PT-symmetry enabled stable modes in multi-core fiber

TL;DR

This paper explores PT-symmetric gain-loss potentials in a two-dimensional multi-core fiber model, revealing complex eigenvalue behaviors, phase transitions, and stable propagating modes, thus extending PT-symmetry studies beyond traditional finite or one-dimensional models.

Contribution

It introduces a novel 2D continuum model of a multi-core fiber with PT-symmetry, demonstrating stable modes and complex spectral phenomena not previously explored in such systems.

Findings

Identification of exceptional points and re-entrant PT phases

Non-monotonic PT-symmetry breaking threshold dependence

Support of propagating modes with gain and loss in the model

Abstract

Open systems with balanced gain and loss, described by parity-time PT-symmetric Hamiltonians have been deeply explored over the past decade. Most explorations are limited to finite discrete models (in real or reciprocal spaces) or continuum problems in one dimension. As a result, these models do not leverage the complexity and variability of two-dimensional continuum problems on a compact support. Here, we investigate eigenvalues of the Schrodinger equation on a disk with zero boundary condition, in the presence of constant, PT-symmetric, gain-loss potential that is confined to two mirror-symmetric disks. We find a rich variety of exceptional points, re-entrant PT-symmetric phases, and a non-monotonic dependence of the PT-symmetry breaking threshold on the system parameters. By comparing results of two model variations, we show that this simple model of a multi-core fiber supports propagating modes in the presence of gain and loss.