Stability and Dispersion Analysis of a TLM Unified Approach for Dispersive Anisotropic Media
Résumé
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
Mots clés
maximum mesh size
stability criterion
discrete time-domain models
Maxwell's equations
anisotropic dispersive media
complex media
Media
Time-domain analysis
Dispersion
Time-varying systems
Mathematical model
Stability criteria
Anisotropic and dispersive media
complex linear media
Hilbert space representation
stability and dispersion analysis
time-domain methods
transmission-line matrix method (TLM)
anisotropic media
dispersive media
finite difference time-domain analysis
Maxwell equations
stability
transmission line matrix methods
FDTD
general linear media
transmission-line matrix method algorithm