Analyzing photonic space-time crystal with FDTD

When space (time) translation symmetry is spontaneously broken, the space crystal (time crystal) forms; when permittivity and permeability periodically vary with space (time), the photonic space crystal (photonic time crystal) forms. We rewrote Maxwell’s equations in photonic time crystal, and discretized Maxwell’s equations with finite difference time domain (FDTD) method, deduced the discretized electric and magnetic field, and simulated electromagnetic wave propagation in two-dimensional (2D) photonic space-time crystal and photonic space crystal (or photonic crystal), and discussed the effect of parameters on the band gap.