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.

Optical trapping force on a stratified chiral particle by high-order Bessel beam.

We examined optical trapping force (TF) exerted on non-uniform chiral stratified spheres by a high-order Bessel beam (HOBB). Present theories were proven to be valid by comparison with the existing reference. Numerical simulations considering the effects of various parameters on TF are displayed in detail. The results show that different chirality distributions in stratified chiral sphere will affect significantly the trapping characteristics, and a stable three-dimensional capture can be realized only by selecting the appropriate parameters of incident beam and particles. The theoretical investigations may provide an analytical method to help understand the interaction of light with more complex stratified chiral cells and thus become an encouraging approach to better design an optical manipulation system.

Analysis of lateral binding force exerted on a bi-sphere induced by an elliptic Gaussian beam.

Based on the generalized Lorentz-Mie theory (GLMT) and the localized approximation of the beam shape coefficients, we derived the expansions of incident elliptic Gaussian (EG) beams in terms of spherical vector wave functions (SVWFs). Utilizing multiple scattering (MS) equations and electromagnetic momentum (EM) theory, the lateral binding force (BF) exerted on a bi-sphere induced by an EG beam is calculated. Numerical effects of various parameters such as beam waist widths, beam polarization states, incident wavelengths, particle sizes, and material losses are analyzed and compared with the results of a circular Gaussian (CG) beam in detail. The observed dependence of the separation of optically bound particles on the incidence of an EG beam is in agreement with earlier theoretical predictions. Accurate investigation of BF induced by an EG beam could provide an effective test for further research on BF between more complex particles, which plays an important role in using optical manipulation on particle self-assembly.

Light scattering of a Laguerre-Gaussian vortex beam by a chiral sphere.

Since the development of the generalized Lorenz-Mie theory, electromagnetic scattering by arbitrary beams has drawn growing interest. The Laguerre-Gaussian (LG) vortex beam is well known for its orbital angular momentum. With the aim of investigating the analytical solution to the scattering of a chiral sphere by a LG vortex beam, particular attention is paid to the expansion expression of the LG vortex beam. The expansion coefficients are derived based on the expansion of a Hermite Guassian beam as the LG vortex beam can be expressed as the superposition of Hermite Guassian modes. The numerical results of the incident beam expansion coefficients convergence and the scattered field comparison with the reference prove the validity of the theoretical analysis and computation codes. The results reveal that there exists an optimal sphere size for the maximum scattered field which is determined by the topological charge, beam waist radius, and beam center position. The investigation could provide a foundation for the optical manipulation of chiral particles by a LG vortex beam.

Geometric detection based on one-dimensional laser range profiles of dynamic conical target.

One-dimensional laser range profiles (LRPs) contain abundant information regarding the shape, size, and attitude of detected objects. For a dynamic conical target, the variation of its size and attitude could have a significant effect on the projections of LRP peaks. Ground coordinates, target coordinates, and incident field coordinates are established to compute the LRP of dynamic cones. In order to inverse the size, a genetic algorithm is adopted. The cone heights and half-cone angles of three different cones are inversed. Moreover, the results are used to inverse the attitude angles at any sampling time in order to verify accuracy of the theory. The inversion mentioned in this paper can be applied in any targets of arbitrary material, shape, and attitude with great efficiency.

Electromagnetic scattering by a uniaxial anisotropic sphere located in an off-axis Bessel beam.

Electromagnetic scattering of a zero-order Bessel beam by an anisotropic spherical particle in the off-axis configuration is investigated. Based on the spherical vector wave functions, the expansion expression of the zero-order Bessel beam is derived, and its convergence is numerically discussed in detail. Utilizing the tangential continuity of the electromagnetic fields, the expressions of scattering coefficients are given. The effects of the conical angle of the wave vector components of the zero-order Bessel beam, the ratio of the radius of the sphere to the central spot radius of the zero-order Bessel beam, the shift of the beam waist center position along both the x and y axes, the permittivity and permeability tensor elements, and the loss of the sphere on the radar cross section (RCS) are numerically analyzed. It is revealed that the maximum RCS appears in the conical direction or neighboring direction when the sphere is illuminated by a zero-order Bessel beam. Furthermore, the RCS will decrease and the symmetry is broken with the shift of the beam waist center.

Analysis of rainbow scattering by a chiral sphere.

