Analytically describing the temperature-dependent constitutive parameters of an electromagnetic metamaterial

Abstract

Analogous to mechanical systems, modeling the electromagnetic (EM) performance of large and complex metamaterial structures requires the use of effective-medium/constitutive properties. Constitutive properties are critical for efficiently bridging the gap between subwavelength geometry and performance at the mesoscale. In this article, the temperature-dependent effective medium properties for a metamaterial electric-inductive-capacitive (ELC) resonator are described analytically. ELC structures are commonly used in metamaterial designs to provide a tailored electric response to EM waves. An equivalent circuit model, coupled with analytic expressions for the capacitances, inductance, and resistance of the ELC resonator, is utilized to describe how thermally induced mechanical strain and changes in material properties manifest as temperature-dependent permittivity and permeability curves for the metamaterial. The resulting analytic expressions account for the effects of spatial dispersion and losses. This article also details how the process may be expanded to similarly describe the temperature-dependent constitutive properties of metamaterial magnetic resonators.