In the plane-wave angular-spectrum representation, we derive the analytical expressions for any order Laguerre-Gaussian beams propagating along the optical axis of uniaxial crystals. We further prove the orthogonality of propagating modes inside the uniaxial crystals, and investigate the energy efficiency as well as the behavior of spin-orbital coupling. Based on the analytical solutions, we propose a scheme for the transmission of structured light fields through the uniaxial crystals, which firstly decomposes the input fields into LG spectrum and then superposes all OAM components inside crystals to obtain the propagating optical fields. We use the trefoil image as an example to demonstrate the effectiveness of our scheme. The evolution of optical fields and spectra of trefoil image are also studied.

中文翻译：

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利用Laguerre-Gaussian谱在单轴晶体中传输结构化光场

在平面波角谱表示中，我们推导了沿单轴晶体的光轴传播的任何阶拉盖尔-高斯光束的解析表达式。我们进一步证明了单轴晶体内部传播模式的正交性，并研究了能量效率以及自旋轨道耦合的行为。基于解析解，我们提出了一种结构化光场通过单轴晶体传输的方案，该方案首先将输入场分解为LG光谱，然后将晶体内部的所有OAM分量叠加以获得传播的光场。我们以三叶形图像为例来说明该方案的有效性。还研究了三叶形图像的光学场和光谱的演变。