Bessel Vortex Beam Research Articles

Scattering of a vector Bessel vortex beam by a charged sphere

The interaction of a vector Bessel vortex beam (VBVB) with a charged sphere is investigated using generalized Lorenz–Mie theory (GLMT). The charges carried by the sphere are expressed by the surface conductivity σs. The incident VBVBs are expanded using a series of beam shape coefficients (BSCs), whose analytical expressions are derived using the angular spectrum decomposition method (ASDM). The expanded coefficients of the scattered fields are calculated by considering the boundary conditions on the surface of the sphere, which are different from that for the case of neutral sphere. The effects of the carried charges on the scattering, absorption, and extinction coefficients are considered, with particular emphasis on the effect of the order, polarization, and half-cone angle of the beams. Various polarizations including linear, circular, radial, azimuthal, and mixed polarizations are considered. Numerical results show that the scattering, extinction, and absorption efficiencies are very sensitive to the beam parameters including polarization, half-cone angle, and order. Thus in practice, the scattering, extinction, and absorption caused by charged particles can be enhanced or reduced by choosing proper beam parameters according to practical demand. Such results have many potential applications. For instance, it is of help to improve the quality of wireless communication by reducing the attenuation caused by charged particles. It can also improve the precision for particle sizing using phase Doppler anemometry by enhancing the scattering of charged spheres.

Intensity, phase, and polarization of a vector Bessel vortex beam through multilayered isotropic media.

This paper investigates the characteristics of reflected and transmitted fields of a vector Bessel vortex beam through multilayered isotropic media on the basis of the vector angular spectrum expansion and presents the effects of media on intensity, phase, and polarization. The method is verified by studying the reflection and transmission on a single interface at vertical incidence. For both paraxial and nonparaxial incident beam cases, numerical simulations of the field components and the time-averaged Poynting vector power density of the reflected and transmitted beams for the three-layered media are presented and discussed in detail. It is shown that as the incident angle increases, the magnitude distribution of the reflected beams illustrates significant distortions and no longer represents similar patterns to that of the incident beam, whereas the magnitude distribution of the transmitted beams can maintain similar profiles to the incident beam, apart from the notable distortion of the central ring. For the same incident angle, the effects of media on the magnitude distribution for the nonparaxial case are more evident than those for the paraxial case. The results of phase distribution and polarization of the reflected and transmitted fields show that as the incident angle increases, the distortion of the phase distribution and polarization for the reflected fields are more significant and the topological charge cannot be preserved.

Vectorial diffraction properties of THz vortex Bessel beams.

A vortex Bessel beam combines the merits of an optical vortex and a Bessel beam, including a spiral wave front and a non-diffractive feature, which has immense application potentials in optical trapping, optical fabrication, optical communications, and so on. Here, linearly and circularly polarized vortex Bessel beams in the terahertz (THz) frequency range are generated by utilizing a THz quarter wave plate, a spiral phase plate, and Teflon axicons with different opening angles. Taking advantage of a THz focal-plane imaging system, vectorial diffraction properties of the THz vortex Bessel beams are comprehensively characterized and discussed, including the transverse (Ex, Ey) and longitudinal (Ez) polarization components. The experimental phenomena are accurately simulated by adopting the vectorial Rayleigh diffraction integral. By varying the opening angle of the axicon, the characteristic parameters of these THz vortex Bessel beams are exhibited and compared, including the light spot size, the diffraction-free range, and the phase evolution process. This work provides the precise experimental and theoretical bases for the comprehension and application of a THz vortex Bessel beam.

Anomalous Bessel vortex beam: modulating orbital angular momentum with propagation

AbstractZero-order and higher-order Bessel beams are well-known nondiffracting beams. Namely, they propagate with invariant profile (intensity) and carry a fixed orbital angular momentum. Here, we propose and experimentally study an anomalous Bessel vortex beam. Unlike the traditional Bessel beams, the anomalous Bessel vortex beam carries decreasing orbital angular momentum along the propagation axis in free space. In other words, the local topological charge is inversely proportional to the propagation distance. Both the intensity and phase patterns of the generated beams are measured experimentally, and the experimental results agree well with the simulations. We demonstrate an easy way to modulate the beam’s topological charge to be an arbitrary value, both integer and fractional, within a continuous range. The simplicity of this geometry encourages its applications in optical trapping and quantum information, and the like.

