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

TL;DR

This paper introduces a novel FDTD modeling approach that incorporates spatial dispersion effects in wire media, enabling accurate simulation of sub-wavelength imaging with improved stability and reduced computational domain size.

Contribution

The authors develop the first FDTD formulation that accounts for spatial dispersion in wire media, analyzing its stability and validating it with sub-wavelength lens simulations.

Findings

Spatial dispersion is effectively incorporated into FDTD modeling.

The stability of the proposed formulation is confirmed with standard Courant limits.

Enhanced simulation accuracy and convergence with modified PML boundaries.

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 sub-wavelength 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.