Supersymmetry-generated complex optical potentials with real spectra

TL;DR

This paper explores how supersymmetry (SUSY) can be used to design complex optical potentials with real spectra, revealing novel properties and behaviors in PT-symmetric and non-PT-symmetric systems.

Contribution

It introduces a SUSY-based framework for creating complex optical potentials with real spectra, including non-PT-symmetric cases, and analyzes their spectral properties and symmetry-breaking regimes.

Findings

SUSY enables removal of bound states in non-Hermitian optical potentials.

Existence of isospectral complex potentials that are non-PT-symmetric yet have real spectra.

Analysis of SUSY effects in spontaneously broken PT-symmetry regimes.

Abstract

We show that the formalism of supersymmetry (SUSY), when applied to parity-time (PT) symmetric optical potentials, can give rise to novel refractive index landscapes with altogether non-trivial properties. In particular, we find that the presence of gain and loss allows for arbitrarily removing bound states from the spectrum of a structure. This is in stark contrast to the Hermitian case, where the SUSY formalism can only address the fundamental mode of a potential. Subsequently we investigate isospectral families of complex potentials that exhibit entirely real spectra, despite the fact that their shapes violate PT-symmetry. Finally, the role of SUSY transformations in the regime of spontaneously broken PT symmetry is investigated.