Fourier Series Approximation of Tensor Green’s Function in Biaxial Anisotropic Media

Abstract

A new approximation algorithm is developed to compute the electromagnetic (EM) tensor Green’s function in the biaxial anisotropic media based on the Fourier series expansion. First, a rectangular region is chosen as the computation region, in which the EM field can be expressed as a 2-D Fourier series. The Fourier coefficients can be regarded as the EM field in discrete wavenumber domain. We further obtain the EM solution in the spatial domain in the form of Fourier series. Then, we use the finite terms of the Fourier series to approximate the EM field for enhancement of computation efficiency. Because the new method avoids the numerical integration in the infinite wavenumber domain, it is more convenient to implement than other methods based on integral transform. Finally, the spatial distribution of the tensor Green’s function for a transversely isotropic medium is presented to verify the proposed approach. The agreements between the results obtained by the present method and the analytic solution demonstrate the validity and the robustness of our algorithm.