Coïc H, Rouyer C, Bonod N
J Opt Soc Am A Opt Image Sci Vis. 2021 Jan 1;38(1):124-139. doi: 10.1364/JOSAA.408363.
Laser beams can carry multi-scale properties in space and time that ultimately impact their quality. The study of their evolution along complex optical sequences is of crucial interest, especially in high-intensity laser chains. For such analysis, results obtained with standard numerical methods strongly depend on the sampling. In this paper, we develop an analytic model for a sinusoidal phase modulation inside a sequence of first-order optics elements based on the Wigner matrix formalism. A Bessel decomposition of the Wigner function gives pseudo-Wigner functions that obey the general ABCD matrix law transformation without approximations and sampling considerations. Applied to a Gaussian beam, explicit expressions are obtained for the projections of the Wigner function in the sub-spaces and give a powerful tool for analyzing the laser beam properties. The formalism is established in the spatial and temporal domains and can be used to evaluate the impact of the phase noise on the beam properties and is not limited to small modulation depths. For the sake of illustration, the model is applied to the Talbot effect with the analysis of the propagation in the spatial and phase-space domains. A comparison with full numerical calculations evidences the high accuracy of the analytic model that retrieves all the features of the diffracted beam.
激光束在空间和时间上可以携带多尺度特性，这些特性最终会影响其质量。研究它们在复杂光学序列中的演化至关重要，特别是在高强度激光链中。对于此类分析，用标准数值方法获得的结果在很大程度上取决于采样。在本文中，我们基于维格纳矩阵形式，为一阶光学元件序列内的正弦相位调制开发了一个解析模型。维格纳函数的贝塞尔分解给出了伪维格纳函数，这些伪维格纳函数遵循一般的ABCD矩阵定律变换，无需近似和采样考虑。应用于高斯光束时，可得到维格纳函数在子空间中的投影的显式表达式，为分析激光束特性提供了一个强大的工具。该形式体系在空间和时间域中建立，可用于评估相位噪声对光束特性的影响，且不限于小调制深度。为了说明，该模型应用于塔尔博特效应，并对空间和相空间域中的传播进行了分析。与全数值计算的比较证明了该解析模型的高精度，它能重现衍射光束的所有特征。
