菲涅耳近似对硬边光阑衍射光束的适用性

Validity of the Fresnel approximation for hard-edged diffracted beams

使用基尔霍夫衍射积分公式和菲涅耳衍射积分公式对高斯光束通过方孔光阑的衍射进行了研究。给出了详细的数值计算结果并作了比较。研究表明 ,对一给定的束腰宽度w0 ,当w0 远大于波长λ时 ,菲涅耳衍射的有效范围与截断参数δ有关 ;若w0 与λ可比拟甚至更小时 ,则必须使用基尔霍夫衍射积分公式。

The diffraction of Gaussian beams at an squa re aperture is studied based on the Kirchhoff and Fresnel diffraction integrals.De tailed numerical results are presented and compared.It is shown that for a given waist width w 0( w 0λ,λ is wavelength),the valid range of the Fre snel diffraction integral depends on the truncation parameter.Otherwise,if the waist width w 0 is comparable to or even less than the wavelength λ,t he Kirchhoff diffraction integral should be used.