Light propagation in 1D inhomogeneous deterministic media: the effect of discontinuities

Abstract

The propagation of light in one-dimensional inhomogeneous deterministic media where the refractive index varies on a wavelength scale is numerically evaluated without approximations. To this end, the field is written in amplitude and phase variables leading to a nonlinear amplitude differential equation. The numerical solutions to this Ermakov-type equation for five different refractive index profiles are presented. The amplitude oscillations are construed in terms of opposite phase or counter-propagating waves. The reflectivity is then evaluated for different interface thicknesses. The discontinuities in the first-and second-order derivatives are shown to produce an enhanced reflectivity even if the functions are continuous and monotonic.