Bessel Vortex Beam Research Articles

Induced radiation force and torque on a viscoelastic particle in an ideal fluid

The interaction of an acoustic wave with a suspended particle may produce radiation force and torque on the particle through linear and angular momentum transfer. Theoretical analysis of the radiation force exerted on a rigid, compressible fluid, elastic solid, and layered spherical particle is abundantly found in the literature. Nevertheless, less attention has been devoted to cases involving a homogeneous viscoelastic particle, even though viscoelastic materials are ubiquitous. Here, the radiation force and torque exerted on this kind of particle is studied in detail using the fractional Kelvin-Voigt viscoelastic model. Analytical expressions are obtained in the monopole-dipole approximation to a small particle in the long-wave limit. Considering a traveling plane wave interacting with a high-density polyethylene (HDPE) particle, we found that the axial radiation force is negative, i.e., the force and the wave propagation are in opposite directions. For a first-order Bessel vortex beam, a full 3D tractor beam develops on the HDPE particle placed in the beam's axis. Furthermore, negative axial radiation torque also appears on the particle, i.e., the torque and the beam's angular momentum are contrariwise. In addition, possible implications of this method to the advancement of acoustophoretic techniques will be outlined.

Acoustics of finite Bessel tractor beams

Surprises and counterintuitive effects occurring in physical phenomena rank high on the list of things that make science discoveries a source of perpetual excitement. Some examples illustrated here include, (i) the effects of attracting (i.e., pulling) a spherical particle placed in the field of a Bessel acoustical beam of progressive waves back towards the radiator’s surface [Mitri, “Single Bessel tractor-beam tweezers,” Wave Motion 51, no. 6, pp. 986–993, 2014], (ii) suppressing some of the sphere’s resonances [Mitri, “Near-field acoustic resonance scattering of a finite Bessel beam by an elastic sphere,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control, 61, no. 4, pp. 696–704, 2014], (iii) and the emergence of a “negative radiation torque,” meaning that an incoming high-order Bessel vortex beam with a positive topological charge (known also as the order of the beam) would rotate a viscoelastic sphere in the opposite sense of the beam handedness [Silva et al., “Radiation torque produced by an arbitrary acoustic wave,” Europhys. Lett., 97, art. no. 54003, 2012]. Results and numerical predictions illustrate the analysis and extensions to other geometries, such as rigid oblate and prolate spheroids [Mitri, “Axisymmetric scattering of an acoustical Bessel beam by a rigid fixed spheroid,” http://arxiv.org/abs/1505.06754v3, ibid. "Acoustic radiation force on oblate and prolate spheroids in Bessel beams,” Wave Motion, 57, pp. 231–238, 2015] are also mentioned.

Ring dislocation of the coherence degree of a vortex Bessel beam in a turbulent atmosphere

Results of the theoretical consideration of the behavior of the coherence degree of a vortex Bessel optical beam propagating in a turbulent randomly inhomogeneous medium are presented. The influence of an optical vortex on the coherence degree of a Bessel beam in a randomly inhomogeneous medium is studied. The analysis of the problem is based on the solution of the equation for the second order mutual coherence function of the optical beam field. Based on this solution, the behavior of the absolute value of the second order mutual coherence function (coherence degree) of the vortex Bessel beam field is studied. It is shown that a ring dislocation the number of rings in which is equal to the value of the topological charge of the optical beam, forms in the central part of the two-dimensional field of the coherence degree of vortex Bessel beams at low levels of fluctuations in a turbulent atmosphere. The structure of the ring dislocation of the coherence degree of vortex Bessel optical beams in a turbulent atmosphere is studied in detail. For this purpose, two characteristics of the ring dislocation are introduced: its spatial coordinate and ring width. The influence of parameters of an optical beam (transverse wavenumber and topological charge) and atmospheric turbulence (coherence radius of a plane optical wave) on these characteristics of the ring dislocation of the coherence degree of a vortex Bessel optical beam is considered.

