FDTD Modeling of Dispersive Bianisotropic Media Using Z-Transform Method

Abstract

The finite-difference time-domain (FDTD) technique for simulating electromagnetic wave interaction with a dispersive chiral medium is extended to include the simulation of dispersive bianisotropic media. Due to anisotropy and frequency dispersion of such media, the constitutive parameters are represented by frequency-dependent tensors. The FDTD is formulated using the Z-transform method, a conventional approach for applying FDTD in frequency-dispersive media. Omega medium is considered as an example of bianisotropic media, the frequency-dependent tensors of which are based on analytical models. The extended FDTD method is used to determine the reflection and transmission coefficients of co-and cross-polarized electromagnetic waves from omega slabs, illuminated by normally incident plane waves. Three cases are simulated: 1) a slab of uniaxial omega medium with its optical axis parallel to the propagation vector; 2) a slab of rotated uniaxial omega medium with its optical axis not parallel to the propagation vector; and 3) a slab of biaxial omega medium. The results are validated by means of comparisons with analytical solutions.Index Terms-Bianisotropic media, chiral medium, dispersive media, finite-difference time-domain (FDTD), omega medium, Z-transform method.

EM modelling of arbitrary shaped anisotropic dielectric objects using an efficient 3D leapfrog scheme on unstructured meshes

“…Bi-anisotropic dispersive materials, such as metamaterials, which involve coupling electric and magnetic fields in the constitutive equations could also be included. This can be achieved using the Z-Transform [21][22][23]. It is also proposed to incorporate a multi-scaling procedure, to allow for the modelling of more complex materials, such as composites.…”

Beam steering of eye shape metamaterial design on dispersive media by FDTD method

“…Z‐transform is another major method in FDTD modeling scheme. In Z‐transform, frequency domain constitutive relations are changing over Z‐domain relations, appropriate structures for deriving FDTD updating equations . After successful invention of the dispersive material, Victor Vassalage in 1968 first discovered a material with simultaneous negative permittivity and permeability and also displayed some exceptional electromagnetic properties at certain frequency .…”

“…In Z-transform, frequency domain constitutive relations are changing over Z-domain relations, appropriate structures for deriving FDTD updating equations. 6 After successful invention of the dispersive material, Victor Vassalage in 1968 first discovered a material with simultaneous negative permittivity and permeability and also displayed some exceptional electromagnetic properties at certain frequency. 7 In 2000, Smith and his colleagues introduced a material that shows simultaneously negative permittivity and permeability in microwave frequency with some exceptional characteristics.…”

Rigorous broadband investigation of liquid-crystal plasmonic structures using finite-difference time-domain dispersive-anisotropic models

“…In the context of FDTD studies, several algorithms for wave propagation in media that exhibit both anisotropy and dispersive tensor elements have been proposed and implemented, indicatively, via recursive convolution (RC) [31], piecewise linear recursive convolution (PLRC) [32], z-transform [33,34], and auxiliary differential equation (ADE) [35] formulations. In these works, the permittivity tensors of the simulated materials, typically magnetized plasma and ferrites, exhibit dispersion types incapable of describing the frequency dependence of LC tensor elements and, hence, they are not suitable for the numerical investigation of LC-based photonic or plasmonic devices.…”