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

•To calculate speckle fields from extended rough surfaces rigorously, a simulator using surface integral equation method accelerated via a fast algorithm MLFMM was implemented. When a proper formulation is chosen, the computation complexity of the solver is reduced from O(N3) to O(N1.3), which makes electrical large problems calculable. We have investigated four accurate formulations for different materials. We find that two non-preconditioned formulations are fast and stable for large dielectric surfaces and a preconditioned one for metallic surfaces. Using ICTF for silicon surfaces we have calculated and compared the speckle fields from extended Si surfaces with a size of 60λ×60λ and with different surface roughness. Thanks to relatively large surface calculation, we can observe the evolution of speckles from near field to far field regime. A full randomization of speckle fields is manifested through investigating the correlation of surface roughness with angular correlation coefficient, speckle contrast and transversal distribution of correlation coefficient of speckle fields in free-space geometry. Our results demonstrate that when the proper formulation is chosen, SIE-MLFMM is a realistic simulation tool for dielectric extended rough surfaces even on a computer with moderate power. This capability would enable more sophisticated investigations concerning speckles.