Parametric Properties of Dielectric Slabs With Large Permittivity Modulation

Abstract

Plane‐wave solutions in a permittivity‐modulated dielectric slab, bordering on each side on an infinite half‐space of constant permittivity, are found both analytically and numerically. The permittivity moduiation assumed, namely ∊(t) = ∊/(1 − 2p cos 2Ωt), permits expressing the time dependence of the waves in terms of Mathieu functions and deriving the wave characteristics from the known properties of Mathieu functions. Exponentially growing waves may be spontaneously generated in the slab if the modulation index 2p and the slab width are sufficiently large. In the analytical approach, existence of increasing waves and their rate of growth is determined by attempting to attain field continuity at the interfaces by a superposition of Mathieu functions. For the case when the modulation index and the slab width are too small to support growing waves, a method is sketched for calculating the complete frequency spectrum of the response of the slab to a normally incident plane wave. The numerical approach involves use of partial difference equations and matching their solutions at the interfaces. Good agreement between analytical and numerical field solutions is demonstrated.