Zhiwei Cui

Scattering of a zero-order Bessel beam by arbitrarily shaped homogeneous dielectric particles

In this paper, we introduce an efficient numerical method based on surface integral equations to characterize the scattering of a zero-order Bessel beam by arbitrarily shaped homogeneous dielectric particles. The incident beam is described by vector expressions in terms of the electric and magnetic fields that perfectly satisfy Maxwells equations. The scattering problems involving homogeneous dielectric particles with arbitrary shapes are formulated with the electric and magnetic current combined-field integral equation and modeled by using surface triangular patches. Solutions are performed iteratively by using the multilevel fast multipole algorithm. Some numerical results are included to illustrate the validity and capability of the proposed method. These results are also expected to provide useful insights into the scattering of a Bessel beam by complex-shaped particles.

Scattering of a zero-order Bessel beam by a concentric sphere

The scattering of an on-axis incident zero-order Bessel beam by a concentric sphere is firstly investigated by using an analytical method. Based on the spherical vector wave functions, the expansion expressions of the incident Bessel beam are derived in terms of the electric and magnetic fields that satisfy Maxwells equations. According to the integral localized approximation, an analytical formula for the calculation of beam shape coefficients is given. The present method is validated by the comparison of the analytical result and the numerical result obtained from the surface integral equation method. The effects of the beam half-angle, the refractive index of inner sphere and the size parameter of concentric sphere on the differential scattering cross section are analyzed in detail. This investigation is expected to provide key theoretical support and practical guidance for the techniques of laser detection on particle and diagnosis.

Internal and near-surface electromagnetic fields for a dielectric spheroid illuminated by a zero-order Bessel beam

Within the framework of generalized Lorenz-Mie theory, scattering from a homogeneous spheroidal particle illuminated by an on-axis zero-order Bessel beam is formulated analytically, with special attention paid to the investigation of internal and near-surface fields. Numerical results concerning the spatial distributions of internal and near-surface fields are presented for various parameter values, such as the half-cone angle of the incident zero-order Bessel beam, the major axis, the minor axis, and the refractive index of the spheroid. The study of internal and near-surface field distributions will contribute to the understanding of Bessel beam scattering by nonspherical particles with sizes close to the incident wavelength.

A Domain Decomposition of the Finite Element-Boundary Integral Method for Scattering by Multiple Objects

Abstract A domain decomposition method based on the hybrid finite element–boundary integral method is presented for analyzing electromagnetic scattering problems involving multiple separable objects. In this method, the finite element formulation is applied inside each object to derive a linear system of equations associated with edge field values. The boundary integral equation is then applied on the surfaces of the objects to truncate the computational domain and to connect the matrix subsystem generated from each object. The coupling system of equations is solved by a hybrid domain decomposition algorithm. Numerical results are presented to demonstrate the accuracy, efficiency, and capability of the proposed method.

Scattering of Gaussian beam by arbitrarily shaped particles with multiple internal inclusions

In this paper, we introduce an efficient numerical method based on surface integral equations to characterize the scattering of an arbitrarily incident Gaussian beam by arbitrarily shaped particles with multiple internal inclusions. The incident Gaussian beam is described by the Davis-Barton fifth-order approximation in combination with rotation Euler angles. For numerical purposes, the surfaces of the host particle and the inclusions are modeled using small triangular patches and the established surface integral equations are discretized with the method of moments. The resultant matrix equation is solved by using a parallel implementation of conjugate gradient method on distributed-memory architectures. Some numerical results are included to illustrate the validity and capability of the developed method. These results are also expected to provide useful insights into the scattering of Gaussian beam by composite particles.

Numerical simulation of multiple scattering by random discrete particles illuminated by Gaussian beams

In this paper, we present an efficient numerical method for the simulation of multiple scattering by random discrete particles illuminated by focused Gaussian beams with arbitrary incidence. Specifically, the Davis first-order approximation in combination with rotation Euler angles is used to represent the arbitrarily incident Gaussian beams. The surface integral equations are applied to formulate the scattering problems involving multiple discrete particles with a random distribution and are numerically discretized by the method of moments. The resultant matrix equation is solved by employing the characteristic basis function method based on the use of macrobasis functions constructed according to the Foldy-Lax multiple scattering equations. Since this method only requires the solution of small-size matrix equations associated with isolated particles and it is also readily parallelized, the computational burden can be significantly relieved. Some numerical results are included to illustrate the validity of the present method and to show the scattering behaviors of random discrete particles when they are illuminated by focused Gaussian beams.

EFFICIENT ANALYSIS OF SCATTERING FROM MULTIPLE 3-D CAVITIES BY MEANS OF A FE-BI-DDM METHOD

A flnite element-boundary integral-domain decomposition method is presented for analyzing electromagnetic scattering problems involving multiple three-dimensional cavities. Speciflcally, the edge- based flnite element method is applied inside each cavity to derive a linear system of equations associated with unknown flelds. The boundary integral equation is then applied on the apertures of all the cavities to truncate the computational domain and to connect the matrix subsystem generated from each cavity. With the help of an iterative domain decomposition method, the coupling system of equations is reduced to a small one which only includes the unknowns on the apertures. To further reduce computational burdens, the multilevel fast multipole algorithm is adopted to solve the reduced system. The numerical results for the near and far flelds of several selected multi-cavity problems are presented to demonstrate the validity and capability of the proposed method.

Multiple scattering of arbitrarily incident Bessel beams by random discrete particles.

In this paper, we introduce an efficient numerical method to characterize the multiple scattering by random discrete particles illuminated by Bessel beams with arbitrary incidence. Specifically, the vector expressions of Bessel beams that perfectly satisfy Maxwells equations in combination with rotation Euler angles are used to represent the arbitrarily incident Bessel beams. A hybrid vector finite element-boundary integral-characteristic-basis function method is utilized to formulate the scattering problems involving multiple discrete particles with a random distribution. Due to the flexibility of the finite element method, the adopted method can conveniently deal with the problems of multiple scattering by randomly distributed homogeneous particles, inhomogeneous particles, and anisotropic particles. Some numerical results are included to illustrate the validity and capability of the proposed method and to show the scattering behaviors of random discrete particles when they are illuminated by Bessel beams.

Scattering of arbitrarily incident Gaussian beams by fractal soot aggregates

A hybridization of the finite element and boundary integral methods is applied to the study of light scattering by fractal soot aggregates illuminated by Gaussian beams with arbitrary incidence. In particular, the Davis–Barton fifth-order approximation in combination with rotation Euler angles is employed to represent the arbitrarily incident Gaussian beams. The finite element method is used to obtain the solution of the vector wave equation inside each primary particle and the boundary integral equations are applied on the surfaces of all the particles as a global boundary condition. The resultant matrix equation is solved by an iterative method, where the multilevel fast multipole algorithm can be employed to speed up the matrix–vector multiplication. Some numerical results are included to illustrate the validity of the present method and to show the scattering behaviors of fractal soot aggregates when they are illuminated by Gaussian beams.

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.