We introduce a new kind of partially coherent source whose cross-spectral density (CSD) function is described as the incoherent superposition of elliptical twisted Gaussian Schell-model sources with different beam widths and transverse coherence widths, named twisted elliptical multi-Gaussian Schell-model (TEMGSM) beams. Analytical expression for the CSD function propagating through a paraxial ABCD optical system is derived with the help of the generalized Collins formula. Our results show that the TEMGSM beam is capable of generating a flat-topped elliptical beam profile in the far field, and the beam spot during propagation exhibits clockwise/anti-clockwise rotation with respect to its propagation axis. In addition, the analytical expressions for the orbital angular momentum (OAM) and the propagation factor are also derived by means of the Wigner distribution function. The influences of the twisted factor and the beam index on the OAM and the propagation factor are studied and discussed in detail.

中文翻译：

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扭曲椭圆形多高斯谢尔模型光束及其传播特性。

我们介绍了一种新型的部分相干源，其交叉谱密度（CSD）函数被描述为具有不同束宽度和横向相干宽度的椭圆形扭曲高斯谢尔模型源的非相干叠加，称为扭曲椭圆多高斯谢尔模型（TEMGSM）光束。借助于广义柯林斯公式，得出了通过近轴ABCD光学系统传播的CSD函数的解析表达式。我们的结果表明，TEMGSM光束能够在远场中产生平顶的椭圆光束轮廓，并且光束在传播过程中相对于其传播轴呈顺时针/逆时针旋转。此外，还利用维格纳分布函数推导了轨道角动量（OAM）和传播因子的解析表达式。研究并讨论了扭曲因数和光束指数对OAM和传输因数的影响。