Integral Equation Analysis of EM Scattering from Multilayered Metallic Photonic Crystal Accelerated with Adaptive Cross Approximation

Abstract EN

A space-domain integral equation method accelerated with adaptive cross approximation (ACA) is presented for the fast and accurate analysis of electromagnetic (EM) scattering from multilayered metallic photonic crystal (MPC).

The method directly solves for the electric field in order to easily enable the periodic boundary condition (PBC) in the spatial domain.

The ACA is a purely algebraic method allowing the compression of fully populated matrices; hence, its formulation and implementation are independent of integral equation kernel (Green’s function).

Therefore, the ACA is very well suited for accelerating integral equation analysis of periodic structure with the integral kernel of the periodic Green’s function (PGF).

The computation of the spatial-domain periodic Green’s function (PGF) is accelerated by the modified Ewald transformation, such that the multilayered periodic structure can be analyzed efficiently and accurately.

An effective interpolation method is also proposed to fast compute the periodic Green’s function, which can greatly reduce the time of matrix filling.

Numerical examples show that the proposed method can greatly save the frequency sweep time for multilayered periodic structure.