Spin Hall effect of light in anisotropic gyroelectric or gyromagnetic metamaterials

The main purpose of the present article is to explore means of enhancing the separation of a light beam polarization, the well-known “spin Hall effect of light” (SHEL), when an electromagnetic wave impinges upon a double negative metamaterial (DNM). The magneto-optical nature of the anisotropic metamaterials is assumed to be activated by an externally applied magnetic field, so that our investigation on the behavior of SHEL is focused on two cases of gyroelectric and gyromagnetic metamaterials. To this end, it is supposed that the permittivity as well as permeability tensors are non-diagonal, whose off-diagonal elements are treated as variational parameters. From the results of our numerical calculation, cast into illustrative figures, we specify the optical characteristics of DNM (permittivity and permeability elements) which optimize the splitting between circularly right and left polarizations (spin states of light), a profound signature of SHEL. The latter specification is done for any angle of incidence, so that the results may be employed in a vast area of application. As a standard procedure, our numerical calculation is based on the transfer matrix method (TMM) and sequential application of rotational matrices from which reflectance and transmittance coefficients, when a Gaussian beam is incident from air onto the metamaterial, are obtained. The so obtained coefficients are then used to present the magneto-optical shifts that occur in the corresponding SHEL. Along these lines, we also calculate and discuss the Faraday and Kerr rotations. As a result of our investigation, we demonstrate how the angle of incidence, along with optical properties of the medium, affect the transverse shifts in such double negative media.