Temporal parity-time phase transition in photonic time-modulated media
Phys. Rev. A 114, 013502 – Published 6 July, 2026
DOI: https://doi.org/10.1103/s8lj-8l7s
Abstract
Temporal modulation of photonic media generally induces effective gain and loss and thus non-Hermitian wave dynamics. Here, we show that under a temporally -symmetric modulation, such media can nevertheless exhibit Hermiticity and a temporal phase transition. We prove that, for a homogeneously modulated photonic medium with complex-valued modulation , the temporal symmetry is a necessary but insufficient condition for obtaining a real eigenvalue spectrum, giving rise to -symmetry phase transition. Specifically, the 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 phase difference—a minimal modulation scheme satisfying the temporal symmetry. We generalize the discretized temporal-interface transfer matrix method to a continuous differential operator framework, confirming the phase transition condition via Magnus expansion and Petermann analysis. Full-wave simulations and analytical calculations jointly confirm the occurrence of transition by examining the scattering behavior of a propagating pulse in such a type of modulated medium. The findings provide a temporal -symmetric paradigm for controlling Hermiticity and non-Hermiticity in spatiotemporal photonic systems.