Generation of vortex beamlet lattices via diffraction of Bessel vortex beams on 2D hole arrays: analytical and numerical calculations and comparison with experiments

Generation of vortex beamlet lattices via diffraction of Bessel vortex beams on 2D hole arrays: analytical and numerical calculations and comparison with experiments

Acoustics of finite asymmetric exotic beams: Examples of Airy and fractional Bessel beams

The purpose of this investigation is to examine the properties of finite asymmetric exotic scalar (acoustic) beams with unusual properties using the angular spectrum decomposition in plane waves. Such beams possess intrinsic uncommon characteristics that make them attractive from the standpoint of particle manipulation, handling and rotation, and possibly other applications in particle clearing and separation. Assuming a specific apodization function at the acoustic source, the angular spectrum function is calculated and used to synthesize the radiated pressure field (i.e., excluding evanescent waves that decay away from the source) in the forward direction of wave motion (i.e., away from the source). Moreover, a generalized hybrid method combining the angular spectrum approach with the multipole expansion formalism in spherical coordinates is developed, which is applicable to any finite beam of arbitrary wavefront. The improved approach allows adequate computation of the resonance scattering, radiation force, and spin torque components on an object of arbitrary shape, located on or off the axis of the incident beam in space. Considering the illustrative example of a viscous fluid sphere submerged in a non-viscous liquid and illuminated by finite asymmetric beams such as the Airy and the Bessel vortex beam with fractional order, numerical computations for the scattering, radiation force, and torque components are performed with an emphasis on the distance from the source, the arbitrary location of the particle ,and the asymmetric nature of the incident field. Moreover, beamforming calculations are presented with supplementary animations for the pressure field distribution in space, with an emphasis on the intrinsic properties of the selected beams. The numerical predictions illustrate the scattering, radiation force, and spin torque properties depending on the beam parameters and the distance separating the sphere from the source. This study provides a generalized hybrid method to analyze quantitatively the scattering, radiation force, and spin torque by any finite asymmetric (or symmetric) acoustic beam with potential applications in various fields of applied physics (such as beam-forming, imaging, and mechanical effects of asymmetric sound beams).

Optical Bessel beam illumination of a subwavelength prolate gold (Au) spheroid coated by a layer of plasmonic material: radiation force, spin and orbital torques

The optical radiation force, spin and orbital torques exerted on a subwavelength prolate gold spheroid coated by a layer of plasmonic material with negative permittivity and illuminated by either a zeroth-order (non-vortex) or a first-order vector Bessel (vortex) beam are computed in the framework of the electric dipole approximation method. Calculations for the Cartesian components of the optical radiation force on a subwavelength spheroid with arbitrary orientation in space are performed, with emphasis on the order (or topological charge), half-cone angle of the beam, and the plasmonic layer thickness on- and off-resonance. A repulsive (pushing) force is predicted for the layered subwavelength prolate spheroid, on- and off-resonance along the direction of wave propagation. Moreover, the Cartesian components of the spin radiation torque are computed where a negative longitudinal spin torque component can arise, suggesting a rotational twist of the spheroid around its center of mass in either the counter-clockwise or the clockwise (negative) direction of spinning. In addition, the longitudinal component of the orbital radiation torque exhibits sign reversal, indicating a revolution around the beam axis in either the counter-clockwise or the clockwise directions. The results show that the plasmonic resonance strongly alters the force, spin and orbital torque components, causing major amplitude enhancements, signs twists, and complex distributions in the transverse plane.

