All-real spectra in optical systems with arbitrary gain and loss distributions

TL;DR

This paper introduces a method to design optical potentials with arbitrary gain and loss distributions that maintain a completely real spectrum, expanding the scope beyond traditional parity-time symmetry and enabling controlled phase transitions.

Contribution

It presents a novel approach to construct non-parity-time-symmetric optical potentials with real spectra, broadening the design possibilities for optical systems with tailored gain and loss profiles.

Findings

Constructed classes of refractive-index profiles with arbitrary gain/loss distributions.

Demonstrated that these potentials can have all-real spectra despite non-PT symmetry.

Identified conditions for phase transitions where eigenvalues become complex.

Abstract

A method for constructing optical potentials with an arbitrary distribution of gain and loss and completely real spectrum is presented. For each arbitrary distribution of gain and loss, several classes of refractive-index profiles with freely tunable parameters are obtained such that the resulting complex potentials, although being non-parity-time-symmetric in general, still feature all-real spectra for a wide range of tuning parameters. When these refractive indices are tuned below certain thresholds, phase transition can occur, where complex-conjugate pairs of eigenvalues appear in the spectrum. These non-parity-time-symmetric complex potentials generalize the concept of parity-time-symmetric potentials to allow for more flexible gain and loss distributions while still maintaining all-real spectra and the phenomenon of phase transition.