Vector wave analysis of an electromagnetic high-order Bessel vortex beam of fractional type α

Light scattering of a uniform uniaxial anisotropic sphere by an on-axis high-order Bessel vortex beam

Analytical solutions to the scattering of a uniform uniaxial anisotropic sphere illuminated by an on-axis high-order Bessel vortex beam (HOBVB) are investigated. Using the vector wave theory, the expansion coefficients of the incident HOBVB in terms of the spherical vector wave functions (SVWFs) are obtained. According to the orthogonality of the associated Legendre function and exponential function, more concise expressions of the expansion coefficients are derived. It can reinterpret the incident HOBVB faster compared with the expansion coefficients of double integral forms. The internal fields of a uniform uniaxial anisotropic sphere are proposed in the integrating form of the SVWFs by introducing the Fourier transform. The differences of scattering characteristics of a uniaxial anisotropic sphere illuminated by a zero-order Bessel beam, Gaussian beam, and HOBVB are exhibited. Influences of the topological charge, conical angle, and particle size parameters on the angle distributions of the radar cross section are analyzed in detail. The scattering and extinction efficiencies varied with the particle radius, conical angle, permeability, and dielectric anisotropy are also discussed. The results provide insights into the scattering and light-matter interactions and may find important applications in optical propagation and optical micromanipulation of biological and anisotropic complex particles.

Unconventional circularly polarized Airy light-sheet spinner tweezers

Standard circularly polarized Airy light-sheets are synthesized by combining two dephased TE and TM wave fields, polarized in the transverse directions of wave propagation, respectively. Somewhat counterintuitively, the present analysis theoretically demonstrates the existence of unconventional circularly polarized Airy light-sheets, where one of the individual dephased wave fields is polarized along the direction of wave propagation. The vector angular spectrum decomposition method in conjunction with the Lorenz gauge condition and Maxwell's equations allow adequate determination of the Cartesian components of the incident radiated electric field components. Subsequently, the Cartesian components of the optical time-averaged radiation force and torque can be determined and computed. The example of a subwavelength light-absorptive (lossy) dielectric sphere is considered based upon the dipole approximation method. The results demonstrate the emergence of negative force components, suggesting retrograde motion and spinning reversal depending on the polarization of the Airy light-sheet and its transverse scale and attenuation parameter. The results are important in the design of light-sheet spinner tweezers and applications involving optical switching and particle manipulation and rotation.

Implementation of nondiffracting Bessel beam sources in FDTD for scattering by complex particles

In this paper, the nondiffracting Bessel beam sources are implemented in finite-difference time-domain (FDTD) method. The high-order scattered-field algorithm of the FDTD (SF-FDTD (2, 4)) method is employed to investigate the scattering of particles illuminated by Bessel beams. In the SF-FDTD (2, 4) method, the scattered fields of the whole region are calculated directly by time stepping and the incident fields are obtained by the vector expressions of the diffraction-free Bessel beam. Some numerical results are included to illustrate the validity and capability of the proposed method. This study is expected to provide a new efficient method to investigate the interactions between nondiffracting beams and complex particles.

Nonlinear generation of Airy vortex beam

Recently, hybrid beams have sparked considerable interest because of their properties coming from different kinds of beams at the same time. Here, we experimentally demonstrate Airy vortex beam generation in the nonlinear frequency conversion process when the fundamental wave with its phase modulated by a spatial light modulator is incident into a homogeneous nonlinear medium. In our experiments, second harmonic Airy circle vortex beams and Airy ellipse vortex beams were generated and the topological charge was also measured. The parabolic trajectory of those Airy vortex beams can be easily adjusted by altering the fundamental wave phase. This study provides a simple way to generate second harmonic Airy vortex beams, which may broaden its future use in optical manipulation and light-sheet microscopy.

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.

Negative optical radiation force and spin torques on subwavelength prolate and oblate spheroids in fractional Bessel-Gauss pincers light-sheets

Fractional Bessel-Gauss light-sheets [J. Opt.19, 055602 (2017)JOOPDB0150-536X10.1088/2040-8986/aa649a], which correspond to finite optical "slices" in 2D and possess asymmetric slit openings and bending characteristics, are examined from the standpoint of optical radiation force and spin torque theories for a subwavelength spheroid with arbitrary orientation in space. The vector angular spectrum decomposition method in addition to the Lorenz gauge condition and Maxwell's equations are used to determine the Cartesian components of the incident radiated electric field of the Bessel-Gauss light-sheets. In the framework of the dipole approximation, the numerical results for the Cartesian components of the optical radiation force and spin torque vectors show that negative forces (oriented in the opposite direction of wave motion) and spin torques arise depending on the beam parameters, the orientation of the subwavelength spheroid in 3D space, and its aspect ratio (i.e., prolate versus oblate). The spin torque sign reversal reveals that counter-clockwise or clockwise rotations around the center of mass of the spheroid can occur. The results find important applications in the application of auto-focusing light-sheets in particle manipulation, rotation, and optical sorting devices.

