In this paper, we propose a new method for the electromagnetic fields with inhomogeneous media mixed a positive and negative regions by the combination of improved Fourier series expansion method using the extrapolation method which obtains the correct value of the eigenvalue and eigenvectors for the case of TM wave. Numerical results are given for the power reflection and transmission coefficient, the energy absorption, the electromagnetic fields, and the power flow in the inhomogeneous medium mixed the positive and negative regions including the case when the permittivity profiles touches zero for the TM wave. The results of our method are in good agreement with exact solution which is obtained the modified multilayer approximation method.

Crosstalk or coupling phenomenon between two parallel conductors with a ground or reference conductor is well known in electromagnetic compatibility and microwave circuit fields. In this paper we consider the characteristics of a long two-conductor line embedded in an inhomogeneous medium while taking account of the difference between two phase constants in independent propagation modes of two parallel lines. The characteristics of near-end and far-end crosstalk and of through-end transmission are discussed for frequencies up to more than the frequency where the line length is 10 times the wavelength. Interesting properties, such as very strong and null crosstalk phenomena that occur at the far end and non-transmission at the through end, appear in the envelope characteristics. The reason for these properties is clarified by making theoretical and experimental investigations.