Investigation of Negative Refractive Index in Reciprocal Chiral Materials

It is well known that there exist both natural materials (such as milk or sugar solution) possessing chiral (or handed) properties, as well as an increasing list of man-made materials (such as sodium bromate) that exhibit chirality. One of the principal properties of chirality is that light of any arbitrary polarization, when propagating through a chiral material, splits up into two circular polarizations propagating in different directions. In the past decade or longer, researchers have investigated electromagnetic transverse (plane) wave propagation across a non-chiral/chiral interface, and determined the electromagnetic Fresnel coefficients for such propagation. Traditionally, such coefficients are derived under the assumption that the transmitted circular polarizations in the chiral material have wave numbers that are numerically positive, and nominally point in the direction of electromagnetic energy flow. However, it turns out that the actual solution for the wavenumbers obtained from applying Maxwell\u27s equations to an unbounded, isotropic chiral material yields four possible values dependent upon the chirality parameter. In this paper, we examine the emergence of these wavenumbers, and thereafter explore the conditions necessary for the resulting field solutions to have counter-propagating energy flow and wave vector. Such conditions, if feasible, represent an environment leading to an effectively negative refractive index being generated within the chiral material. Accordingly, propagation within a chiral medium through the mechanism of negative refractive indices may be studied in order to better understand the corresponding optical properties of such materials vis-a-vis transmission of an electromagnetic wave into and out of such a region. The results obtained may be applied to compare negative index chiral materials with the broader emerging field of negative index metamaterials, and explore possible applications