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

Parity-time (PT) symmetry and broken in micro-/nanophotonic 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 the 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-/nanophotonic 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 example, we obtain periodic energy exchange in the PT-symmetry phase and exponential gain or loss in the 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.