Analysis of electromagnetic fields in inhomogeneous medium by Fourier series expansion methods

In this paper, a new method is proposed for the electromagnetic fields with inhomogeneous medium mixed the positive/negative by the combination of improved Fourier series expansion method using the extrapolation method. Numerical results are given for the reflection and transmission coefficients, and the electromagnetic fields in the inhomogeneous region of the positive and contained the singular point (zero) for the case of TM wave using the eigenvalue and eigenvectors obtained by the extrapolation method.