Spectral analysis of polygonal cavities containing a negative-index material
Analyse spectrale de cavités polygonales contenant un matériau d'indice négative
Abstract
The purpose of this paper is to investigate the spectral effects of an interface between vacuum
and a negative-index material (NIM), that is, a dispersive material whose electric permittivity and
magnetic permeability become negative in some frequency range. We consider here an elementary
situation, namely, 1) the simplest existing model of NIM : the non dissipative Drude model, for which
negativity occurs at low frequencies; 2) a two-dimensional scalar model derived from the complete
Maxwell’s equations; 3) the case of a simple bounded cavity: a polygonal domain partially filled with
a portion of Drude material. Because of the frequency dispersion (the permittivity and permeability
depend on the frequency), the spectral analysis of such a cavity is unusual since it yields a nonlinear
eigenvalue problem. Thanks to the use of an additional unknown, we linearize the problem and we
present a complete description of the spectrum. We show in particular that the interface between
the NIM and vacuum is responsible for various resonance phenomena related to various components
of an essential spectrum.
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