Effect of Spatial Dispersion on the Properties of a Semi-Infinite Dielectric

Abstract

In this paper, we explore the properties of a model of a semi-infinite nonlocal dielectric to assess the effect of spatial dispersion on the reflectivity of the material and on the properties of surface polaritons. For the model, the nonlocal form of Maxwell's equations may be solved exactly. The additional boundary conditions follow from Maxwell's equations, and it is not necessary to introduce microscopic considerations to complete the theory. We exhibit closed expressions for the reflectivity of the material, for the case where the electric field is parallel to the plane of incidence, and for the case where it is perpendicular to the plane of incidence. At non-normal incidence, when the electric field vector is parallel to the plane of incidence, structure which owes its origin to spatial-dispersion effects appears in the reflectivity. We show that in the presence of spatial dispersion, the surface polaritons acquire a finite lifetime even in the case where the dielectric is lossless; i.e., in the presence of spatial dispersion the surface polaritons become virtual surface waves. In the quasistatic limit, we obtain an analytic expression for the dependence of the real and imaginary part of the surface-polariton frequency on wave vector in the long-wavelength limit. We then present the theory of frustrated internal reflection of radiation from a prism and crystal configuration similar to that employed in several recent experiments. In a final section, we present the results of some numerical calculations of the reflectivity of the crystal, and the width and position of the dip observed in the frustrated-internal-reflection method, for parameters characteristic of the fundamental exciton line in ZnSe.