Theoretical conversion of the hypergeometric-Gaussian beams family into a high-order spiraling Bessel beams by a curved fork-shaped hologram

Based on the process of the Fresnel diffraction, the possibility of generating a new type of laser beams family by illuminating a curved fork-shaped hologram, with an input hypergeometric-Gaussian beams family of orders n and m is studied in this paper. The theoretical and the numerical results showed that, at the output plane, a high order spiraling Bessel vortex beam is produced. This vortex beam is divergence or non-divergence depending upon the waist position of the input hypergeometric-Gaussian beams, regarding the plane where the curved fork-shaped hologram is situated. Analytical expressions of the amplitude and the intensity distribution of the diffracted wave field are calculated and deduced using the stationary phase method. The actual work generalizes also the Fresnel diffraction study of some subfamilies of the hypergeometric-Gaussian beams family, such as: fundamental Gaussian, hollow Gaussian, modified quadratic Bessel–Gaussian and elegant Laguerre–Gaussian beams.

Optical spin torque induced by vector Bessel (vortex) beams with selective polarizations on a light-absorptive sphere of arbitrary size

The optical spin torque (OST) induced by vector Bessel (vortex) beams can cause a particle to rotate around its center of mass. Previous works have considered the OST on a Rayleigh absorptive dielectric sphere by a vector Bessel (vortex) beam, however, it is of some importance to analyze the OST components for a sphere of arbitrary size. In this work, the generalized Lorenz-Mie theory (GLMT) is used to compute the OST induced by vector Bessel (vortex) beams on an absorptive dielectric sphere of arbitrary size, with particular emphasis on the beam order, the polarization of the plane wave component forming the beam, and the half-cone angle. The OST is expressed as the integration of the moment of the time-averaged Maxwell stress tensor, and the beam shape coefficients (BSCs) are calculated using the angular spectrum decomposition method (ASDM). Using this theory, the OST exerted on the light-absorptive dielectric sphere in the Rayleigh, Mie or the geometrical optics regimes can be considered. The axial and transverse OSTs are numerically calculated with particular emphasis on the sign reversal of the axial OST and the vortex-like character of the transverse OST, and the effects of polarization, beam order, and half-cone angle are discussed in detail. Numerical results show that by choosing an appropriate polarization, order and half-cone angle, the sign of the axial OST can be reversed, meaning that the sphere would spin in opposite handedness of the angular momentum carried by the incident beam. The vortex-like structure of the total transverse OSTs can be observed for all cases. When the sphere moves radially away from the beam axis, it may rotate around its center of mass in either the counter-clockwise or the clockwise direction. Conditions are also predicted where the absorptive sphere experiences no spinning. Potential applications in particle manipulation and rotation in optical tweezers and tractor beams would benefit from the results.

OAM mode of the Hankel–Bessel vortex beam in weak to strong turbulent link of marine-atmosphere

We study the turbulent effects of maritime atmosphere on the propagation of the orbital angular momentum (OAM) modes of a vortex beam. Based on the modified Rytov approximation, we model the effective marine-atmospheric spectrum and the normalized energy weight of the vortex modes of Hankel–Bessel beams in a paraxial marine turbulent channel. Our results show that the intensity of the signal vortex modes of Hankel–Bessel beams in a non-turbulence channel increases with increasing the quantum number of the OAM of vortex modes from one to higher. We can utilize OAM eigenstates of the Hankel–Bessel vortex beam to increase the channel capacity in optical communication of the remote link. The normalized energy weight of signal OAM modes increases and that of crosstalk OAM modes decreases from the worst to the best turbulent maritime climate. The normalized energy weight of signal OAM modes reduces with the increasing of the turbulent outer scale from to and the receiving diameter, but it increases with increasing the turbulent outer scale when the outer scale is greater than . The effects of the inner scale on the normalized energy weight of OAM modes can be ignored. We can mitigate the effects of turbulence by the choice of the longer wavelength and smaller receiver aperture.

