Efficient Interpolation of Multilayer Periodic Green’s Functions with Electric and Magnetic Sources

Description

This work presents a generalization of an efficient interpolation method for periodic Green’s functions in multilayer media containing transverse electric current densities and transverse equivalent magnetic current densities at different interfaces. The formulation is based on Maxwell’s equations and exploits the asymptotic behavior of the electromagnetic potentials for large spectral variables and small spatial distances. This approach enables the use of Mixed Potential Integral Equation (MPIE) formulations in the spectral domain and provides the asymptotic expressions required to characterize the singular behavior of scalar and vector potential Green’s functions for both electric and magnetic sources. By identifying the spatial singularities associated with these asymptotic behaviors, the method yields regularized multilayer periodic Green’s functions that can be efficiently interpolated throughout the entire unit cell using Chebyshev polynomials. The proposed approach offers an effective framework for improving the accuracy and computational efficiency of electromagnetic analysis in complex multilayer periodic structures.