Numerical Investigation On The Scattering Of An Arbitrarily Incident Gaussian Beam By Complex Particles

In this dissertation, the scattering of an arbitrarily incident Gaussian beam by systems of complex particles is systematically investigated. Specifically, the systems of complex particles include arbitrarily shaped metallic particles, arbitrarily shaped homogeneous dielectric particles, arbitrarily shaped inhomogeneous particles, random discrete particles and fractal soot aggregates. The main work and results are as follows:1. Based on the Davis-Barton fifth-order Gaussian beam model and combining the coordinates rotation matrix in the Cartesian coordinates, the electromagnetic field components of the arbitrarily incident Gaussian beam are derived, which provides the basis for the analysis of Gaussian beam scattering by complex particles by using the numerical method.In comparison with commonly used paraxial and first-order Gaussian beam descriptions, the fifth-order Gaussian beam description can accurately describe the incident Gaussian beam, particularly for tightly focused conditions.2. The method of moments (MOM) and the fast multipole method (FMM) for solving the integral equations are intensively studied, especially for the procession of the singular elements of the impedance matrix. The MOM and FMM are firstly applied to investigate the scattering of an arbitrarily incident focused Gaussian beam by arbitrarily shaped metallic particles. The calculated results for a conducting sphere are compared with those obtained from the generalized Lorenz-Mie theories (GLMT). Very good agreements are achieved which indicate the validity of the proposed method as well as our implemented program. It is also indicated that the application of numerical method to investigate Gaussian beam scattering problems is feasible.3. The PMCHW formulation and the JMCFIE formulation for analyzing the scattering problems involving arbitrarily shaped homogeneous dielectric particles are intensively studied. The MOM based on PMCHW and JMCFIE formulations are firstly applied to investigate the scattering of an arbitrarily incident focused Gaussian beam by arbitrarily shaped homogeneous dielectric particles. The calculated results for a homogeneous dielectric sphere are compared with those obtained from the GLMT. Very good agreements are achieved which indicate the validity of the proposed method as well as our implemented program. Some numerical results not presented yet in the literature are also given. These results can be used as references for other numerical methods in analyzing the light scattering properties of arbitrary shaped dielectric particles illuminated by a Gaussian beam. 4. We first employed the MOM based on the surface integral equations to investigate the scattering of an arbitrarily incident Gaussian beam by two typical inhomogeneous particles of arbitrary shape, namely, the arbitrarily shaped particles with multiple arbitrarily shaped metallic inclusions and the arbitrarily shaped particles with multiple dielectric inclusions of arbitrary shape. The surface integral equations for characterizing the scattering problems involving arbitrarily shaped particles with multiple internal inclusions of arbitrary shape are presented. The calculated results for a spherical particle with a concentric metallic inclusion and a spherical particle with an eccentrically located spherical inclusion are compared with those obtained from the GLMT. Very good agreements are achieved which indicate the validity of the proposed method as well as our implemented program. Some numerical results for the scattering of Gaussian beam by complex inhomogeneous particles are also given.5. We first employed the characteristic basis function method (CBFM) based on the surface integral equations to investigate the scattering of an arbitrarily incident focused Gaussian beam by multiple randomly distributed metallic and homogeneous dielectric particles. The surface integral equations for characterizing the scattering problems involving multiple metallic and homogeneous dielectric particles are presented in detail. The characteristic basis function method for solving the resultant matrix equation is discussed especially. A hybrid finite element-boundary integral-characteristic basis function method is proposed for an efficient simulation of light scattering by multiple randomly distributed inhomogeneous particles. Some numerical examples are presented to demonstrate the validity and capability of the proposed methods.6. A novel numerical method is presented for characterizing the light scattering by fractal aggregates that are made up of a number of non-overlapping spherical particles. This method is an extension of the hybrid finite element and boundary integral method. The theoretical and implementation of the proposed method are discussed in detail. The proposed method is then applied to examine the scattering behavior of fractal soot aggregates illuminated by Gaussian beams with arbitrary incidence. Some numerical examples are presented to demonstrate the validity and capability of the proposed method. Results involving single soot aggregates and ensembles of randomly distributed fractal soot aggregates are presented.