Optical torque on a magneto-dielectric Rayleigh absorptive sphere by a vector Bessel (vortex) beam

The optical torque exerted on an absorptive megneto-dielectric sphere by an axicon-generated vector Bessel (vortex) beam with selected polarizations is investigated in the framework of the dipole approximation. The total optical torque is expressed as the sum of orbital and spin torques. The axial orbital torque component is calculated from the z-component of the cross-product of the vector position r and the optical force exerted on the sphere F. Depending on the beam characteristics (such as the half-cone angle and polarization type) and the physical properties of the sphere, it is shown here that the axial orbital torque vanishes before reversing sign, indicating a counter-intuitive orbital motion in opposite handedness of the angular momentum carried by the incident waves. Moreover, analytical formulas for the spin torque, which is divided into spin torques induced by electric and magnetic dipoles, are derived. The corresponding components of both the optical spin and orbital torques are numerically calculated, and the effects of polarization, the order of the beam, and half-cone angle are discussed in detail. The left-handed (i.e., negative) optical torque is discussed, and the conditions for generating optical spin and orbital torque sign reversal are numerically investigated. The transverse optical spin torque has a vortex-like character, whose direction depends on the polarization, the half-cone angle, and the order of the beam. Numerical results also show that the vortex direction depends on the radial position of the particle in the transverse plane. This means that a sphere may rotate with different directions when it moves radially. Potential applications are in particle manipulation and rotation, single beam optical tweezers, and other emergent technologies using vector Bessel beams on a small magneto-dielectric (nano) particle.

Electromagnetic scattering by multiple dielectric particles under the illumination of unpolarized high-order Bessel vortex beam

This study investigates the electromagnetic scattering of a high-order Bessel vortex beam by multiple dielectric particles of arbitrary shape based on the surface integral equation (SIE) method. In Cartesian coordinates, the mathematical formulas are given for characterizing the electromagnetic field components of an arbitrarily incident high-order Bessel vortex beam. By using the SIE, a numerical scheme is formulated to find solutions for characterizing the electromagnetic scattering by multiple homogeneous particles of arbitrary shape and a home-made FORTRAN program is written. The presented theoretical derivations as well as the home-made program are validated by comparing to the scattering results of a Zero-Order Bessel Beam by the Generalized Lorenz-Mie theory. From our simulations, the beam’s order, half-cone angles, and the ways of particles’ arrangement have a great influence upon the differential scattering cross section (DSCS) for multiple particles. Furthermore, for a better understanding of the scattering characteristic in three dimension (3-D) space, the 3-D distribution of the DSCS for different cases is presented. It is anticipated that these results can be helpful to understand the scattering mechanisms of a high-order Bessel vortex beam on multiple dielectric particles of arbitrary shape.

Generation of high-order Bessel vortex beam carrying orbital angular momentum using multilayer amplitude-phase-modulated surfaces in radiofrequency domain

A high-order Bessel vortex beam carrying orbital angular momentum (OAM) is generated by using multilayer amplitude-phase-modulated surfaces (APMSs) at 10 GHz. The APMS transmitarray is composed of four-layer conformal square-loop (FCSL) surfaces with both amplitude and phase modulation. The APMS can transform a quasi-spherical wave emitted from the feeding source into a pseudo non-diffractive high-order Bessel vortex beam with OAM. The APMS for a second-order Bessel beam carrying OAM in the n = 2 mode is designed, fabricated, and measured. Full-wave simulation and measurement results confirm that Bessel vortex beams with OAM can be effectively generated using the proposed APMS transmitarray.

Two-color above-threshold ionization of atoms and ions in XUV Bessel beams and intense laser light

The two-color above-threshold ionization (ATI) of atoms and ions is investigated for a vortex Bessel beam in the presence of a strong near-infrared (NIR) light field. While the photoionization is caused by the photons from the weak but extreme ultraviolet (XUV) vortex Bessel beam, the energy and angular distribution of the photoelectrons and their sideband structure are affected by the plane-wave NIR field. We here explore the energy spectra and angular emission of the photoelectrons in such two-color fields as a function of the size and location of the target atoms with regard to the beam axis. In addition, analog to the circular dichroism in typical two-color ATI experiments with circularly polarized light, we define and discuss seven different dichroism signals for such vortex Bessel beams that arise from the various combinations of the orbital and spin angular momenta of the two light fields. For localized targets, it is found that these dichroism signals strongly depend on the size and position of the atoms relative to the beam. For macroscopically extended targets, in contrast, three of these dichroism signals tend to zero, while the other four just coincide with the standard circular dichroism, similar as for Bessel beams with a small opening angle. Detailed computations of the dichroism are performed and discussed for the $4s$ valence-shell photoionization of ${\mathrm{Ca}}^{+}$ ions.

