光栅Talbot效应的光子学研究

采用光的波粒二象性观点，用概率波对光栅的塔尔博特（Talbot）效应进行了研究，得到了正、偏自成像和分数成像的相关结果，这些结果与采用光的波动性观点的惠更斯一菲涅耳原理和傅里叶变换等常规方法所得结果相同。引人了调节参量口，并研究了成像过程中，在像的正、偏，像与原物的相位关系和分数成像等相关问题中该参数所起的作用；还利用相关结果讨论了倏逝波问题，得到了与常规方法相同的结果。所采用的光子学方法有助于对光子的波函数及其统计意义的理解。与此同时，提出了塔尔博特效应实际上是光子对周期性空间信息的记忆与再现的过程，从而对光子在光传播过程中携带空间信息产生了一定认识。由于数学处理方法上的简明扼要，所采用的光子学研究方法更易于在基础领域中推广和应用。

A Study of Talbot Effect Based on Photonic Theory

Talbot effect is explained by probability-wave based on the viewpoint of photonic wave-particle dualism in Quantum Mechanics,the same conclusions to positive serf-imaging, negative serf-imaging and fraction imaging with Huygens-Fresnel pnnciple or Fourier transform be obtained. The adjnstable coefficient q for Talbot-effect is adanced, its actions for positive serf-imaging, negative serf-imaging and fraction imaging, as well as the phase relations between the object and the image be discussed. At the same time, the evanescent-wave concerned Talboteffect is studied by Photonic method, the same results with conventional methods are once obtained. The method that used could help one to understand the concept about photonic wave function and its statistical meaning in quantum theory. It is suggested that the nature of Talbot serf-imaging is the recordation and reappearance for periodic space information of object by photons. The method which used could help one to know the ability of photon to transfer information and its wave-particle dualism. The coefficients of Talbot formula could be understood well by the method it was used. Being its simplicity in Math,photonic method is easy to use widely.