BI-FDTD: A Novel Finite-Difference Time-Domain Formulation for Modeling Wave Propagation in Bi-Isotropic Media

Abstract

This paper presents a newly developed finite-difference time-domain (FDTD) technique, referred to as BI-FDTD, for modeling electromagnetic wave interactions with bi-isotropic (BI) media. The theoretical foundation for the BI-FDTD method will be developed based on a wavefield decomposition. The main advantage of this approach is that the two sets of wavefields are uncoupled and can be viewed as propagating in an equivalent isotropic medium, which makes it possible to readily apply conventional FDTD analysis techniques. The BI-FDTD scheme will also be extended to include the dispersive nature of chiral media, an important subclass of bi-isotropic media. This extension represents the first of its kind in the FDTD community. Validations of this new model are demonstrated for a chiral half-space and a chiral slab.

Time-Domain Finite-Difference and Finite-Element Methods for Maxwell Equations in Complex Media

“…BI-ANISOTROPIC, BI-ISOTROPIC, AND CHIRAL MEDIA FDTD algorithms for bianisotropic media, in which the constitutive relations exhibit magnetoelectric coupling of the form and have been developed in [222] and, for the uniaxial case, in [223]. FDTD algorithms for bi-isotropic media where there exists an isotropic magnetoelectric coupling of the form , have been presented in [224] and [225]. An important case of bi-isotropic media is chiral media, where the frequency-domain constitutive relations can be written as and , where is the chirality parameter, and is the speed of light in vacuum.…”

Time-Domain Integral Equation Solver for Radiation From Dipole Antenna Loaded With General Bi-Isotropic Objects

“…It is not very difficult for us to extend the proposed method for frequency dependent materials. The TDIE method based on the MOD procedure is one of the recursive convolution techniques that allow linear dispersion to be incorporated like FDTD [31,32] formulation. The extention of the MOD based TDIE method for radiation problems of arbitrarily shaped wire antenna interacting with dispersive BI objects will be considered as the future work.…”

Lod-Like Method That Characterizes the Analytical Solution

“…However, these unconditionally stable algorithms are generally applied to the FDTD methods for isotropic media. As to the FDTD methods for bi-isotropic media [4][5][6][7][8][9][10], none of them is unconditionally stable except the one presented in [10]. The new discretization approach proposed in [4] considered the characteristics of the constitutive relations for bi-isotropic media [11][12][13][14][15][16].…”