Based on the scattering theory of a chiral sphere, rainbow phenomenon of a chiral sphere is numerically analyzed in this paper. For chiral spheres illuminated by a linearly polarized wave, there are three first-order rainbows, with whose rainbow angles varying with the chirality parameter. The spectrum of each rainbow structure is presented and the ripple frequencies are found associated with the size and refractive indices of the chiral sphere. Only two rainbow structures remain when the chiral sphere is illuminated by a circularly polarized plane wave. Finally, the rainbows of chiral spheres with slight chirality parameters are found appearing alternately in E-plane and H-plane with the variation of the chirality.

Analysis of the radiation force and torque exerted on a chiral sphere by a Gaussian beam.

Under the framework of generalized Lorenz-Mie theory, we calculate the radiation force and torque exerted on a chiral sphere by a Gaussian beam. The theory and codes for axial radiation force are verified when the chiral sphere degenerates into an isotropic sphere. We discuss the influence of a chirality parameter on the radiation force and torque. Linearly and circularly polarized incident Gaussian beams are considered, and the corresponding radiation forces and torques are compared and analyzed. The polarization of the incident beam considerably influences radiation force of a chiral sphere. In trapping a chiral sphere, therefore, the polarization of incident beams should be chosen in accordance with the chirality. Unlike polarization, variation of chirality slightly affects radiation torque, except when the imaginary part of the chirality parameter is considered.

Calculation of electromagnetic scattering by a large chiral sphere.

Expressions of scattering coefficients for calculating scattering by large chiral spheres are derived by using logarithmic derivatives and ratios of Riccati-Bessel functions. The improved expressions can be easily applied to the case of an arbitrarily shaped beam incidence. A simplified expression of the scattered field in the far field is obtained for the case of x-polarized plane-wave incidence. To verify the correctness and accuracy of the theory and codes, our results are compared with those in literature and those calculated by Mie theory. Radar cross sections of a large chiral sphere are numerically studied. It is found that the rainbow phenomenon of a chiral sphere is very different from that of an isotropic sphere.

Multiple scattering of electromagnetic waves by an aggregate of uniaxial anisotropic spheres.

An exact analytical solution is obtained for the scattering of electromagnetic waves from a plane wave with arbitrary directions of propagation and polarization by an aggregate of interacting homogeneous uniaxial anisotropic spheres with parallel primary optical axes. The expansion coefficients of a plane wave with arbitrary directions of propagation and polarization, for both TM and TE modes, are derived in terms of spherical vector wave functions. The effects of the incident angle α and the polarization angle ß on the radar cross sections (RCSs) of several types of collective uniaxial anisotropic spheres are numerically analyzed in detail. The characteristics of the forward and backward RCSs in relation to the incident wavelength are also numerically studied. Selected results on the forward and backward RCSs of several types of square arrays of SiO2 spheres illuminated by a plane wave with different incident angles are described. The accuracy of the expansion coefficients of the incident fields is verified by comparing them with the results obtained from references when the plane wave is degenerated to a z-propagating and x- or y-polarized plane wave. The validity of the theory is also confirmed by comparing the numerical results with those provided by a CST simulation.

Calculation of radiation forces exerted on a uniaxial anisotropic sphere by an off-axis incident Gaussian beam.

Using the theory of electromagnetic scattering of a uniaxial anisotropic sphere, we derive the analytical expressions of the radiation forces exerted on a uniaxial anisotropic sphere by an off-axis incident Gaussian beam. The beam's propagation direction is parallel to the primary optical axis of the anisotropic sphere. The effects of the permittivity tensor elements ε(t) and ε(z) on the axial radiation forces are numerically analyzed in detail. The two transverse components of radiation forces exerted on a uniaxial anisotropic sphere, which is distinct from that exerted on an isotropic sphere due to the two eigen waves in the uniaxial anisotropic sphere, are numerically studied as well. The characteristics of the axial and transverse radiation forces are discussed for different radii of the sphere, beam waist width, and distances from the sphere center to the beam center of an off-axis Gaussian beam. The theoretical predictions of radiation forces exerted on a uniaxial anisotropic sphere are hoped to provide effective ways to achieve the improvement of optical tweezers as well as the capture, suspension, and high-precision delivery of anisotropic particles.

Scattering of a partially coherent Gaussian-Schell beam from a diffuse target in slant atmospheric turbulence.

On the basis of the extended Huygens-Fresnel principle, the scattering of partially coherent Gaussian-Schell-model (GSM) beams from a diffuse target in slant double-passage atmospheric turbulence is studied and compared with that of fully coherent Gaussian beams. Using the cross-spectral density function of the GSM beams, we derive the expressions of the mutual coherence function, angle-of-arrival fluctuation, and covariance and variance of the intensity of the scattered field, taking into account the fluctuations of both the log-amplitude and phase. The numerical results are presented, and the influences of the wavelength, propagation distance, and waist radius on scattering properties are discussed. The perturbation region of the normalized intensity variance of the partially coherent GSM beam is smaller than that of the fully coherent Gaussian beam at the middle turbulence level. The normalized intensity variance of long-distance beam propagation is smaller than that of beam propagation along a short distance.

