Padé approximations in inverse homogenization and numerical simulation of electromagnetic fields in composites

The paper considers rational Padé approximation of the spectral function of composites with fine microstructure and discusses its use in characterization of the microgeometry of composite materials and in numerical simulation of time-domain electromagnetic fields in composites. It is assumed that the scale of the structure is much smaller than the smallest wavelength of the applied field. We use Stieltjes representation of the effective complex permittivity of the composite and derive its Padé approximation. The spectral function in this representation contains all information about the microgeometry of the mixture. Having reconstructed the Padé approximation, we recover information about the composite structure. The resulting time-domain equations governing the electromagnetic fields are of convolution type. We use rational Padé approximation to derive equations for internal variables for time-domain simulation. We show that electromagnetic fields computed using such internal variables, correspond to the fields in S-equivalent composite structures.