为了得到一种新型椭圆扭曲多高斯-谢尔模(TMGSM)光束, 采用Mercer模式展开的方法进行了理论分析和验证, 证明了多高斯-谢尔模关联结构可携带扭曲相位, 详细研究了其在梯度折射率光纤中传输时的光强和相干度演化。结果表明, 椭圆TMGSM光束在梯度折射率光纤中传输时, 光强和相干度分布随着传输距离的增加发生周期性旋转, 并在0.5L(L为周期)的整数倍处偏转π/2, 其旋转角速度呈非线性变化且与扭曲因子的大小有关; 增大多高斯模数, 焦平面处光强分布的平顶区域增大, 相干度分布轮廓变小。此研究结果在光纤通信、聚焦成像、光学捕获等方面具有潜在的应用前景。

In order to obtain a new elliptically twisted multi-Gaussian-Schell model beam, a Mercer model expansion method was adopted, the theoretical analysis and verification were carried out. It is proved that the twisted phase can be carried in the multi-Gaussian-Shell model correlation structure, and the intensity and coherence evolution of the beam propagating in gradient index fibers was studied. The results show that when elliptically twisted multi-Gaussian-Schell model beams are propagating in the graded index fibers, the distribution of intensity and coherence rotates periodically with the increase of transmission distance, and the deflection is π/2 degrees at the integer multiples of 0.5L (L is a cycle). The rotation angular velocity is nonlinear and related to the size of the twist factor. With the increase of multi-Gaussian modulus, the flat top region of the intensity distribution at the focal plane increases, and the coherence distribution contour becomes smaller. The research results have potential applications in optical fiber communication, focused imaging, optical capture and so on.