We employ a homogenization technique based on the Lorentz electronic theory to show that planar chiral structures (PCSs) can be described by an effective dielectric tensor similar to that of biaxial elliptically dichroic crystals. Such a crystal is shown to behave like a PCS insofar as it exhibits its characteristic optical properties, namely, corotating elliptical polarization eigenstates and asymmetric, direction-dependent transmission for left- or right-handed incident wave polarization.
The electronic Lorentz theory is employed to explain the optical properties of planar split-ring metamaterials. Starting from the dynamics of individual free carriers, the electromagnetic response of an individual split-ring meta-atom is determined, and the effective permittivity tensor of the metamaterial is calculated for normal incidence of light. Whenever the split ring lacks in-plane mirror symmetry, the corresponding permittivity tensor has a crystallographic structure of an elliptically dichroic medium, and the metamaterial exhibits optical properties of planar chiral structures. Its transmission spectra are different for right-handed versus left-handed circular polarization of the incident wave, so the structure changes its transmittance when the direction of incidence is reversed. The magnitude of this change is shown to be related to the geometric parameters of the split ring. The proposed approach can be generalized to a wide variety of metal-dielectric metamaterial geometries.
An integral approach is presented in the theory of surface electromagnetic waves propagating along the plane interface of bianisotropic non-absorbing media including optically active gyrotropic and bigyrotropic ones. This approach gives a uniform way of obtaining the dispersion equation for surface polaritons for an arbitrary cut section of the bianisotropic crystals and allows us to establish the existence conditions of surface polaritons. An example of application of this approach for the boundary of bianisotropic and isotropic media is given.
The problem of the surface polariton existence in symmetry planes of nonmagnetic biaxial crystals is studied theoretically. The plane interface of such a crystal and a semi-infinite isotropic medium is considered. With the use of the integral formalism formulated in our earlier work, the dispersion equation is derived for the polaritons under consideration. The existence conditions for the dispersion equation solutions are obtained in the form of algebraic inequalities for principal values of inverse dielectric permittivity tensors. If these conditions are satisfied, then excitation of surface waves is possible along the allowed propagation directions, which constitute sectors in the interface plane. Exact expressions are obtained that determine location of these sectors with respect to the symmetry axes of the crystal.
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