Observation of wave amplification and temporal topological state in a genuine photonic time crystal

Abstract

Photonic time crystals (PTCs) are materials whose dielectric permittivity is periodically modulated in time, giving rise to bandgaps not in energy-as in conventional photonic crystals-but in momentum, known as k-gaps. These k-gaps enable wave amplification by extracting energy from temporal modulation, offering a mechanism for coherent light generation that bypasses traditional optical gain. PTCs also extend the concept of topological insulators to the time domain, inducing a temporal topological state at the mid-gap of the k-gap, characterized by the Zak phase-a topological invariant originally defined for spatial lattices. Here, we experimentally demonstrate the properties of a k gap in a genuine PTC, realized in a dynamically modulated transmission-line metamaterial. Wave amplification within the k-gap is observed, with an initial power spectrum narrowing and shifting toward the gap. To probe the mid-gaptopological state, we introduce a temporal interface separating two PTCs with distinct topological phases. The measured phase shift between time-reflected and time-refracted waves, together with the temporal confinement of the topological state, provides direct evidence of nontrivial temporal topology. By integrating kgap amplification with time-domain topological features, our work opens new avenues for light generation and manipulation in time-varying photonic materials.