Swiss roll lattices: numerical and asymptotic modeling

Abstract

The design of metamaterials for microwave devices with new properties is an active field of research. Various kinds of structures such as the ‘Swiss roll’ are proposed as candidates with innovative properties. In order to model such structures, we consider the out-of-plane propagation of electromagnetic waves in a lattice with arbitrary dielectric or perfectly conducting inclusions. The problem is reduced to finding Bloch modes characterized by a transverse Bloch propagation vector, a longitudinal propagation constant, and a pulsation. The dispersion curves obtained give the relevant information on the physical properties of the equivalent material. Eventually, an asymptotic approach is given which allows us not only to foresee the first dispersion curves but also to determine precisely enough the main characteristics of the map of the corresponding modes.