TLM numerical solution of Bloch's equations for magnetized gyrotropic media

Abstract

The transmission-line matrix (TLM) method, introduced by P. B. Johns more than two decades ago, is today commonly used for the numerical simulation of wave propagation and transport phenomena. With increasing evidence the method involves a rich potentiality of yet unknown applications. In this paper a TLM solution of the linearized Bloch-Maxwell equations is presented using a nonorthogonal hexahedral mesh cell. Our approach is in fact very general and yields solutions of finite-difference equations perturbed by a linear or nonlinear causal function of the fields. Recursive relations between the scattering operations of the perturbed and unperturbed TLM processes are derived that are largely independent of the kind of FD equations or causal function. A natural description of the perturbed TLM process is given in terms of recursively shifted (deflected) scattered quantities. Specifically the TLM solution of the coupled Bloch-Maxwell relations for gyrotropic matter in a “strong” static field is presented. A gyromagnetic node is derived, and the conditions for algorithm stability are inferred for finite spin-spin relaxation time. Numerical results are compared to experimental data at the example of a waveguide Y-circulator.