一维光子晶体的量子透射率

The quantum transmissivity of one-dimensional photonic crystals

在光的量子波动方程的基础上提出了研究一维光子晶体的量子理论方法,通过在两介质分界面上波函数及其波函数导数连续,即可得到一维光子晶体的量子变换矩阵、量子透射率和量子反射率,分别计算了无缺陷层介质和有缺陷层介质时的量子透射率和量子反射率.把量子理论方法与经典电磁理论方法计算结果进行了比较,发现两者的计算结果是一致的.这说明该量子理论方法也是研究光子晶体的正确方法,该方法还可以进一步研究二维和三维光子晶体的透射特性以及光子晶体的量子Zak相、量子拓扑特性,这些特性包括量子陈数、边缘态和光子的量子霍尔效应等.

On the basis of the quantum wave equation of light,a quantum theoretical method for studying one-dimensional photonic crystals was proposed.The quantum transformation matrix,the quantum transmissivity and the quantum reflectivity of the one-dimensional photonic crystal could be obtained.The quantum transmissivity and the quantum reflectivity of the defect-free layer and the defect-layer were calculated,respectively.The results of the quantum theory method were compared with those of the classical method,and it was found that their results were consistent.It showed that the quantum theory method was also the correct method for studying photonic crystals,and the method could further study the transmission properties of two-dimensional and three-dimensional photonic crystals,as well as the quantum Zak phase and quantum topological properties of photonic crystals,including the quantum Chen,edge states and photon quantum hall effect.