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(N 3) to O(N 1.3), 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 60 λ × 60 λ 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. 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. [ABSTRACT FROM AUTHOR]