We propose stochastic ray tracing for laser beam propagation in Fresnel diffraction to find the duality between wave and ray representations. We transform from the Maxwell equations to the Schrödinger equation for a monochromatic laser beam in the slowly varying envelope approximation. The stochastic ray tracing method interprets this Schrödinger equation as a stochastic process, of an analogy of Nelson’s stochastic mechanics. It can illustrate the stochastic paths and the wavefront of an optical beam. This ray tracing method includes Fresnel diffraction effects naturally. We show its general theoretical construction and numerical tests for a Gaussian laser beam with diffraction, that stochasticity realizes the beam waist around the Rayleigh range.

中文翻译：

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菲涅耳衍射的随机光线追踪

我们提出了菲涅耳衍射中激光束传播的随机光线追踪，以找到波和光线表示之间的对偶性。对于慢变包络近似中的单色激光束，我们将麦克斯韦方程转换为薛定谔方程。随机光线追踪方法将此薛定谔方程解释为随机过程，类似于纳尔逊随机力学。它可以说明光束的随机路径和波前。这种光线追踪方法自然包括菲涅尔衍射效应。我们展示了具有衍射的高斯激光束的一般理论结构和数值测试，随机性实现了瑞利范围附近的光束腰。