Parity-time symmetry phase transition in photonic time-modulated media

TL;DR

This paper demonstrates that parity-time symmetry phase transition can occur in time-modulated photonic media, revealing conditions under which real eigenvalues emerge and providing a new paradigm for controlling Hermiticity in spatiotemporal systems.

Contribution

It introduces a theoretical framework for $ ext{PT}$-symmetry phase transition in time-modulated media and generalizes the transfer matrix method to analyze this phenomenon.

Findings

$ ext{PT}$-symmetry phase transition depends on modulation depth contrast.

Full-wave simulations confirm the phase transition.

Analytical methods validate the scattering behavior analysis.

Abstract

Time modulation can cause gain and loss in photonic media, leading to complex modal behaviors and enhanced wave controllability in the non-Hermitian regime. Conversely, we reveal that Hermiticity and parity-time $\mathcal{PT}$-symmetry phase transition are possible under the temporal $\mathcal{PT}$-symmetry in time-modulated photonic media. We prove that, for a homogeneously modulated photonic medium with complex-valued modulation, temporal $\mathcal{PT}$-symmetry is a necessary but insufficient condition for obtaining a real eigenvalue spectrum, giving rise to $\mathcal{PT}$-symmetry phase transition. Specifically, the $\mathcal{PT}$ phase transition critically depends on the contrast between the modulation depth of the real and imaginary parts of permittivity when they are sinusoidally modulated with a $\pi/2$ phase difference. We generalize the discretized temporal-interface transfer matrix method to a continuous differential operator framework, which facilitates the confirmation of the phase transition condition via Magnus expansion analysis. Full-wave simulations and analytical calculations jointly confirm the occurrence of $\mathcal{PT}$-transition by examining the scattering behavior of a propagating pulse in such a type of modulated medium. The findings provide a temporal $\mathcal{PT}$-symmetric paradigm for controlling Hermiticity and non-Hermiticity in spatiotemporal photonic systems.