Balanced Gain-and-Loss Optical Waveguides: Exact Solutions for Guided Modes in Susy-QM

TL;DR

This paper develops exactly solvable complex refractive indices for optical waveguides using supersymmetric quantum mechanics, enabling balanced gain and loss with conserved optical power.

Contribution

It introduces a method to construct complex refractive indices with zero total gain or loss, extending beyond parity-time symmetry using Darboux-Crum transformations.

Findings

Refractive indices with zero total area imaginary part are obtained.

All-real eigenvalues are achieved in the spectrum of these complex indices.

The approach generalizes PT-symmetric optical systems.

Abstract

The construction of exactly solvable refractive indices allowing guided TE modes in optical waveguides is investigated within the formalism of Darboux-Crum transformations. We apply the finite-difference algorithm for higher-order supersymmetric quantum mechanics to obtain complex-valued refractive indices admitting all-real eigenvalues in their point spectrum. The new refractive indices are such that their imaginary part gives zero if it is integrated over the entire domain of definition. This property, called condition of zero total area, ensures the conservation of optical power so the refractive index shows balanced gain and loss. Consequently, the complex-valued refractive indices reported in this work include but are not limited to the parity-time invariant case.