Time domain simulation of electromagnetic cloaking structures with TLM method

Abstract

Abstract:The increasing interest in invisible cloaks has been prompted in part by the availability of powerful computational resources which permit numerical studies of such a phenomenon. These are usually carried out with commercial software. We report here a full time domain simulation of cloaking structures with the Transmission Line Modeling (TLM) method. We first develop a new condensed TLM node to model metamaterials in two dimensional situations; various results are then presented, with special emphasis on what is not easily achievable using commercial software.

Numerical determination of frequency behavior in cloaking structures based on L-C distributed networks with TLM method

“…This approach consists basically in substituting the anisotropic medium of the shell by a concentric layered structure of alternating homogeneous isotropic materials. Furthermore, the permittivity and permeability of the layers are calculated very close to their inner boundary (but not rigorously in the vicinity of the boundary in order to avoid divergence of the EM parameters in the first layer) since this procedure has been shown to give the best results [5]. The cloaking entity is illuminated by a Gaussian pulse, which theoretically contains all the frequencies.…”

“…The scattering matrix, as well as Eqs. (3)(4)(5), is absolutely unaltered with respect to the classical node, which renders the technique very comfortable to use. For propagation on the x-y plane, the only non-zero field components for a TE mode are E z , H x , and H y .…”

“…Considering that these artificial media are on the cutting-edge of current research, it is of first interest to render more comfortable the modeling involving MM. In this sense, it has been shown recently that such a drastic modification is not necessary for the 2D case; a simple 2D condensed node with only three new stubs is perfectly able to model materials with negative parameters [5]. This new technique offers the possibility of easily modeling complex structures involving MM whilst maintaining the potentiality of a time domain method.…”

“…Second, the description, already given in [5], of the parallel node associated with a TE mode is completed. Third, by using the approximation presented by Huang et al [9], a cloaked Perfectly Electric Conducting (PEC) cylinder is modeled, while the time-domain nature of TLM is exploited so as to study, with a single simulation run, its frequency behavior over a wide spectral range.…”

Dispersion inherent to TLM nodes for modelling of metamaterials

“…However, it is well known that a network of left-handed transmission lines (with the position of L and C interchanged) can support backward electromagnetic waves. A TLM node capable of assuming metamaterials naturally arises from these dual structures [3] and, what is more, it was shown that the only modification compared to the usual version is the value of the impedances of the stubs [4].…”