Analysis of electromagnetic scattering by uniaxial anisotropic bispheres.

Based on the generalized multiparticle Mie theory and the Fourier transformation approach, electromagnetic (EM) scattering of two interacting homogeneous uniaxial anisotropic spheres with parallel primary optical axes is investigated. By introducing the Fourier transformation, the EM fields in the uniaxial anisotropic spheres are expanded in terms of the spherical vector wave functions. The interactive scattering coefficients and the expansion coefficients of the internal fields are derived through the continuous boundary conditions on which the interaction of the bispheres is considered. Some selected calculations on the effects of the size parameter, the uniaxial anisotropic absorbing dielectric, and the sphere separation distance are described. The backward radar cross section of two uniaxial anisotropic spheres with a complex permittivity tensor changing with the sphere separation distance is numerically studied. The authors are hopeful that the work in this paper will help provide an effective calibration for further research on the scattering characteristic of an aggregate of anisotropic spheres or other shaped anisotropic particles.

Electromagnetic scattering for a uniaxial anisotropic sphere in an off-axis obliquely incident Gaussian beam.

An analytical solution to the scattering of an off-axis Gaussian beam obliquely incident on a uniaxial anisotropic sphere is obtained in the particle-centered system. Based on the local approximation to the off-axis beam shape coefficients and the coordinate rotation theory, the off-axis obliquely incident Gaussian beam is expanded with the spherical vector wave functions in the primary coordinate of the uniaxial anisotropic sphere. The internal fields of the uniaxial anisotropic sphere are proposed in the integrating form of the spherical vector wave functions by introducing the Fourier transform. By matching the fields on the boundary and solving matrix equations, the expansion coefficients are analytically derived. The influences of the beam waist center positioning and the obliquely incident angles, as well as the permittivity tensors on the far scattered field distributions, are numerically presented. The correctness of the theory is verified by comparing our numerical results in special cases with results from the references and with calculations by other algorithms.

Three-dimensional scattering by an infinite homogeneous anisotropic elliptic cylinder in terms of Mathieu functions.

A solution to the problem of three-dimensional scattering by an infinite homogeneous anisotropic elliptic cylinder for an obliquely incident plane wave of an arbitrary linear polarization is proposed. The axial components of the electromagnetic fields inside an anisotropic elliptic cylinder are represented as two coupled integrals of suitable eigenfunctions in elliptic coordinates in terms of Mathieu functions. Scattering by an anisotropic elliptic cylinder is different from scattering by a sphere or a circular cylinder because of the nonorthogonality properties of Mathieu functions at the interface between two different media. In order to solve this problem, Galerkin's method is applied to the boundary conditions to solve the unknown coefficients. Numerical results are presented, discussed, and compared with available data.

Internal and external electromagnetic fields for on-axis Gaussian beam scattering from a uniaxial anisotropic sphere.

Scattering of an on-axis Gaussian beam by a uniaxial anisotropic sphere is studied. The incident on-axis Gaussian beam is expanded in terms of spherical vector wave functions, and the beam shape coefficients are obtained by applying the local approximation. The internal fields of a uniaxial anisotropic sphere are proposed in the integrating form of the spherical vector wave functions by introducing the Fourier transform. Utilizing the continuous tangential boundary conditions, both the scattered and the internal field coefficients are derived analytically. Numerical calculations are presented. The effects of the beam width, beam waist center positioning, and anisotropy on scattering properties are analyzed. The internal and near-surface field distributions are also discussed, and the two eigenmodes are characterized. The continuity on the surface of a uniaxial anisotropic sphere is well confirmed.

Scattering by an infinite homogenous anisotropic elliptic cylinder in terms of Mathieu functions and Fourier series.

An exact solution to the two-dimensional scattering properties of an anisotropic elliptic cylinder for transverse electric polarization is presented. The internal field in an anisotropic elliptic cylinder is expressed as integral representations of Mathieu functions and Fourier series. The coefficients of the series expansion are obtained by imposing boundary conditions on the anisotropic-free-space interface. A matrix is developed to solve the nonorthogonality properties of Mathieu functions at the interface between two different media. Numerical results are given for the bistatic radar cross section and the amplitude of the total magnetic field along the x and y axes. The result is in agreement with that available as expected when an elliptic cylinder degenerates to a circular one.