Resonance scattering of a dielectric sphere illuminated by electromagnetic Bessel non-diffracting (vortex) beams with arbitrary incidence and selective polarizations

A complete description of vector Bessel (vortex) beams in the context of the generalized Lorenz–Mie theory (GLMT) for the electromagnetic (EM) resonance scattering by a dielectric sphere is presented, using the method of separation of variables and the subtraction of a non-resonant background (corresponding to a perfectly conducting sphere of the same size) from the standard Mie scattering coefficients. Unlike the conventional results of standard optical radiation, the resonance scattering of a dielectric sphere in air in the field of EM Bessel beams is examined and demonstrated with particular emphasis on the EM field’s polarization and beam order (or topological charge). Linear, circular, radial, azimuthal polarizations as well as unpolarized Bessel vortex beams are considered. The conditions required for the resonance scattering are analyzed, stemming from the vectorial description of the EM field using the angular spectrum decomposition, the derivation of the beam-shape coefficients (BSCs) using the integral localized approximation (ILA) and Neumann–Graf’s addition theorem, and the determination of the scattering coefficients of the sphere using Debye series. In contrast with the standard scattering theory, the resonance method presented here allows the quantitative description of the scattering using Debye series by separating diffraction effects from the external and internal reflections from the sphere. Furthermore, the analysis is extended to include rainbow formation in Bessel beams and the derivation of a generalized formula for the deviation angle of high-order rainbows. Potential applications for this analysis include Bessel beam-based laser imaging spectroscopy, atom cooling and quantum optics, electromagnetic instrumentation and profilometry, optical tweezers and tractor beams, to name a few emerging areas of research.

General Metasurface Synthesis Based on Susceptibility Tensors

A general method, based on susceptibility tensors, is proposed for the synthesis of metasurfaces transforming arbitrary incident waves into arbitrary reflected and transmitted waves. The proposed method exhibits two advantages: 1)it is inherently vectorial, and therefore better suited for full vectorial (beyond paraxial) electromagnetic problems, 2) it provides closed-form solutions, and is therefore extremely fast. Incidentally, the method reveals that a metasurface is fundamentally capable to transform up to four independent wave triplets (incident, reflected and refracted waves). In addition, the paper provides the closed-form expressions relating the synthesized susceptibilities and the scattering parameters simulated within periodic boundary conditions, which allows one to design the scattering particles realizing the desired susceptibilities. The versatility of the method is illustrated by examples of metasurfaces achieving the following transformations: generalized refraction, reciprocal and non-reciprocal polarization rotation, Bessel vortex beam generation, and orbital angular momentum multiplexing.

Light scattering of a non-diffracting zero-order Bessel beam by uniaxial anisotropic bispheres

Based on the generalized multi-particle Mie theory and the Fourier transformation approach, light scattering of two interacting homogeneous uniaxial anisotropic spheres with parallel primary optical axes illuminated by a zero-order Bessel beam (ZOBB) is investigated. The size and configuration of the particles are arbitrary. The expansion expressions of the ZOBB are given in terms of the spherical vector wave functions (SVWFs) and the expansion coefficients are derived. Utilizing the vector addition theorem of the SVWFs, the interactive scattering coefficients are derived through the continuous boundary conditions on which the interaction of the bispheres is considered. The effects of the conical angle, beam centre position, sphere separation distance, and anisotropic parameters on the far-region field distributions are numerically analyzed in detail. Some results are compared with those results for a Gaussian beam incidence. Selected results of bispheres consisting of typical medium such as TiO2, SiO2, Silicon, water are exhibited. This investigation could provide an effective test for further research on the scattering characteristic of an aggregate of anisotropic spheres by a high-order Bessel vortex beam and radiation forces, which are important in optical tweezers and particle manipulation applications.

Acoustic radiation force and torque on an absorbing compressible particle in an inviscid fluid.

Exact formulas of the acoustic radiation force and torque exerted by an arbitrary time-harmonic wave on an absorbing compressible particle that is suspended in an inviscid fluid are presented. It is considered that the particle diameter is much smaller than the incident wavelength, i.e., the so-called Rayleigh scattering limit. Moreover, the particle absorption assumed here is due to the attenuation of compressional waves only. Shear waves inside and outside the particle are neglected, since the inner and outer viscous boundary layer of the particle are supposed to be much smaller than the particle radius. The obtained radiation force formulas are used to establish the trapping conditions of a particle by a single-beam acoustical tweezer based on a spherically focused ultrasound transducer. In this case, it is shown that the particle absorption has a pivotal role in single-beam trapping at the transducer focal region. Furthermore, it is found that only the first-order Bessel vortex beam can generate the radiation torque on a small particle. In addition, numerical evaluation of the radiation force and torque exerted on a benzene and an olive oil droplet suspended in water are presented and discussed.