Computation of radiation pressure force exerted on arbitrary shaped homogeneous particles by high-order Bessel vortex beams using MLFMA.

Due to special characteristics of nondiffraction and self reconstruction, the Bessel beams have attracted wide attention in optical trapping and appear to be a dramatic alternative to Gaussian beams. We present in this paper an efficient approach based on the surface integral equations (SIE) to compute the radiation pressure force (RPF) exerted on arbitrary shaped homogeneous particles by high-order Bessel vortex beam (HOBVB). The incident beam is described by vector expressions perfectly satisfy Maxwell's equations. The problem is formulated with the combined tangential formulation (CTF) and solved iteratively with the aid of the multilevel fast multipole algorithm (MLFMA). Then RPF is computed by vector flux of the Maxwell's stress tensor over a spherical surface tightly enclosing the particle and analytical expression for electromagnetic fields of incident beam in near region are used. The numerical predictions are compared with the results of the rigorous method for spherical particle to validate the accuracy of the approach. Some numerical results on relative large particles of complex shape, such as biconcave cell-like particles with different geometry parameters are given, showing powerful capability of our approach. These results are expected to provide useful insights into the RPF exerted on complex shaped particles by HOBVB.

Numerical investigation of flat-topped vortex hollow beams and Bessel beams propagating in a turbulent atmosphere.

In this paper, the aperture averaged scintillation, mean signal-to-noise ratio (SNR), and average bit error rate (BER) for both flat-topped vortex hollow beams and Bessel beams propagating in a turbulent atmosphere are evaluated. Investigations are also made illustrating the variation of aperture averaged scintillation, mean SNR, and average BER against the beam type, propagation distance, and size of the receiver aperture. Compared with the flat-topped vortex hollow beams, the Bessel beams have a smaller aperture averaged scintillation, higher mean SNR, and lower average BER when the receiver aperture is relatively small under the same conditions.

Negative pulling acoustic radiation force on spheroids in Bessel vortex beams

The emergence of a negative pulling acoustic radiation force on rigid spheroids is examined, with the use of acoustical Bessel vortex (helicoidal) “tractor” beams. Numerical predictions based on the acoustical scattering phenomenon [F. G. Mitri, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 62, 1809-1818 (2015); Ann. Phys. (NY) 363, 262-274 (2015)] that is extended to calculate the longitudinal acoustic radiation force (i.e., acting along the direction of wave propagation) illustrate the theory, with particular emphasis on the aspect ratio of the spheroid, the half-cone angle and order of the beam, as well as the dimensionless frequency parameter. It is shown that the Bessel vortex beam composed of progressive (i.e., traveling) waves is capable of generating a negative pulling force acting in opposite direction of the forward linear momentum density flux associated with the incident waves [F. G. Mitri, Europhys. Lett. 112, 34002 (2015)]. The scope of the analysis is further expanded to include the cases of standing and quasi-standing Bessel beam tweezers [F. G. Mitri, Wave Motion 57, 231-238 (2015)]. The results potentially suggest the use of Bessel “tractor” vortex beams for pulling, propelling, or manipulating arbitrary-shaped objects deviating from the spherical geometry for applications in remote sampling, particle manipulation, and handling, to name a few areas.

