将LP01模表示成用拉盖尔-高斯模线性叠加的形式,利用柯林斯公式推导出单模光纤波导模通过傍轴ABCD光学系统的解析传输公式。用所得的解析公式对LP01模在自由空间的传输和聚焦特性作了研究,并和高斯基模进行了比较。数值计算结果表明,用高斯基模描述LP01模会产生一定误差。LP01模经过透镜聚焦后存在焦移,且焦移随着菲涅尔数传输特性的减小而增大。选择合适的菲涅尔数聚焦后,LP01模会出现长焦深,这是与聚焦的高斯模所不同的。

By expanding the LP01 mode into a linear superposition of Laguerre-Gaussian modes and using Collins formula,the analytical propagation equation of wave-guide modes in a single-mode fiber through paraxial ABCD optical systems is derived. The free-space propagation and focusing properties of the LP01 mode are studied and compared with those of the fundamental Gaussian mode. It is shown that the Gaussian mode in place of the LP01 mode may introduce some errors. In the focused field of the LP01 mode there exists the focal shift which increases with decreasing Fresnel number. By a suitable choice of the Fresnel number,a long focusing depth may appear for the LP01 mode which is quite different from that of the focused Gaussian mode.