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基于麦克斯韦方程组,借助矢势理论,经适当推导得出薄理想导电平面衍射光栅的矢量衍射积分公式。在特定偏振光入射下,给出了塔尔博特距离处衍射场强度分布公式。不作可能影响理论结果的近似条件下,分析了严格的积分形式解的意义。在无法得到解析解的情况下,采用离散化方法对不同光栅周期条件下第一塔尔博特距离处的衍射场进行了实验模拟,并对相同光栅周期下,更短波长的衍射结果进行模拟。结果表明,当光栅周期在微米量级,小于2倍波长的情况下,塔尔博特现象不再明显,其塔尔博特距离处的强度分布与光栅出射面的强度分布差异很大。同时,在更短波长的条件下,塔尔博特效应依然有效,对微米结构或者更小的结构应用塔尔博特效应可以采用更短波长的电磁波来实现。
Based on the Maxwell’s equations, the vector diffraction integral formula of a thin, perfectly-conducting planar diffraction grating is deduced with the help of the vector potential theory. Under the incident of specific polarized light, the distribution formula of diffraction field at Talbot distance is given. Without making any possible approximation to the theoretical result, we analyze the meaning of strict integral form solutions. The diffraction field at the first Talbot distance at different grating periods was experimentally simulated by the discretization method when the analytical solution was not available, and the diffraction results at shorter wavelengths under the same grating period were simulated . The results show that the Talbot phenomenon is no longer obvious when the grating period is on the order of microns or less, and the intensity distribution at the Talbot distance and the exit surface of the grating differ greatly. At the same time, the Talbot effect is still effective at shorter wavelengths, and the Talbot effect can be achieved with shorter wavelength electromagnetic waves for microstructures or for smaller structures.