Axial acoustic radiation force on rigid oblate and prolate spheroids in Bessel vortex beams of progressive, standing and quasi-standing waves

The analysis using the partial-wave series expansion (PWSE) method in spherical coordinates is extended to evaluate the acoustic radiation force experienced by rigid oblate and prolate spheroids centered on the axis of wave propagation of high-order Bessel vortex beams composed of progressive, standing and quasi-standing waves, respectively. A coupled system of linear equations is derived after applying the Neumann boundary condition for an immovable surface in a non-viscous fluid, and solved numerically by matrix inversion after performing a single numerical integration procedure. The system of linear equations depends on the partial-wave index n and the order of the Bessel vortex beam m using truncated but converging PWSEs in the least-squares sense. Numerical results for the radiation force function, which is the radiation force per unit energy density and unit cross-sectional surface, are computed with particular emphasis on the amplitude ratio describing the transition from the progressive to the pure standing waves cases, the aspect ratio (i.e., the ratio of the major axis over the minor axis of the spheroid), the half-cone angle and order of the Bessel vortex beam, as well as the dimensionless size parameter. A generalized expression for the radiation force function is derived for cases encompassing the progressive, standing and quasi-standing waves of Bessel vortex beams. This expression can be reduced to other types of beams/waves such as the zeroth-order Bessel non-vortex beam or the infinite plane wave case by appropriate selection of the beam parameters. The results for progressive waves reveal a tractor beam behavior, characterized by the emergence of an attractive pulling force acting in opposite direction of wave propagation. Moreover, the transition to the quasi-standing and pure standing wave cases shows the acoustical tweezers behavior in dual-beam Bessel vortex beams. Applications in acoustic levitation, particle manipulation and acousto-fluidics would benefit from the results of the present investigation.

Probing the energy flow in Bessel light beams using atomic photoionization

The two-color above-threshold ionization (ATI) of atoms and ions is investigated for a vortex Bessel beam in the presence of a strong near-infrared (NIR) light field. While the photoionization is caused by the photons from the weak but extreme ultra-violet (XUV) vortex Bessel beam, the energy and angular distribution of the photoelectrons and their sideband structure are affected by the plane-wave NIR field. We here explore the energy spectra and angular emission of the photoelectrons in such two-color fields as a function of the size and location of the target (atoms) with regard to the beam axis. In addition, analogue to the circular dichroism in typical two-color ATI experiments with circularly polarized light, we define and discuss seven different dichroism signals for such vortex Bessel beams that arise from the various combinations of the orbital and spin angular momenta of the two light fields. For localized targets, it is found that these dichroism signals strongly depend on the size and position of the atoms relative to the beam. For macroscopically extended targets, in contrast, three of these dichroism signals tend to zero, while the other four just coincide with the (standard) circular dichroism, similar as for Bessel beams with small opening angle. Detailed computations of the dichroism are performed and discussed for the $4s$ valence-shell photoionization of Ca$^+$ ions.

Optical pulling force on a magneto-dielectric Rayleigh sphere in Bessel tractor polarized beams

The optical radiation force induced by Bessel (vortex) beams on a magneto-dielectric subwavelength sphere is investigated with particular emphasis on the beam polarization and order l (or topological charge). The analysis is focused on identifying the regions and some of the conditions to achieve retrograde motion of the sphere centered on the axis of wave propagation of the incident beam, or shifted off-axially. Exact non-paraxial analytical solutions are established, and computations for linear, circular, radial, azimuthal and mixed polarizations of the individual plane wave components forming the Bessel (vortex) beams by means of the angular spectrum decomposition method (ASDM) illustrate the theory with particular emphasis on the tractor (i.e. reversal) behavior of the force. This effect results in the pulling of the magneto-dielectric sphere against the forward linear momentum density flux associated with the incoming waves. Should some conditions related to the choice of the beam parameters as well as the permittivity and permeability of the sphere be met, the optical force vanishes and reverses sign. Moreover, the beam polarization is shown to affect differently the axial negative pulling force for either the zeroth- or the first-order Bessel beam. When the sphere is centered on the beam′s axis, the axial force component is always negative for the zeroth-order Bessel beam except for the radial and azimuthal polarization configurations. Nonetheless, for the first-order Bessel beam, the axial force is negative for the radial polarization case only. Additional tractor beam effects arise when the sphere departs from the center of the beam. It is also demonstrated that the tractor beam effect arises from the force component originating from the cross-interaction between the electric and magnetic dipoles. Potential applications are in particle manipulation, optical levitation, tractor beam tweezers, and other emergent technologies using polarized Bessel beams on a small (Rayleigh) magneto-dielectric particle.