关键词: 光子晶体, 量子几率密度, 量子几率流密度, Zak相

Abstract: We gave the probability density, probability current density and topological phase of photon in one-dimensional photonic crystal
s (AB)^N by using the quantum theory of photon. When the refractive index of media B was n_b=1.12, we gave the band Zak phases by using the quantum method. The results show that when the incident angle θ and periodic number N change, the probability density and probability current density of photonic crystals change approximately periodically, and its amplitude increases with the increase of incident angles θ and periodic number N. When the frequency of incident photon corresponds to transmissivity T=100%, the amplitude of the probability density is the largest. When the frequency of incident photon corresponds to transmissivity T=0, the probability density is not zero, but the amplitude of the probability density attenuates to zero rapidly, so there is a quantum tunnel effect of photon in photonic crystals. 

Key words: photonic crystal, quantum probability density, quantum probability current density, Zak phase