This article introduces a streamlined method for ray-tracing Gaussian laser beams in optical systems, drawing from traditional matrix optics and J. A. Arnaud’s complex rays. It provides an intuitive tool for optical engineers, accommodating arbitrary initial beam curvatures and spot radii for versatile system analyses. Examples, including beam focusing, mode matching, and zoom lens systems, demonstrate its applicability. We present a user-friendly Microsoft Excel tool for simulations and optimization, along with a Python-coded 3D beam propagation model. This method enhances understanding and equips professionals with practical tools for various optical configurations. This work also explores the application to 3D virtual reality.
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.
New graphical methods using the Delano y-ybar diagram are shown to yield simple alternative derivations of the M2 beam quality factor for Gaussian-like laser beams. Using M2 as a scaler for the Lagrange optical invariant, powerful methods of interpreting and calculating the beam factor become apparent. Elegant methods of determining M2 using strategic beam sample locations are also developed, taking advantage of the property that a freely propagating beam trace in the Gaussian beam y-ybar plane is a straight line. Application to non-Gaussian beams is explored.
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