Phase‐Controlled Momentum Bandgaps in Dual‐Channel Dispersive Photonic Time Crystals

Dispersive photonic time crystals (PTCs) offer a versatile platform for manipulating light–matter interactions through temporal modulation of material responses, enabling dynamic control of optical gain and loss. Previous multi‐parameter temporal modulation studies provide additional degrees of freedom for engineering the band structure. Quantitatively characterizing momentum‐bandgap splitting and understanding the interplay between distinct modulation channels are essential for achieving precise control over Floquet coupling and amplification–attenuation dynamics. Here, we systematically investigate a Lorentz‐dispersive PTC with simultaneous modulation of the plasma frequency and damping factor. Using Floquet expansion, we investigate how these two modulation channels individually and jointly modify the band structure. We show that the modulation amplitudes and relative phase jointly determine the effective coupling between Floquet modes, enabling flexible control over the bandgap size and the imaginary part of the eigenfrequency. Furthermore, the competition between modulation‐induced amplification and intrinsic material damping allows the relative phase to control transitions between net temporal amplification and attenuation. Floquet spectral calculations and finite‐difference time‐domain simulations further reveal the corresponding phase‐dependent spectral and field‐evolution characteristics. These findings establish a quantitative analytical approach for multi‐parameter band structure engineering and open new opportunities for phase‐controlled optical gain and loss in time‐varying photonic systems.