On the signs of the imaginary parts of the effective permittivity and permeability in metamaterials

TLDR: In this article, it was shown that the Lorentzian model often used to describe the effective parameters (i.e., the permittivity and permeability) of these metamaterials does not physically allow their imaginary parts to be negative.

Abstract: The signs of the imaginary parts of the permittivity and permeability in metamaterials such as split ring resonators and strip wires are investigated. It is shown that the Lorentzian model often used to describe the effective parameters (i.e., the permittivity and permeability) of these metamaterials does not physically allow their imaginary parts to be negative. Moreover, a popular technique used to retrieve the effective parameters of a structure from its S-parameters is also investigated. By comparing the effective parameters for an array of dielectric spheres obtained both from S-parameter simulations and analytical calculations, it is shown that an often observed negative imaginary permittivity obtained from the S-parameters is a result of numerical error in the simulations. This is shown both for the finite element method and finite-difference time-domain simulations.