Andrews L C, Miller W B, Ricklin J C
Appl Opt. 1993 Oct 20;32(30):5918-29. doi: 10.1364/AO.32.005918.
Geometric relations are used to study the propagation environment of a Gaussian beam wave propagating through a complex paraxial optical system characterized by an ABCD ray matrix in two naturally linked complex planes. In the plane defined by beam transmitter parameters Ω(o) and Ω, the propagation path is described by a ray line similar to the ray line in the y? diagram method, whereas the path in the plane of beam receiver parameters θ and Λ is described by a circular arc. In either plane the amplitude, phase, spot size, and radius of curvature of the Gaussian beam are directly related to the modulus and argument of the complex number designating a particular transverse plane along the propagation path. These beam parameters also lead to simple geometric relations for locating the beam waist, Rayleigh range, focal plane, and sister planes, which share the same radius of curvature but have opposite signs. Combined with the paraxial wave propagation technique based on a Huygens-Fresnel integral and complex ABCD ay matrices, this geometric approach provides a new and powerful method for the analysis and design of laser systems.
几何关系用于研究高斯光束波在由两个自然关联的复平面中的ABCD光线矩阵表征的复杂傍轴光学系统中传播时的传播环境。在由光束发射器参数Ω(o)和Ω定义的平面中，传播路径由类似于y? 图方法中的光线的射线描述，而在光束接收器参数θ和Λ的平面中的路径由圆弧描述。在任一平面中，高斯光束的振幅、相位、光斑尺寸和曲率半径都与指定沿传播路径的特定横向平面的复数的模和辐角直接相关。这些光束参数还导致用于定位束腰、瑞利范围、焦平面和具有相同曲率半径但符号相反的姐妹平面的简单几何关系。结合基于惠更斯-菲涅耳积分和复ABCD光线矩阵的傍轴波传播技术，这种几何方法为激光系统的分析和设计提供了一种新的强大方法。
