Spaces of electromagnetic and mechanical constitutive parameters for dissipative media with either positive or negative index

Abstract

Propagation of electromagnetic and acoustic plane waves in dissipative isotropic homogeneous media is described in terms of the Poynting vector and of the complex-valued wave vector. The negative sign of the refractive index, which is explained by the presence of backward bulk waves, is then directly related to the phase angle of the complex-valued wavenumber. Attention is focused on an alternative description dealing with the complex-valued dynamic material parameters: the relative permittivity ϵ and the relative permeability μ for the electromagnetic wave motion, and the bulk modulus κ and the mass density ρ for the acoustic wave motion. The 2D spaces of material parameters (ϵ,μ) and (κ,ρ) are found to be split into regions characterized by their abilities both to induce wave attenuation and to exhibit opposite directions between the energy flow and the direction of the plane wave propagation. Finally, the relevance of such representations is illustrated by superimposing experimentally retrieved and simulated constitutive parameters of media supporting both forward and backward wave motions.