Floquet topological phases in nonlinear photonic crystals driven in space and time [Invited]

We theoretically analyze Floquet topological crystalline phases in temporally and spatially modulated one-dimensional photonic crystals with second-order optical nonlinearity. We identify a space-time symmetry that governs the degeneracy of photonic crystal band structures. By adjusting a system parameter to break or preserve this symmetry, we achieve a Zak phase transition. We also investigate the physical consequences of this transition, focusing on edge states and filling anomalies. These findings suggest a potential approach to realizing topologically protected strong light confinement.