Refractive index profiles for a $\mathcal{PT}$-symmetric optical structure

TL;DR

This paper explores the behavior of $ ext{PT}$-symmetric optical structures by mapping the scalar Helmholtz equation to a Schrödinger form, deriving new analytical solutions for refractive index profiles, and analyzing their supersymmetric partners.

Contribution

It introduces a novel approach by mapping the Helmholtz equation to Schrödinger form and derives new analytical solutions for $ ext{PT}$-symmetric refractive index profiles.

Findings

Derived new analytical solutions for refractive index profiles.

Mapped Helmholtz equation to Schrödinger form for $ ext{PT}$-structures.

Identified supersymmetric partners of refractive index profiles.

Abstract

By mapping the scalar Helmholtz equation (SHE) to the Sch\"{r}odinger form we investigate the behaviour of $\mathcal{PT}$ optical structure when the refractive index distribution $n$ admits variation in the longitudinal direction only. Interpreting the Sch\"{r}odinger 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.