Ablation of metal thin films using femtosecond laser Bessel vortex beams

Femtosecond lasers can provide submicron ablation resolution, making them suitable and attractive for various micro/nanofabrication applications. Laser beam shaping lends further advantages and increases the versatility of these sources. In this work, we report on the use of femtosecond laser pulses with first-order Bessel function (Bessel vortex) beam profiles in ablation of metal thin films. The diffraction-free nature of Bessel beams provides significant convenience regarding alignment and repeatability. Ablation profiles with Bessel vortex beams generally consist of single or multiple concentric rings, determined by pulse fluence on target. We investigate single-pulse ablation behavior with two laser wavelengths (1,030 and 515 nm) and three different Bessel beam cone angles. For each case, we measure inner and outer ring diameters and compare our results with theoretical calculations.

Mean intensity of vortex Bessel beams propagating in turbulent atmosphere.

Transformation of vortex Bessel beams during propagation in turbulent atmosphere is theoretically analyzed. Deforming influence of the random inhomogeneity of the turbulent medium on propagation of diffraction-free beams leads to disappearance of their invariant properties. In the given research, features of evolution of the spatial structure of distribution of mean intensity of vortex Bessel beams in turbulent atmosphere are analyzed. A quantitative criterion of possibility of carrying over of a dark central domain by vortex Bessel beams in a turbulent atmosphere is derived. The analysis of the behavior of several physical parameters of mean-level optical radiation shows that the shape stability of a vortex Bessel beam increases with the topological charge of this beam during its propagation in a turbulent atmosphere.

Generation of TH- and TE-polarized Bessel light beams at acousto-optic interaction in anisotropic crystals

This paper lays out a theory of acousto-optic (AO) interaction of TH- and TE-polarized Bessel light beams (BLBs) for the case when incident and diffracted optical fields and plane acoustic wave propagate along the optical axis of an uniaxial crystal. We have solved a system of coupled equations and calculated the diffraction efficiency of AO interaction, which has been shown to be close to one limited case of plane–wave interaction. We look at some particular cases of isotropic and anisotropic scattering, which can or cannot be accompanied by a change of the polarization state of vector BLBs. The paper explores acousto-optic processes of transferring optical singularities onto the wave front of BLBs and considers the transformation and generation of high-order phase dislocations (optical vortices) at AO interaction of BLBs along the optic axis of uniaxial crystals. Also under examination are peculiarities of AO interaction of Bessel vortex beams in the condition of the transverse and longitudinal phase-matching for uniaxial crystals of hexagonal, tetragonal and trigonal symmetries. The acousto-optic process under study can be used as a method for generation of the TH- and TE-polarized BLBs, which allows manipulating the polarization state of the output optical field in time.

Axial and transverse acoustic radiation forces on a fluid sphere placed arbitrarily in Bessel beam standing wave tweezers

The axial and transverse radiation forces on a fluid sphere placed arbitrarily in the acoustical field of Bessel beams of standing waves are evaluated. The three-dimensional components of the time-averaged force are expressed in terms of the beam-shape coefficients of the incident field and the scattering coefficients of the fluid sphere using a partial-wave expansion (PWE) method. Examples are chosen for which the standing wave field is composed of either a zero-order (non-vortex) Bessel beam, or a first-order Bessel vortex beam. It is shown here, that both transverse and axial forces can push or pull the fluid sphere to an equilibrium position depending on the chosen size parameter ka (where k is the wave-number and a the sphere’s radius). The corresponding results are of particular importance in biophysical applications for the design of lab-on-chip devices operating with Bessel beams standing wave tweezers. Moreover, potential investigations in acoustic levitation and related applications in particle rotation in a vortex beam may benefit from the results of this study.

Femtosecond laser fabrication of micro and nano-disks in single layer graphene using vortex Bessel beams

We report the fabrication of micro and nano-disks in single layer chemical vapor deposition graphene on glass substrate using femtosecond laser ablation with vortex Bessel beams. The fabricated graphene disks with diameters ranging from 650 nm to 4 μm were characterized by spatially resolved micro-Raman spectroscopy. The variation of ablation threshold was investigated as a function of the number of pulses showing an incubation effect. A very high degree of size control of the fabricated graphene disks is enabled using a sequence of femtosecond pulses with different vortex orders.

