorting nanodiamonds (ND); GR: 532-nm laser, NIR: 1064-nm laser, PD: photodiodes, CCD: charged-coupled device.(b) Time sequential images at 2 s intervals; Particles 1 and 4 represent NDs with nitrogen vacancy centers, while 2 and 3 represent those without; the dashed line represents the nanofiber.(a), (b) reprinted with permission from [31] © Science Advances.(c) Experimental setup for the manipulation of Janus particles; PC: polarization compensator, PBS: polarizing beam splitter.(d)-(e) Variation of propulsion speed of silica and Janus particles of the same size as a function of laser power in the ONF.Here, d is the coating thickness of Au on the silica sphere used to make the Janus particle.(c) (d), (e) reprinted with permission from [32] © Springer Nature.