Surface-integral-equation solution for solid particles with wavelength-scale surface roughness

Abstract

A Surface Integral Equation (SIE) method has been implemented to analyze light scattering by arbitrarily shaped solid dielectric particles. Specifically, the Poggio–Miller–Chang–Harrington–Wu–Tsai formulation is discretized using the Galerkin method, employing Rao–Wilton–Glisson basis functions. The numerical solution is further accelerated through the application of the high-frequency Multilevel Fast Multipole Algorithm (MLFMA). This MLFMA-accelerated SIE solution demonstrates efficiency for homogeneous particles with moderately rough surfaces, even in the absence of advanced preconditioning techniques and broadband MLFMA. Notably, as the number of unknowns scales with the surface area, the SIE solution offers a distinct advantage over traditional volumetric methods, such as the discrete-dipole approximation and finite-element methods, where the number of unknowns scales with the volume of the scatterer. The SIE method is employed to investigate light scattering by homogeneous particles with rough surfaces, and the results are compared to the geometric optics approximation. It is demonstrated that the geometric optics approximation yields poor accuracy for particles with self-affine surface roughness.