一维光子晶体中的几率密度和拓扑相

Probability Density and Topological Phases in One-Dimensional Photonic Crystals

用光量子理论给出一维光子晶体(AB)^(N)中光子的几率密度、几率流密度和Zak相,当介质B的折射率n_(b)=1.12时,用量子方法计算出三条带的Zak相.结果表明:当入射角θ和周期数N改变时,光子晶体的几率密度和几率流密度近似为周期变化,且其振幅随入射角θ和周期数N的增加而增大;当入射光的频率与透射率T=100%相对应时,几率密度的振幅最大,当入射光的频率与透射率T=0相对应时,几率密度不为零,但几率密度的振幅迅速衰减到零,即光子晶体中存在光子的量子隧道效应.

We gave the probability density,probability current density and topological phase of photon in one-dimensional photonic crystals(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 angleθand 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 anglesθand 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.