Rigorous speckle simulator for large area rough penetrable surfaces using surface integral equations and multilevel fast multipole method

Scattering of electromagnetic waves from rough surfaces has been actively studied for more than a century, since it is involved in wide-ranging applications, among which optical metrology for surface inspection is especially interesting for us. Through analyzing the speckle fields, profound information of the surface under inspection can be retrieved. Hence, calculation of scattered near and far fields from rough surfaces is indispensable for understanding the statistical properties of speckles and for evaluating the roughness of the optical surfaces. We report a rigorous speckle simulator developed for large area rough surfaces of general material including metals using surface integral equations and multilevel fast multipole method (MLFMM) implemented using Fortran. Via MLFMM combined with an iterative solver of generalized minimum residual (GMRES) method, the computation cost is reduced from O(N2) to O(NlogN). Convergence performance of different formulations of linearly combined tangential electric field integral equation and magnetic field integral equation are discussed.