Complex‐Frequency Selective Resonances in Disordered Time‐Varying Cavities

A mechanism is proposed for achieving unique ‐space resonance modes in 1D time‐varying cavities where periodic temporal modulation generates momentum bandgaps through Floquet dynamics. By engineering the synergy between cavity resonance conditions and Floquet mode in photonic time crystals, the emergence of a single dominant momentum state that exhibits remarkable robustness against temporal disorder is demonstrated. It is demonstrated that Floquet dynamics in periodically time‐varying media induces the amplification of specific spatial mode components within the initial Gaussian pulse wave. Concurrently, the multiple wave splitting caused by periodically time‐varying media gives rise to resonances, which in turn necessitate the discretization of ‐space modes, ultimately forming a single resonant mode—a standing wave. Considering the behavior of all supported eigenmodes—standing waves in time‐varying cavities—as parametric resonators, this phenomenon is also explained from the perspective of parametric resonance. Since the wave splitting always occurs simultaneously, the excited resonant mode intrinsically exhibits immunity to temporal disorder. This mechanism is also present in the circuit model of the designed time‐varying transmission line. These findings provide a method for exploiting momentum bandgaps of limited width in time‐varying systems, opening new opportunities for photonic systems with enhanced temporal coherence.