Study on the stability of the FDTD extension for modeling transient propagation in dispersive bi-isotropic media

This paper addresses the problem of the stability analysis and the numerical dispersion of a recently developed extension of the conventional FDTD scheme to incorporate bi-isotropic media. This FDTD formulation developed is a second order accurate conditionally stable algorithm that allows computing transient wave propagation in general dispersive lossy bi-isotropic media. The von Neumann technique is applied to compute the associated characteristic polynomial. The stability condition is that all the roots of this polynomial have modulus less than or equal to unity. For full bi-isotropic media the roots have to be numerically computed as a function of the medium and simulation parameters. The dispersion relation for a dispersive bi-isotropic medium is derived.