Longitudinal optical phonons in photonic time crystals containing a stationary charge

Photonic time crystals (PTCs) enable exotic light-matter interactions but typically require significant modulation strength to open a wide momentum band gap, limiting their practical realization. Here, the authors demonstrate that a Lorentzian medium-based PTC with a stationary charge cannot only excite but also amplify longitudinal optical phonons, with a band gap spanning the entire momentum space. This infinite momentum band gap can be achieved with a minimal modulation depth, enriching time-varying photonics by incorporating the distinct wave characteristics of longitudinal excitations.