Technique for the Evaluation of Chirality, Permittivity, and Permeability of a Reciprocal Chiral Slab Through the Utilization of the Time-Harmonic Green Functions

In this paper, a technique is developed to compute values of the chirality, permittivity, and permeability of a dielectric reciprocal chiral slab from the knowledge of limited laboratory measurement information. The chirality parameter is a function of frequency and depth of the slab. The developed technique is based on the use of coupled differential equations for the Green functions associated with electromagnetic propagation through the slab. The technique makes use of the Nth degree interpolation polynomials to approximate the Green functions and the chiral parameter among other functions using Legendre-Gauss-Lobatto collocation points. Numerical results from a laboratory measurement simulation are given to demonstrate the validity of the proposed technique.

I. Introduction

Samples of chiral materials have been fabricated by embedding miniature helices in nonchiral host media [1], and potential applications for artificial chiral materials were presented in [2] and [3]. Chirality is defined by geometry; an object is called chiral if it cannot be superimposed on its mirror image by translations and rotations [4]. Thus, one can define left- and right-handed chiral objects. For example, helices of one or several turns are chiral objects. The concept of chirality has played an important role in diverse fields such as chemistry, life science, optics, radar cross section, and electromagnetic shielding [5], [6]. In chiral media, the permittivity, permeability, and chiral admittance couple the electric field to the magnetic field, and vice versa [7]. For a biisotropic and nonreciprocal chiral medium with permittivity , permeability , and general chirality parameters and , the effects of handedness in its electrodynamics result in two coupled vector equations [8]. These equations are constitutive relations that relate the electric and magnetic fields, i.e., and , respectively, to the electric and magnetic fluxes, i.e., and , respectively. Notably, the scientific and engineering community has shown interest in electromagnetic scattering from and propagation through chiral media (see, for example, [9] and the references therein). In this paper, the case of a transversely polarized time-harmonic electromagnetic plane wave normally incident on a dielectric reciprocal chiral stratified slab is considered. In this case, the slab's permittivity, permeability, and chirality parameter are considered unknown functions of a depth variable into the slab, i.e., , where represents the known thickness of the slab. Significantly, in addition to being a function of depth, the chirality parameter is a complex function of frequency. The geometry of the problem considered here is shown in Fig. 1, where , , and are the incident, transmitted, and reflected electric fields, respectively. Fig. 1.

Geometry of the problem.