Counterpropagating nondiffracting vortex beams with linear and angular momenta

Closed-form analytical expressions for the electric and magnetic (EM) field components of a high-order Bessel vortex beam of fractional type \ensuremath{\alpha} (HOBVB-F\ensuremath{\alpha}) are derived based on the axial polarization of the vector potentials [denoted by ($z,\ensuremath{-}z$)]. The fields' components correspond to the most generalized case of quasi-standing-waves that reduce to perfect (i.e., equiamplitude) standing waves or progressive waves with appropriate choice of the quasi-standing-wave coefficient $0\ensuremath{\le}\ensuremath{\Upsilon}\ensuremath{\le}1$. The beam components are exact solutions of the vector wave equation (Helmholtz equation) and Maxwell's equations. Moreover, computations of the EM components and comparison with the results obtained from a transverse polarization scheme [denoted by (x,\ensuremath{-}y)] illustrate the analysis. In addition, the time-averaged angular momentum density and flux are evaluated with particular emphasis on the axial and transverse polarization states of the vector potentials. It is found that the quasi-standing-wave effect does not influence the spatial distributions of the EM components in the transverse polarization scheme (x,\ensuremath{-}y); however, it affects the transverse EM field components in the axial polarization (z,\ensuremath{-}z). Moreover, both the linear and angular momenta density fluxes are shown to reverse sign for a particular value of the half-cone angle \ensuremath{\beta}. These phenomena anticipate the production of a ``tractor'' beam where particulate matter may be pulled back toward the source, and a spinning reversal effect in which particulate matter may rotate with opposite handedness to a HOBVB-F\ensuremath{\alpha}. The results are particularly useful in applications involving optical laser tweezers, tractor beams, optical spanners, arbitrary scattering, radiation force, angular momentum, and torque.

Off-axial acoustic radiation force of repulsor and tractor bessel beams on a sphere.

Acoustic Bessel beams are known to produce an axial radiation force on a sphere centered on the beam axis (on-axial configuration) that exhibits both repulsor and tractor behaviors. The repulsor and the tractor forces are oriented along the beam's direction of propagation and opposite to it, respectively. The behavior of the acoustic radiation force generated by Bessel beams when the sphere lies outside the beam's axis (off-axial configuration) is unknown. Using the 3-D radiation force formulas given in terms of the partial wave expansion coefficients for the incident and scattered waves, both axial and transverse components of the force exerted on a silicone- oil sphere are obtained for a zero- and a first-order Bessel vortex beam. As the sphere departs from the beam's axis, the tractor force becomes weaker. Moreover, the behavior of the transverse radiation force field may vary with the sphere's size factor ka (where k is the wavenumber and a is the sphere radius). Both stable and unstable equilibrium regions around the beam's axis are found, depending on ka values. These results are particularly important for the design of acoustical tractor beam devices operating with Bessel beams.

Polarization and topological charge conversion of exact optical vortex beams at normal incidence on planar dielectric interfaces

We report on the exact resolution of the problem of reflection and refraction of exact circularly polarized Bessel vortex beams impinging at normal incidence on a planar dielectric interface between two isotropic and lossless media. On the one hand, we demonstrate the generation of a new vortex state both in the reflected and refracted fields. On the other hand, we show the possibility to completely convert, at reflection, the incident vortex beam into a vortex beam with orthogonal polarization and topological charge changed by ±2. The spin-orbit interaction of light occurring at the planar interface is identified as the mechanism responsible for these effects.

Acoustic radiation force and radiation torque on Rayleigh particles

In this work, the acoustic radiation force and radiation torque exerted by an arbitrary shaped wave on a spherical particle in the Rayleigh approximation (i.e. the incident wavelength is much smaller than the particle dimensions) are discussed. The host fluid in which the particle is suspended is assumed to be inviscid. Expressions for the force and the torque are obtained in terms of the incident acoustic fields, namely pressure and particle velocity. As it turns out, the obtained radiation force expression represents a generalization of Gor'kov's formula [Sov. Phys. Dokl. 6, 773-775 (1962)]. Moreover, the radiation torque can be expressed in terms of the incident Reynolds' stress tensor. The method is applied to calculate both radiation force and radiation torque produced by Bessel beams. It is demonstrated that only the first-order Bessel vortex beam generates radiation torque on a particle placed in the beam's axis. In addition, results involving off-axial particles and Bessel beams of different order are illustrated.

