Gain-gain and gain-lossless PT-symmetry broken from PT-phase diagram

TL;DR

This paper predicts and maps new PT-symmetry breaking phases, including gain-gain and gain-lossless, in micro/nano photonic structures, providing a comprehensive phase diagram that enhances understanding and potential applications in photonics.

Contribution

It introduces a full-parameter phase diagram for PT-symmetry breaking, including gain-gain and gain-lossless cases, expanding the understanding beyond traditional loss-loss or gain-loss systems.

Findings

Defined boundaries between PT-symmetry and PT-broken phases in full parameter space.

Derived transmission matrices for coupled waveguides in different phases.

Confirmed periodic energy exchange and exponential gain/loss behaviors in respective phases.

Abstract

Parity-time (PT) symmetry and broken in micro/nano photonic structures have been investigated extensively as they bring new opportunities to control the flow of light based on non-Hermitian optics. Previous studies have focused on the situations of PT-symmetry broken in loss-loss or gain-loss coupling systems. Here, we theoretically predict the gain-gain and gain-lossless PT-broken from phase diagram, where the boundaries between PT-symmetry and PT-broken can be clearly defined in the full-parameter space including gain, lossless and loss. For specific micro/nano photonic structures, such as coupled waveguides, we give the transmission matrices of each phase space, which can be used for beam splitting. Taking coupled waveguides as an example, we obtain periodic energy exchange in PT-symmetry phase and exponential gain or loss in PT-broken phase, which are consistent with the phase diagram. The scenario giving a full view of PT-symmetry or broken, will not only deepen the understanding of fundamental physics, but also will promote the breakthrough of photonic applications like optical routers and beam splitters.