Revealing the Resonant Physics of Open Photonic Time Crystals

ABSTRACT Photonic time crystals (PTCs) are media whose permittivity is modulated periodically in time, enabling momentum bandgaps and parametric amplification of light. Their realization at the nanoscale can revolutionize the study of light‐matter interactions. While prior works have focused on spatially uniform or periodic PTCs, practical implementations inevitably involve modulating complex nanostructures, whose dynamics are dominated by resonant modes that radiate into the environment. While there exist studies investigating specific geometries, the general physical mechanisms underlying the response of such “open” PTCs remain largely unexplored. Here, we establish a first‐principles framework that captures the resonant behavior of open PTCs with arbitrary geometry. We reveal a number of unique features, such as the emergence of infinite ladders of “replica” radiative eigenmodes and a universal scaling law for the modulated resonance frequencies and the radiative losses. Contrary to conventional wisdom, we show that parametric amplification in these systems arises from discrete resonant processes, rather than from bandgap physics. Leveraging our new insights, we design parametric resonances in a realistic microcavity as well as in subwavelength nanoresonators. Our results establish a foundation for understanding and engineering open PTCs, with implications for nanophotonics, quantum optics, and other areas of wave physics.