Direct perturbative-framework analysis of the effective electromagnetic parameters for lossless nonlinear left-handed optical metamaterials possessing an inversion symmetry

Abstract

In the present work, we derive the expressions of the effective material parameters of a lossless nonlinear left-handed optical material medium that possesses an inversion symmetry. Here, the left-handed optical material considered is an array of split-ring resonators and thin metal wires that are embedded in a nonlinear dielectric substrate material which is assumed to possess an inversion symmetry at the molecular level. Starting from the unit cell of the considered left-handed material lattice, we derive the lattice equations in terms of the charges induced by the incident field. We then employ a perturbative scheme and direct calculation method to mathematically obtain the effective permeability and permittivity of the left-handed material medium. From these findings, it appears that the behaviors of the effective electromagnetic material parameters are affected by the magnitudes of the third-order nonlinearities, which provide a new approach for better understanding of the electromagnetic responses of continuous medium.