Broadband temporal localization and delocalized temporal edge states in a time photonic crystal

Time photonic crystals have attracted growing attention in recent years owing to their abilities to enable broadband field enhancements, e.g., free-space electromagnetic waves, dipolar emissions, free-electron radiation, etc. While the non-Hermitian nature of time photonic crystals is primarily attributed to their dependence on external temporal modulations, the constituent materials are oftentimes assumed to be Hermitian. How the material-induced non-Hermiticity interplays with the intrinsic non-Hermitian dynamics of time photonic crystals remains rarely explored. In this work, we demonstrate that the non-Hermiticity arising from the bi-anisotropic electromagnetic response of materials introduces a new mechanism to manipulate the localization of temporal bulk and edge states in time photonic crystals. To be specific, the temporal bulk states in our configurations exhibit remarkable attenuation or amplification, which is theoretically predicted by extending the generalized Brillouin zone framework to the temporal domain. Our analysis reveals that the attenuation or amplification strength, quantified by the temporal penetration depth, is directly governed by electromagnetic constitutive parameters. By appropriately tuning these parameters, we uncover new phenomena including broadband temporal localization, i.e. the collective concentration of energy towards a certain time moment, and delocalized temporal edge states.