A Radially-Dependent Dispersive Finite-Difference Time-Domain Method for the Evaluation of Electromagnetic Cloaks

Abstract

A radial-dependent dispersive finite-difference time-domain (FDTD) method is proposed to simulate electromagnetic cloaking devices. The Drude dispersion model is applied to model the electromagnetic characteristics of the cloaking medium. Both lossless and lossy cloaking materials are examined and their operating bandwidth is also investigated. It is demonstrated that the perfect "invisibility" from electromagnetic cloaks is only available for lossless metamaterials and within an extremely narrow frequency band.

FDTD Modeling of a Cloak with a Nondiagonal Permittivity Tensor

“…Since the FDTD stability depends on the eigenvalues of ε i j and μ i j , to analyze nondiagonal cases, we must first find the eigenvalues and diagonalize ε i j and μ i j . After the diagonalization, the FDTD method for diagonal cases [31][32][33][34][35][36][37][38] can be applied. For diagonal ε i j and μ i j , elements having values less than one are replaced by dispersive quantities to avoid violating the causality and numerical stability [40][41][42][43][44].…”

“…The FDTD method has gained popularity for several reasons: it is easy to implement, it works in the time domain, and its arbitrary shapes can be calculated [26][27][28][29]. FDTD modelings of cloaks with a diagonal (uniaxial) permittivity tensor have been demonstrated [30][31][32][33][34][35][36][37][38], but a cloak with a nondiagonal permittivity tensor has never been calculated by the FDTD method. The diagonal case can be stably calculated by mapping material parameters having values less than one to a dispersion model [31].…”

An Extended FDTD Method for the Analysis of Electromagnetic Field Rotators and Cloaking Devices

“…In addition, the simulation result agrees remarkably well with the experimental ones obtained in [2] for the fabricated cloaking device, which is justified since the present model accurately incorporates the dispersive nature of the materials involved (including the experimental dumping factor). It is worth mentioning at this point that we have not utilized a radialdependent dumping factor as is done in [14]. Here, Γ is constant throughout the cylinder.…”

“…To do so, the frequency dispersion of the metamaterial was taken into account through a Lorentz material model, resulting in a dispersive cloak. Dispersive approaches based on the two-dimensional finite difference time domain (2D-FDTD) method have been suggested simultaneously by us [12] and [13,14] for the analysis of cloaking applications. In both cases, the dispersive nature of the materials was accounted for in terms of the Drude material model.…”

Finite Difference Time-Domain Modelling of Metamaterials: GPU Implementation of Cylindrical Cloak

“…The first FDTD implementation was by Zhao et. al [3] and implemented on Comsol, a commercial electromagnetic simulation software. Simulations are implemented on Matlab, C++ and GPU.…”