Revealing non-Hermitian band structures of photonic Floquet media.

Periodically driven systems, characterised by their inherent non-equilibrium dynamics, are ubiquitously found in both classical and quantum regimes. In the field of photonics, these Floquet systems have begun to provide insight into how time periodicity can extend the concept of spatially periodic photonic crystals and metamaterials to the time domain. However, despite the necessity arising from the presence of non-reciprocal coupling between states in a photonic Floquet medium, a unified non-Hermitian band structure description remains elusive. Here, we experimentally reveal the unique Bloch-Floquet and non-Bloch band structures of a photonic Floquet medium emulated in the microwave regime with a one-dimensional array of time-periodically driven resonators. Specifically, these non-Hermitian band structures are shown to be two measurable distinct subsets of complex eigenfrequency surfaces of the photonic Floquet medium defined in complex momentum space. In the Bloch-Floquet band structure, the driving-induced non-reciprocal coupling between oppositely signed frequency states leads to opening of momentum gaps along the real momentum axis, at the edges of which exceptional phase transitions occur. More interestingly, we show that the non-Bloch band structure defined in the complex Brillouin zone supplements the information on the morphology of complex eigenfrequency surfaces of the photonic Floquet medium. Our work paves the way for a comprehensive understanding of photonic Floquet media in complex energy-momentum space and could provide general guidelines for the study of non-equilibrium photonic phases of matter.