平面波经小圆孔衍射轴上传播函数的特性

Characteristics of Propagation Function of Plane Wave Diffracted by Small Circular Aperture

从标量衍射理论出发,采用瑞利-索末菲衍射边界条件,通过求解第一类瑞利-索末菲衍射积分得到的平面波经小圆孔衍射轴上波函数的精确解,分析并总结轴上光强极值数量、极值位置和极值大小的一般规律;比较用振幅表示光强和光强的精确表示之间的差异及用振幅表示光强的条件,为研究其他衍射问题的准确性提供了一准确的判断标准;又由于角谱理论和第一类瑞利-索末菲衍射积分的一致性,同时也就得到角谱理论在处理小孔衍射时不可积积分的解析表达式,为进一步研究小孔非傍轴衍射提供了新的方法.

Based on the scalar diffraction theory and the boundary condition of Rayleigh-Sommerfeld, by solving the first integral of Rayleigh-Sommerfel, the accurate on-axis propagating wave function of plan wave diffracted by small circular aperture is obtained. By means of the different expressions of light intensity, the extremas of on-axis light intensity, their locations and number as a function of the radius of small circular aperture have been analyzed, and the discrepancy has been discussed. Compared with the spectrum theory, the method of the first integral of Ray-leigh-Sommerfeld used here is simpler and more applicable.