物理与工程

高斯光束经过薄透镜后的变换是激光原理课程的重要内容,该内容有助于加强学生对激光光学系统设计的理解,但是由于课程缺少一般激光光束通过线性光学系统的变换过程,学生在拓展发散的学习过程中会产生疑问。本文推导了二阶矩定义下的一般激光束的腰斑直径、腰斑位置和远场发散角,通过一个由光线矩阵表示的线性光学系统后的变化规律。此外,本文采用q参数的方法进行光束参数变换的证明,证实了两种推导方法的一致性,有助于加强学生对激光光束的理解。可以预见,一般激光光束参量的变换理论可以应用于透镜组光束变换系统设计之中。

The transformation of a Gaussian beam by a thin lens is an important component of the laser principles course, as it enhances students' understanding of laser optical system design. However, because the course usually omits the general propagation of arbitrary laser beams through linear optical systems, students often raise questions when they try to extend their knowledge. This paper derives, under the second-order moment definition, the waist diameter, waist position, and far-field divergence angle of a general laser beam after passing through a linear optical system represented by a ray-transfer matrix. In addition, we retrace the beam-parameter transformation with the q-parameter method, demonstrating the consistency of the two approaches and thereby reinforcing students' understanding of laser-beam behavior. The general beam-parameter transformation theory can be expected to find direct application in the design of multi-lens beam-transformation systems.