Double Laguerre-Gaussian beams

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-12-01 DOI:10.18287/2412-6179-co-1177

V. Kotlyar, E. Abramochkin, A. Kovalev, A. Savelyeva

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引用次数: 2

Abstract

We show here that the product of two Laguerre-Gaussian (LG) beams, i.e. double LG beams (dLG), can be represented as finite superposition of conventional LG beams with certain coeffi-cients that are expressed via zero-argument Jacobi polynomials. This allows obtaining an explicit expression for the complex amplitude of the dLG beams in the Fresnel diffraction zone. Generally, such beams do not retain their structure, changing shape upon free-space propagation. However, if both LG beams are of the same order, we obtain a special case of a "squared" LG beam, which is Fourier-invariant. Another special case of the dLG beams is obtained when the azimuthal indices of the Laguerre polynomials are equal to n – m and n + m. For such a beam, an explicit expression is obtained for the complex amplitude in the Fourier plane. We show that if the lower indices of the constituent LG beams are the same, such a double LG beam is also Fourier-invariant. Similar to conventional LG beams, the product of LG beams can be used for optical data transmission, since they are characterized by azimuthal orthogonality and carry an orbital angular momentum equal to the topological charge.

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双拉盖尔-高斯光束

我们在这里证明了两个拉盖尔-高斯(LG)光束的乘积，即双LG光束(dLG)，可以表示为具有一定系数的常规LG光束的有限叠加，这些系数通过零参数雅可比多项式表示。这允许在菲涅耳衍射区获得dLG光束的复振幅的显式表达式。一般来说，这样的梁不会保持其结构，在自由空间传播时改变形状。然而，如果两个LG光束的阶数相同，我们就得到了“平方”LG光束的一种特殊情况，它是傅里叶不变的。当拉盖尔多项式的方位角指数等于n - m和n + m时，得到了dLG梁的另一种特殊情况。对于这种梁，得到了复振幅在傅里叶平面上的显式表达式。我们证明了如果组成LG光束的下标相同，这样的双LG光束也是傅里叶不变的。与传统的LG光束类似，LG光束的产物可以用于光学数据传输，因为它们具有方位正交的特征，并且携带与拓扑电荷相等的轨道角动量。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.