激光束的传输特性在激光技术应用中有着重要的意义。光束的解析传输问题是激光光学中的难点之一。从Collins公式出发,详细研究了离轴高斯光束(OAGB)通过有光阑近轴ABCD光学系统的传输特性,推导出了受硬边光阑、高斯光阑或余弦光阑限制的离轴高斯光束通过近轴ABCD光学系统的解析传输公式,并讨论了硬边光阑、高斯光阑或余弦光阑之间的关系。数值计算证明了所得公式的正确性和优点。分析了求解受多光阑限制的激光束通过近轴ABCD光学系统的解析传输公式的困难性,结果表明,其困难性在于受单光阑限制激光束的解析传输公式中含有误差函数。

The propagation properties of laser beams are of much significance in applications of laser technology. The analytical propagation equation for beams is one of the focuses in laser optics. Starting from the Collins formula, the properties of the off-axis Gaussian beam (OAGB) propagating through a paraxial ABCD optical system with an aperture are studied in detail. Moreover, the analytical equations for the off-axis Gaussian beam propagating through a paraxial ABCD optical system with hard-edged aperture, Gaussian aperture or cosine aperture are derived. The relationship among hard-edged aperture, Gaussian aperture and cosine aperture is discussed. The validity and advantage of results are confirmed and illustrated by numerical calculations. The difficulty of finding the analytical propagation formula of laser beams propagating through a paraxial ABCD optical system with multi-aperture is analyzed. It is shown that the difficulty is due to the existence of an error function in the analytical propagation formula for single-apertured laser beams.