Twisted Gaussian Schell-model beams. I. Symmetry structure and normal-mode spectrum
Twisted Gaussian Schell-model beams. I. Symmetry structure and normal-mode spectrum
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DOI：
10.1364/josaa.10.002008
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发表时间：
1993-09
影响因子：
1.9
通讯作者：
R. Simon;K. Sundar;N. Mukunda
中科院分区：
文献类型：
--
作者：
R. Simon;K. Sundar;N. Mukunda
我们提出了一个全面的正常模式分解分析最近推出的[J。A10，95（1993）]类扭曲高斯谢尔模型场的部分相干光束光学。在二维量子力学的形式类比被利用。我们还有效地利用了这些场的动力学SU（2）对称性来实现模式分解和确定谱。扭曲相位在本质上是不可分离的，使其成为非平凡的二维。这样做的后果，导致需要使用拉盖尔-高斯函数，而不是厄米-高斯的产品，仔细分析。一个重要的身份，涉及这些特殊的功能集的建立，并用于推导频谱。
We present a comprehensive normal-mode decomposition analysis for the recently introduced [ J. Opt. Soc. Am. A10, 95 ( 1993)] class of twisted Gaussian Schell-model fields in partially coherent beam optics. The formal analogies to quantum mechanics in two dimensions are exploited. We also make effective use of a dynamical SU(2) symmetry of these fields to achieve the mode decomposition and to determine the spectrum. The twist phase is nonseparable in nature, rendering it nontrivially two dimensional. The consequences of this, resulting in the need to use Laguerre–Gaussian functions rather than products of Hermite–Gaussians, are carefully analyzed. An important identity involving these sets of special functions is established and is used in deriving the spectrum.