Fundamental issues with light propagation through PT -symmetric systems

Abstract

We analyze the emergence of unphysical superluminal group velocities in Su-Schrieffer-Heeger (SSH) parity-time ($\mathcal{PT}$) symmetric chains, and explore the origins of such a behavior. By comparing the band structure of an infinite loss-gain SSH chain with that of a continuous realization---a one-dimensional Bragg stack governed by the Helmholtz equation---we first exclude insufficient coupling consideration in the tight-binding description as the cause of group-velocity divergence. We then focus on material dispersion, and show that indeed, restoring causality in the description of both the lossy and the gain components resolves the problem and recovers finite group velocities, whose real part can only exceed the speed of light in vacuum when accompanied by a significant imaginary part. Our analysis introduces thus the required practical limits in the performance of common $\mathcal{PT}$-symmetric systems.