Simulation of realistic speckle fields by using surface integral equation and multi-level fast multipole method

Abstract

This report presents a speckle simulator which calculates rigorously speckle fields with full randomization from rough surfaces. To achieve this, surface integral equation (SIE) method accelerated via multilevel fast multipole method (MLFMM) is implemented. Among several linear formulations to combine the electric and magnetic field integral equations, we demonstrate that one is most suitable for dielectric rough surfaces and one for metallic rough surfaces. As examples, silver and silicon rough surfaces are simulated at a wavelength of 500 nm. To investigate speckles from extended areas, silicon rough surfaces with a size of 30×30 µm2 and two million unknowns are calculated. Based on the resultant speckle fields, speckle contrast, angular speckle-correlation and transverse autocorrelation function of intensity in the van Cittert-Zernike zone are further calculated and known relations versus surface roughness are manifested, indicating that sufficient statistic surface information is encoded in the speckle fields. The SIE-MLFMM method with the suitable formulation proves to be an efficient rigorous simulation tool for relatively large rough surface problems and would enable more profound numerical studies for speckle involved optical metrologies.