Temporally periodic photonic crystals develop an ω-k dispersion relation with momentum band gaps. While conventional photonic crystals induce forbidden bands in the frequency spectrum of photons, photonic time crystals create forbidden regions in the momentum spectrum of photons. This effect allows for enhanced control over many optical processes that require both photonic energy and momentum conservations such as nonlinear harmonic generation. The simulation results show that more intensive scatter fields can obtained in photonic space time crystal. Also, we investigate topological phase transitions of photonic time crystals systems.