基于运算符的Whittaker和Helmholtz高斯光束传播
Operator based propagation of Whittaker and Helmholtz Gauss beams
AI总结：
本文提出一种基于运算符的高效方法，用于传播Whittaker和Helmholtz高斯光束，通过闭合形式表达保留高斯宽度，实现有限能量光束的描述，并验证了其在非衍射结构中的应用效果。
摘要：
我们介绍了一种紧凑的基于运算符的技术，用于求解偏振波方程的一类广泛结构光场。利用空间演化的运算符来传播两个物理上衰减的输入家族，即高斯衰减的Whittaker积分和高斯衰减的Helmholtz场，我们推导出闭合形式的表达式，保留高斯宽度，因此描述有限能量的光束。该方法统一并扩展了Helmholtz高斯家族，并可方便地推广到非分离的非衍射架构。对叠加的Bessel高斯光束的实验验证了预测的横向旋转，证明了这种运算符方法是快速、透明且实用的替代标准衍射积分处理方法。
英文摘要：
We introduce a compact operator-based technique that solves the paraxial wave equation for a broad class of structured light fields. Using the spatial evolution operator to propagate two families of physically apodized inputs, Gaussian apodized Whittaker integrals and Gaussian apodized Helmholtz fields, we derive closed form expressions that retain the Gaussian width and therefore describe finite energy beams. The method unifies and extends the Helmholtz Gauss families and readily generalizes to nonseparable nondiffracting architectures. Experiments on superposed Bessel Gauss beams confirm the predicted transverse rotations, demonstrating that this operator approach is a fast, transparent, and practical alternative to standard diffraction ntegral treatments
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