圆孔受限波差高斯光束的远场近似及发散度分析

引入复高斯函数对衍射受限的圆孔进行了复高斯分解,得到了波差高斯光束远场衍射的近似解析式。在各种参量条件下,近似解析式所表示的衍射图样与严格的夫琅和费衍射积分的衍射图样完全一致,这表明用此解析式表征远场衍射是正确的。它的形式相对简单,为计算带来极大的方便。基于此,对有波差的高斯光束的远场发散度进行了深入的研究,检验了确定参量的光束随距离的改变而发散度不被改变的特性;同时,探讨了在圆孔限制下,发散度随高斯光束的束腰及波差的改变而变化的关系曲线,结果表明,这两个参量是影响发散度的主要因素。

Far-Field Approximation and Divergence of Gaussian Beam with Phase Aberrations Diffracted by a Circular Aperture

By expanding the circular function into a linear superposition of a set of complex Gaussian functions,the approximative analytic expression for the far-field of Gaussian beam with phase aberrations diffracted by a circular aperture is obtained.For different parameters,the diffraction patterns of the expression of the Fraunhofer diffraction are identical,indicating the correctness of the expression.For its relatively simple form,the calculation becomes more convenient.Based on these,the far-field divergence of Gaussian beam with phase aberrations is completely studied.The divergence of the certain beam does not change with the transmission distance,but with the beam-waist radius and the phase aberrations under the limit of circular aperture,and the result indicates that two parameters are the key factors affecting the divergence.