Topologically protected edge states in time photonic crystals with chiral symmetry

Time photonic crystals are media in which their electromagnetic parameters are modulated periodically in time, showing promising applications in non-resonant lasers and particle accelerators, among others. Traditionally utilized to study space photonic crystals, topological band theory has also been translated recently to analyze time photonic crystals with time inversion symmetry, enabling the construction of the temporal version of topological edge states. However, temporal disorder can readily break time inversion symmetry in practice, hence likely destroying the edge states associated with this type of time photonic crystals. To overcome this limitation, here we propose a new class of time photonic crystals presenting chiral symmetry instead, whose edge states exhibit superior robustness over the time-reversal-symmetry-protected counterparts. Our time photonic crystal is equivalent to a temporal version of the Su-Schrieffer-Heeger model, and the chiral symmetry of this type of time photonic crystals quantizes the winding number defined in the Bloch frequency band. Remarkably, random temporal disorders do not impact the eigenfrequencies of these chiral-symmetry-protected edge states, while instead enhancing their temporal localizations. Our findings thus provide a promising paradigm to control field amplification with exceptional robustness as well as being a feasible platform to investigate various topological phases in time-varying media.