Diffraction of light by a periodically modulated dielectric half-space

Abstract

We present an exact solution for the diffraction of $p$-polarized light incident from a vacuum onto a half-space whose dielectric constant is periodically modulated along the longitudinal direction. We use a "modal theory," in which the amplitude of modulation is not assumed to be small. In contrast with earlier treatments of this problem the average dielectric constant of the half-space is assumed to be negative. As a result of this assumption the incident light can couple into the surface polaritons that propagate along the planar vacuum-dielectric interface, through the periodicity of the dielectric constant of the substrate. We have implemented the theory numerically for models of an artificial metallic superlattice and for modulation-doped GaAs, both employing the Drude dielectric constant with a sinusoidally varying plasma frequency and damping parameter. Reflectivity dips down to 0.5 are found together with ninefold enhancements in the squared modulus of the field at the surface.