Stability and Dispersion Analysis of a TLM Unified Approach for Dispersive Anisotropic Media

With the advancement of technology, modern equipment involves new functionalities that require complex media (e.g., anisotropic dispersive media such as ferrite, lossy dielectrics, or graphene) for a variety of applications. This imposes the necessity to extend simulation techniques capable of solving Maxwell's equations in such media. However, as far as discrete time-domain models are concerned, their performance in terms of dispersion and stability criterion has not been thoroughly investigated in the presence of complex media. More particularly, a question arises about which maximum mesh size can be used and the resulting time step to ensure stability. Starting from a transmission-line matrix method algorithm for the general linear media, procedures for dispersion and stability analysis are given and special cases are presented. It is found that the proposed approach allows, in certain cases, some significant reduction in the computer cost compared to the approximate rules generally used. The same procedures can be easily extended to other time-domain schemes such as FDTD.