论文标题
衍射对光场Wigner分布以及如何在光学谐振理论中使用的影响。我 - 稳定的谐振器和高斯光束
Effect of Diffraction on Wigner Distributions of Optical Fields and how to Use It in Optical Resonator Theory. I -- Stable Resonators and Gaussian Beams
论文作者
论文摘要
本文的第一部分致力于衍射现象，该现象可以由分数傅立叶变换表示，其顺序为实数。根据标量理论，衍射作用于电场及其球形角光谱的幅度，并且可以在空间频率相空间上定义Wigner分布。相位空间配备了欧几里得结构，因此衍射的效果是与光场相关的Wigner分布的旋转。这种旋转显示为分成两个特定的椭圆旋转。与谐振器的横向模式相关的Wigner分布在这些旋转中是不变的，并且根据该特性的基础，开发了稳定的光学谐振器和高斯梁的完整理论，包括腰部存在和相关的配方，并且自然引入了鼠标阶段。
The first part of the paper is devoted to diffraction phenomena that can be expressed by fractional Fourier transforms whose orders are real numbers. According to a scalar theory, diffraction acts on the amplitude of the electric field as well as on its spherical angular spectrum, and Wigner distributions can be defined on a space-frequency phase space. The phase space is equipped with an Euclidean structure, so that the effects of diffraction are rotations of Wigner distributions associated with optical fields. Such a rotation is shown to split into two specific elliptical rotations. Wigner distributions associated with transverse modes of a resonator are invariant in these rotations, and a complete theory of stable optical resonators and Gaussian beams is developed on the basis of this property, including waist existence and related formulae, and naturally introducing the Gouy phase.
