Refractive index profiles for a 𝒫𝒯-symmetric optical structure

Abstract

By mapping the scalar Helmholtz equation (SHE) to the Schrödinger form we investigate the behavior of [Formula: see text] optical structure when the refractive index distribution n admits variation in the longitudinal direction only. Interpreting the Schrödinger equation in terms of a superpotential we determine the supersymmetric partners for n. We also obtain new analytical solutions for the refractive index profiles and provide graphical illustrations for them.