Inverse scattering problem for gratings with deep modulation

The similarity between one-dimensional Schrödinger and Helmholtz equations is discussed. The Helmholtz equation in optical coordinate is shown to reduce to the Schrödinger equation with an effective potential. Two examples of scattering problem are considered: sinusoidal Bragg grating with deep modulation and smooth hyperbolic secant layer. The inverse scattering problem is solved numerically for both cases. For the layer an analytical solution is presented as well. The analysis of the effective potential allows one to qualitatively predict some properties of the reflection spectrum.