Vector wave analysis of an electromagnetic high-order Bessel vortex beam of fractional type α: II. The cases of standing and quasi-standing waves

Stemming from the vector Maxwell's equations and Lorenz’ gauge condition, a full vector-wave derivation for the electric and magnetic fields components of a high-order Bessel vortex beam of fractional type α (HOBVB-Fα) is provided. The field corresponds to the most generalized case of quasi-standing waves that reduce to perfect (i.e. equi-amplitude) standing waves or progressive waves with appropriate choice of the quasi-standing wave coefficient ϒ. The results are of particular importance in the study of the optical/electromagnetic wave scattering, radiation force and torque in optical tweezers operating with this fractional type of non-diffracting vortex beams.

Generalized theory of resonance excitation by sound scattering from an elastic spherical shell in a nonviscous fluid

This work presents the general theory of resonance scattering (GTRS) by an elastic spherical shell immersed in a nonviscous fluid and placed arbitrarily in an acoustic beam. The GTRS formulation is valid for a spherical shell of any size and material regardless of its location relative to the incident beam. It is shown here that the scattering coefficients derived for a spherical shell immersed in water and placed in an arbitrary beam equal those obtained for plane wave incidence. Numerical examples for an elastic shell placed in the field of acoustical Bessel beams of different types, namely, a zero-order Bessel beam and first-order Bessel vortex and trigonometric (nonvortex) beams are provided. The scattered pressure is expressed using a generalized partial-wave series expansion involving the beam-shape coefficients (BSCs), the scattering coefficients of the spherical shell, and the half-cone angle of the beam. The BSCs are evaluated using the numerical discrete spherical harmonics transform (DSHT). The far-field acoustic resonance scattering directivity diagrams are calculated for an albuminoidal shell immersed in water and filled with perfluoropropane gas, by subtracting an appropriate background from the total far-field form function. The properties related to the arbitrary scattering are analyzed and discussed. The results are of particular importance in acoustical scattering applications involving imaging and beam-forming for transducer design. Moreover, the GTRS method can be applied to investigate the scattering of any beam of arbitrary shape that satisfies the source-free Helmholtz equation, and the method can be readily adapted to viscoelastic spherical shells or spheres.

Attraction by sound—examples on the negative acoustic radiation forces of Bessel “tractor” beams on a sphere

Expressions for the axial (i.e. acting along the axis of wave propagation) and transverse (lateral) acoustic radiation forces on a suspended object in an ideal fluid are derived for arbitrary shaped beams. These expressions are obtained from the integration of the radiation stress tensor in the far-field. Numerical examples on non-vortex and vortex Bessel beams on a spherical target are presented. It is demonstrated the existence of both “pushing” and “tractor” behaviors for which the axial force can be oriented, respectively, along the direction of wave propagation or opposite to it. This can be adjusted by choosing specific values of the beam cone angle and the sphere size factor ka (where k is the wavenumber and a is the sphere's radius). Furthermore, by changing the topological charge m of the beam and the position of the sphere, the transverse force may be oriented radially (outward or inward) for m=0 or may exhibit a vortex pattern for m ≥ 1.

Creation of two vortex-entangled beams in a vortex-beam collision with a plane wave

Physics of photons and electrons carrying orbital angular momentum (OAM) is an exciting field of research in quantum optics and electron microscopy. Usually, one considers propagation of these vortex beams in a medium or external fields and their absorption or scattering on fixed targets. Here we consider instead a beam-beam collision. We show that elastic scattering of a Bessel vortex beam with a counterpropagating plane wave naturally leads to two vortex-entangled outgoing beams. The vortex entanglement implies that the two final particles are entangled not only in their orbital helicities but also in opening angles of their momentum cones. Our results are driven by kinematics of vortex-beam scattering and apply to particle pairs of any nature: e-gamma, e^+e^-, ep, etc. This collisional vortex entanglement can be used to create pairs of OAM-entangled particles of different nature, and to transfer a phase vortex, for example, from low-energy electrons to high-energy protons.