基于Rayleigh-Sommerfeld积分的矢量衍射理论的适用范围

摘要

The application of the vector diffraction theory based on Rayleigh-Sommerfeld integration has been studied using Laguerre-Gaussian beams with radial polarization.It is found that the Rayleigh-Sommerfeld vector diffraction theory is valid when the numerical aperture is less than 0.4 in comparison with the calculation results of Richards-Wolf vector diffraction theory.However,for short-focus large-numercial-aperture systems,the Rayleigh-Sommerfeld theory underestimates the diffraction effect and the vector property of light waves.Thus,the Rayleigh-Sommerfeld theory cannot be used for short-focus large-numercial-aperture systems.%以径向偏振的Laguerre-Gaussian光束为例,探讨了基于Rayleigh-Sommerfeld积分的矢量衍射理论的适用范围.经与Richards-Wolf理论计算结果比较发现,在有效数值孔径小于0.4的情况下,Rayleigh-Sommerfeld理论可以适用,并可用于探讨小菲涅耳数的焦移问题.但对于紧聚焦大数值孔径系统,Rayleigh-Sommerfeld理论不再适用,因为这种理论低估了光波的衍射效应和矢量性,使得计算所得的聚焦光斑尺寸偏小.