为了研究光子态在大气湍流中的变化规律, 基于拉盖尔-高斯光束横向空间波函数(光子轨道角动量的本征函数)以及湍流大气中拉盖尔-高斯光束光子态(可由各本征光子态叠加构成),得到了湍流大气中光子态的探测概率, 并分析了大气湍流、传输距离、质量因子对光子态的影响。结果表明, 质量因子是决定发射光子态跳变的重要因素, 相同质量因子的光子态在接受端的测量权重基本相同, 且质量因子值越大原光子态测量权重越小。同时, 在湍流大气的影响下, 从原光子态跳变到轨道角动量增加某值的光子态的测量权重总和与跳变到减小相应轨道角动量的光子态的测量权重总和基本相同; 随着湍流强度或传输距离的增加, 发射光子态在接受端的光子测量权重不断减小, 而且湍流强度对光子态测量权重的影响比距离的大。

In order to study the change regularity of photon states in atmospheric turbulence, the photon state detection probability was derived based on facts that transverse spatial wave function of Laguerre-Gaussian beam is the eigenfunction of a photon and transverse spatial wave function of Laguerre-Gaussian beam propagation in turbulent atmosphere approaches to superimposition of all photon state eigenfunctions. Effect of atmospheric turbulence, propagation length, quality factor on detection probability was analyzed. The results present that the change of the photon state largely relies on beam quality factor. With the same quality factor, the measurement weight at the receiving plane is nearly the same. In addition, the total measurement weight from initial photon to state at which the orbital angular momentum increases to a certain value, is equivalent to the total measurement weight of the corresponding decrease. The stronger the turbulence is, the smaller the photon state measurement weight of the initial photon state at the receiving side is. That is also true of the propagating distance. However, distance puts much less effect on photon states than atmospheric turbulence.