Self-bending scalar and vector bottle sheets

This work demonstrates the generation of auto-bending cylindrical/tubular Bessel-Gauss bottle beams in homogeneous two-dimensional (2D) space. The corresponding wave fields flow through a two-dimensional curved trajectory leaving a singularity hollow central region, exhibiting the characteristic of circumventing obstacles. Scalar and vector fields are derived based on the angular spectrum decomposition method, the Helmholtz equation, the Lorenz gauge condition, and Maxwell's equations. The profile and area of the 2D bottle beams, together with the location of the autofocusing spots, are controlled by the intrinsic parameters of the illuminating waves and polarizations of the vector potential forming the incident fields. The demonstrated auto-bending cylindrical bottle beam solutions may find potential applications in acoustical and optical cloaking, auto-bending beam tweezers, imaging around steep corners, therapeutic investigations with unconventional autofocusing beams, acoustical and light sheets (i.e., slice of beams in 2D), and other related particle manipulation, isolation, and sorting devices, to name a few examples.

Reverse propagation and negative angular momentum density flux of an optical nondiffracting nonparaxial fractional Bessel vortex beam of progressive waves

Energy and angular momentum flux density characteristics of an optical nondiffracting nonparaxial vector Bessel vortex beam of fractional order are examined based on the dual-field method for the generation of symmetric electric and magnetic fields. Should some conditions determined by the polarization state, the half-cone angle as well as the beam-order (or topological charge) be met, the axial energy and angular momentum flux densities vanish (representing Poynting singularities), before they become negative. These negative counterintuitive properties suggest retrograde (negative) propagation as well as a rotation reversal of the angular momentum with respect to the beam handedness. These characteristics of nondiffracting nonparaxial Bessel fractional vortex beams of progressive waves open new capabilities in optical tractor beam tweezers, optical spanners, invisibility cloaks, optically engineered metamaterials, and other applications.

Turbulent effects of strong irradiance fluctuations on the orbital angular momentum mode of fractional Bessel Gauss beams

The turbulent effects of strong irradiance fluctuations on the probability densities and the normalized powers of the orbital angular momentum (OAM) modes are modeled for fractional Bessel Gauss beams in paraxial turbulence channel. We find that the probability density of signal OAM modes is a function of position deviation from the beam center, and the farther away from the beam center the detection position is, the smaller the probability density is. For fractional OAM quantum numbers, the average probability densities of signal/crosstalk modes oscillate along the beam radius except the half-integer. When the beam waist of source decreases or the irradiance fluctuation increases, the average probability density of the signal OAM mode drops. The peak of the average probability density of crosstalk modes shifts to outward of the beam center as beam waist gets larger. In the nearby region of beam center, the larger the quantum number deviation of OAM, the smaller the beam waist and the turbulence fluctuations are, the lower average probability densities of crosstalk OAM modes are. Especially, the increase of turbulence fluctuations can make the crosstalk stronger and more concentrated. Lower irradiance fluctuation can give rise to higher the normalized powers of the signal OAM modes, which is opposite to the crosstalk normalized powers.

Observation of the asymmetric Bessel beams with arbitrary orientation using a digital micromirror device

Recently, V. V. Kotlyar et al. [Opt. Lett.39, 2395 (2014)] have theoretically proposed a novel kind of three-parameter diffraction-free beam with a crescent profile, namely, the asymmetric Bessel (aB) beam. The asymmetry degree of such nonparaxial modes was shown to depend on a nonnegative real parameter c. We present a more generalized asymmetric Bessel mode in which the parameter c is a complex constant. This parameter controls not only the asymmetry degree of the mode but also the orientation of the optical crescent, and affects the energy distribution and orbital angular momentum (OAM) of the beam. As a proof of concept, the high-quality generation of asymmetric Bessel-Gauss beams was demonstrated with the super-pixel method using a digital micromirror device (DMD). We investigated the near-field properties as well as the far field features of such beams, and the experimental observations were in good agreement with the theoretical predictions. Additionally, we provided an effective way to control the beam's asymmetry and orientation, which may find potential applications in light-sheet microscopy and optical manipulation.

Vector spherical quasi-Gaussian vortex beams

Model equations for describing and efficiently computing the radiation profiles of tightly spherically focused higher-order electromagnetic beams of vortex nature are derived stemming from a vectorial analysis with the complex-source-point method. This solution, termed as a high-order quasi-Gaussian (qG) vortex beam, exactly satisfies the vector Helmholtz and Maxwell's equations. It is characterized by a nonzero integer degree and order (n,m), respectively, an arbitrary waist w(0), a diffraction convergence length known as the Rayleigh range z(R), and an azimuthal phase dependency in the form of a complex exponential corresponding to a vortex beam. An attractive feature of the high-order solution is the rigorous description of strongly focused (or strongly divergent) vortex wave fields without the need of either the higher-order corrections or the numerically intensive methods. Closed-form expressions and computational results illustrate the analysis and some properties of the high-order qG vortex beams based on the axial and transverse polarization schemes of the vector potentials with emphasis on the beam waist.

Cylindrical quasi-Gaussian beams

Making use of the complex-source-point method in cylindrical coordinates, an exact solution representing a cylindrical quasi-Gaussian beam of arbitrary waist w(0) satisfying both the Helmholtz and Maxwell's equations is introduced. The Cartesian components of the electromagnetic field are derived stemming from different polarizations of the magnetic and electric vector potentials based on Maxwell's vectorial equations and Lorenz's gauge condition, without any approximations. Computations illustrate the theory for tightly focused and quasi-collimated cylindrical beams. The results are particularly useful in beam-forming design using high-aperture or collimated cylindrical laser beams in imaging microscopy, particle manipulation, optical tweezers, and the study of scattering, radiation forces, and torque on cylindrical structures.