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

• Published in: IEEE transactions on microwave theory and techniques Vol. 65; no. 4; pp. 1141 - 1149
• Main Authors: Ijjeh, Abdelrahman Abdallah, Ney, Michel M., Andriulli, Francesco P.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.04.2017; The Institute of Electrical and Electronics Engineers, Inc. (IEEE); Institute of Electrical and Electronics Engineers
• Subjects: Algorithms; Anisotropic and dispersive media; Anisotropic media; Anisotropy; complex linear media; Complex media; Dispersion; Electromagnetism; Engineering Sciences; Finite element method; Graphene; Hilbert space representation; Mathematical analysis; Mathematical model; Matrix methods; Maxwell's equations; Media; Stability analysis; stability and dispersion analysis; Stability criteria; Time-domain analysis; time-domain methods; Time-varying systems; Transmission-line matrix; transmission-line matrix method (TLM); transmission-line matrix method (TLM); Hilbert space representation; Maxwell's equations; time-domain methods; Time-domain analysis; dispersive media; Maxwell equations; FDTD; Mathematical model; finite difference time-domain analysis; maximum mesh size; stability; complex linear media; general linear media; stability criterion; Media; transmission line matrix methods; discrete time-domain models; complex media; Dispersion; Time-varying systems; transmission-line matrix method algorithm; stability and dispersion analysis; Anisotropic and dispersive media; Stability criteria; anisotropic dispersive media; anisotropic media
• ISSN: 0018-9480; 1557-9670
• DOI: 10.1109/TMTT.2016.2635651

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.