Quantum effect of one-dimensional photonic crystal

In this paper, we have studied the quantum transmission characteristics of one-dimensional photonic crystal with and without defect layer by the quantum theory approach, and compared the calculation results of classical with quantum theory. We have found some new quantum effects in the one-dimensional photonic crystal. When the incident angle $\theta=0$, there is no quantum effect. When the incident angle $\theta\neq0$, we find there are obvious quantum effect with the incident angle increase. At the incident angle $\theta\neq0$, there are also quantum effect with the change of thickness and refractive indexes of medium $B$ or $A$. We think the new quantum effect of photonic crystal shall help us to design optical devices.