Generalized eigenproblem of hybrid matrix method for stable analysis of periodic multilayered bianisotropic media

摘要

Electromagnetic wave propagation in periodic multilayered bianisotropic media has been a topic of considerable interest for many years. One of the celebrated techniques for analysis of such media is based on the combination of transfer matrix method and Floquet (Bloch) wave theory [1]. Once the transfer matrix for a unit cell has been determined through proper cascading, Floquet waves are found simply as its eigenvectors with the associated eigenvalues being the exponentials of Floquet wavenumbers. Despite being very useful, the transfer matrix method has been known to suffer from the inherent numerical instabilities [2], particularly when the layer thickness is large and/or the frequency is high. There have been various techniques proposed to alleviate the numerical problem including recursive transformation, eigen-, or Riccati-based admittance, impedance, and reflection or scattering matrix methods [2]-[5]. However, these techniques cannot be applied to find Floquet waves directly. The objective of this paper is to devise a stable method to determine the Floquet waves without appealing to the transfer matrix. The method is based on the solutions to a generalized eigenproblem of hybrid matrix, which is always stable for any thickness or frequency [6].