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arXiv 2203.14546physics.optics
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衍射对光场维格纳分布的影响及其在光学谐振腔理论中的应用。II --非稳定谐振器

Effect of Diffraction on Wigner Distributions of Optical Fields and how to Use It in Optical Resonator Theory. II -- Unstable Resonators

Pierre Pellat-Finet, Éric Fogret

摘要:

文章的第二部分致力于场转移的衍射表示的分数傅立叶变换的订单是复数。与光场相关的维格纳分布上的相应效应仍然由在缩放相空间上操作的$4\times4$矩阵表示,但与第一部分中涉及的矩阵不同,这些矩阵分解成基本上表示2维双曲旋转而不是椭圆旋转的两个矩阵。结果应用于非稳腔理论。

英文摘要:

The second part of the article is devoted to field transfers by diffraction that are represented by fractional Fourier transformations whose orders are complex numbers. The corresponding effects on the Wigner distributions associated with optical fields are still represented by $4\times4$ matrices operating on the scaled phase-space, but unlike matrices involved in the first part, those matrices decompose into two matrices that essentially represent 2--dimensional hyperbolic rotations, not elliptical rotations. The result is applied to the theory of unstable resonators.

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