We use the Fourier transform and Snell’s law to demonstrate how refraction at a flat interface induces astigmatism and transforms the spatial distribution of a stigmatic beam. Refraction makes the beam parameters for the transverse dimensions perpendicular and parallel to the plane of incidence grow differently and gives rise astigmatism. The decompositions of the orbital angular momentum of the beam before and after refraction are different. A single-value state of orbital angular momentum of the incident photon in a Laguerre–Gaussian mode is transformed into a superposition state.

中文翻译：

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折射引起的像散对光轨道角动量的影响

我们使用傅里叶变换和斯涅尔定律来证明平面界面上的折射如何引起像散并改变像散光束的空间分布。折射使垂直和平行于入射平面的横向尺寸的光束参数不同地增长，并产生像散。光束在折射前后的轨道角动量分解不同。在Laguerre-Gaussian模式下，入射光子的轨道角动量的单值状态被转换为叠加状态。