Gap solitons in spatiotemporal photonic crystals

We generalize the concept of nonlinear periodic structures to systems that show arbitrary spacetime variations of the refractive index. Nonlinear pulse propagation through these spatiotemporal photonic crystals can be described, for shallow nonstationary gratings, by coupled mode equations which are a generalization of the traditional equations used for stationary photonic crystals. Additional gap soliton solutions are found analytically. They represent a generalization of the gap solitons in static photonic crystals and resonance solitons found in dynamic gratings.