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

A generalization of the efficient interpolation of periodic Green’s functions is presented for a multilayer medium hosting transverse electric current densities and transverse equivalent magnetic current densities at different interfaces. The mathematical model is realized in terms of Maxwell’s equations for multilayer media with isolated electric and magnetic equivalent current densities for large values of spectral variables or small values of spatial variables. This fact enables the use of Mixed Potential Integral Equation (MPIE) approaches in the spectral domain and provides asymptotic behaviors for Green’s functions of vector and scalar potentials for both electric and magnetic sources. Consequently, the singular behaviors of the Green’s functions around the source point are obtained as the spatial counterpart of the proposed spectral asymptotic behaviors. Thus, regularized multilayer periodic Green’s functions are obtained, which can be efficiently interpolated over the entire unit cell using Chebyshev’s polynomials.