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    Temporal parity-time phase transition in photonic time-modulated media

    Rui-Chuan Zhang, Shu Yang, Yixin Sha, Zetao Xie, and Yi Yang*

    • Department of Physics and HK Institute of Quantum Science and Technology, The University of Hong Kong, Pokfulam, Hong Kong, China and State Key Laboratory of Optical Quantum Materials, The University of Hong Kong, Pokfulam, Hong Kong, China

    • *Contact author: yiyg@hku.hk

    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 PT-symmetric modulation, such media can nevertheless exhibit Hermiticity and a temporal PT phase transition. We prove that, for a homogeneously modulated photonic medium with complex-valued modulation ε(t), the temporal PT symmetry ε(−t)=ε*(t) is a necessary but insufficient condition for obtaining a real eigenvalue spectrum, giving rise to PT-symmetry phase transition. Specifically, the 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 π/2 phase difference—a minimal modulation scheme satisfying the temporal PT 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 PT transition by examining the scattering behavior of a propagating pulse in such a type of modulated medium. The findings provide a temporal PT-symmetric paradigm for controlling Hermiticity and non-Hermiticity in spatiotemporal photonic systems.

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