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

Abstract

Abstract:The increasing interest in metamaterials with negative refractive index has been prompted by a variety of promising optical and microwave applications. Often, the resulting electromagnetic problems to be solve are not analytically derivable; therefore, numerical modeling must be employed and the Transmission Line Modeling (TLM) method constitutes a possible choice. After having greatly simplified the existing TLM techniques for the modeling of metamaterials, we propose in this paper to carry out a frequency study of cloaking structure.

Response of dispersive cylindrical cloaks to a nonmonochromatic plane wave

“…Given that the interconnection between all the TLM nodes constitutes a usual distributed L -C network, TLM cannot process the exotic values of and in its original form. The problem can be fixed by substituting the L -C network by a dual one, i.e., the positions of inductors and capacitors are simply interchanged [10,13]. Such a left handed transmission line system is dispersive, which is in agreement with the necessary dispersive nature of metamaterials.…”

“…Dealing with quasi-monochromatic waves is delicate since they do not differ much from perfectly monochromatic waves; consequently, numerical errors in the modeling have to be minimized. In this sense, Cartesian coordinates, which are usually employed [13,14], lead to staircase approximations when one wants to model the curved shape of the layered cloak. To avoid this undesirable phenomenon, we will use TLM cylindrical nodes whose shape assumes the geometry of the cloaking shell [15,16].…”

Importance of the singular constitutive parameters of cylindrical cloaks: illustration on the anticloak concept

“…When reaching the center of the nodes, the voltage pulses are scattered according to a scattering matrix, S, we give hereinafter. Finally, metamaterials are easily modeled by inverting the capacitive and inductive stubs of the node [20,21]. While the scattering matrix presented in [21] was expressed in Cartesian coordinates, use of cylindrical coordinates in the present work leads to a new expression: Note that the node is made up of a total of 8 lines that should lead to an 8 ϫ 8 matrix.…”

“…Finally, metamaterials are easily modeled by inverting the capacitive and inductive stubs of the node [20,21]. While the scattering matrix presented in [21] was expressed in Cartesian coordinates, use of cylindrical coordinates in the present work leads to a new expression: Note that the node is made up of a total of 8 lines that should lead to an 8 ϫ 8 matrix. However, as no incident voltages are coming from the lossy stubs, S can be reduced to a matrix of 7 columns by 8 rows.…”