近年来离轴正支共焦非稳腔被广泛用于大功率板条结构激光器, 由于其横向尺寸较大, Collins公式的计算精度需要验证。通过Fox-Li迭代, 对比了采用Collins公式和直接利用菲涅尔-基尔霍夫衍射公式计算的输出模式, 数值研究了几何放大率M和有效菲涅尔数Neq对Collins公式计算精度的影响并分析了原因。结果显示, 计算误差主要集中在光轴附近, 复振幅巨大的相位误差导致模值的大小、分布误差。另一方面, 计算精度会随M的增加, Neq的减小呈现跳变增加, 阶跃点Neq与M具有线性关系, 斜率约为133, 即Collins公式在菲涅尔数为266以内是有效的。

In recent years, the off-axial positive branch confocal unstable resonators are widely used in high-power slab lasers. Because of its large transverse size, the calculation accuracy of the Collins formula needs to be verified. Through the Fox-Li iteration, the output mode calculated by Collins formula and Fresnel-Kirchhoff diffraction formula are compared. The influence of geometric magnification M and equivalent Fresnel number Neq on calculation accuracy of the Collins formula are studied numerically and the reasons are analyzed. The results show that the calculation error is mainly concentrated near the optical axis. The large phase error of the complex amplitude leads to the magnitude and distribution error of the modulus. On the other hand, with the increase of M and the decrease of Neq, the accuracy of the calculation will show an increase in the jump. The Neq value of the jump point has a linear relationship with the value of M, and the slope is about 133. That is, the Collins formula is valid within the Fresnel number of 266.