Modelling of Wave Propagation in Wire Media Using Spatially Dispersive Finite-Difference Time-Domain Method: Numerical Aspects

Abstract

Abstract-The finite-difference time-domain (FDTD) method is applied for modelling of wire media as artificial dielectrics. Both frequency dispersion and spatial dispersion effects in wire media are taken into account using the auxiliary differential equation (ADE) method. According to the authors' knowledge, this is the first time when the spatial dispersion effect is considered in the FDTD modelling. The stability of developed spatially dispersive FDTD formulations is analysed through the use of von Neumann method combined with the Routh-Hurwitz criterion. The results show that the conventional stability Courant limit is preserved using standard discretisation scheme for wire media modelling. Flat sub-wavelength lenses formed by wire media are chosen for validation of proposed spatially dispersive FDTD formulation. Results of the simulations demonstrate excellent subwavelength imaging capability of the wire medium slabs. The size of the simulation domain is significantly reduced using the modified perfectly matched layer (MPML) which can be placed in close vicinity of the wire medium. It is demonstrated that the reflections from the MPML-wire medium interface are less than -70 dB, that lead to dramatic improvement of convergence compared to conventional simulations.

Spatially dispersive finite-difference time-domain analysis of sub-wavelength imaging by the wire medium slabs

“…The particular details concerning numerical aspects of proposed spatially dispersive FDTD method such as stability analysis and numerical dispersion are available in [16].…”

FDTD Modeling of a Cloak with a Nondiagonal Permittivity Tensor

“…The central average operator improves the stability and accuracy [40,49,50]. Similarly, D x and D y are discretized, and we obtain the E x -update equation…”

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

“…An FDTD formulation for "wire media", a type of metamaterial with spatial dispersion, is presented in [80]. Special cases of spatially dispersive media are bianisotropic and biisotropic media, which are considered in Section V ahead.…”