Simulation of Gaussian laser beam propagation has many practical applications in teaching optics behavior and in laser design engineering. For the case of laser resonator cavity studies, most current techniques use the widely taught self-consistency round trip method to analyze the beam radius envelope through the cavity. We present a simpler method for simulating a confined Gaussian beam by modeling the real components of a complex ray. The procedure relies heavily on the classic multi-lens ABCD formulations for ray tracing optical cavities developed by Kogelnik, though it avoids the use of the q-parameter and its ABCD transfer law traditionally carried within the matrix optics transfer computations. Arnaud’s pioneering complex ray formulation and the Delano y-ybar ray theory provide the essential framework. The result is an easy computer simulation technique, which only requires a single calculation of the one-way complete traverse optical matrix. We present multiple detailed examples of our procedure for representative laser resonator beam simulations. The complex ray method significantly improved the efficiency of Gaussian beam ray tracing in cavities compared to the conventional q-parameter method. The optical elements considered only include end mirrors and intracavity thin lenses.

中文翻译：

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使用复杂射线的简单多透镜腔内高斯激光束模拟

高斯激光束传播的模拟在光学行为教学和激光设计工程中具有许多实际应用。对于激光谐振腔研究的情况，大多数当前技术使用广泛教授的自洽往返方法来分析通过腔的光束半径包络。我们提出了一种更简单的方法，通过对复杂射线的实部进行建模来模拟受限高斯光束。该过程在很大程度上依赖于 Kogelnik 开发的用于光线追踪光学腔的经典多透镜 ABCD 公式，尽管它避免了使用 q 参数及其传统上在矩阵光学传递计算中进行的 ABCD 传递定律。Arnaud 开创性的复杂射线公式和 Delano y-ybar 射线理论提供了基本框架。结果是一种简单的计算机模拟技术，只需要单向完整遍历光学矩阵的一次计算。我们提出了代表性激光谐振器光束模拟程序的多个详细示例。与传统的q参数方法相比，复合射线方法显着提高了腔内高斯光束射线追踪的效率。考虑的光学元件仅包括端镜和腔内薄透镜。