Vector vortex beams are conventionally created as the superposition of orbital angular momentum (OAM) modes with orthogonal polarizations, limiting the available degrees of freedom (DoFs) to 2, while their creation by complex optical devices such as metasurfaces, liquid crystals, and interferometers has hindered their versatility. Here we demonstrate a new class of vector vortex beam constructed from four DoFs as multiple ray-like trajectories with wave-like properties, which we create by operating a simple anisotropic microchip laser in a frequency-degenerate state. Our new structure is obtained by the superposition of two stable periodic ray trajectories, simultaneously fulfilling a completed oscillation in the cavity. By a simple external modulation, we can transform our ray trajectories into vortex beams with large OAM, multiple singularities, as well as exotic helical star-shaped patterns. Our experimental results are complemented by a complete theoretical framework for this new class of beam, revealing parallels to hybrid SU(2) coherent states. Our approach offers in principle unlimited DoFs for vectorial structured light with concomitant applications, for example, in engineering classically entangled light and in vectorial optical trapping and tweezing.

中文翻译：

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激光具有多个自由度的结构化射线波矢量涡旋光束

通常将矢量涡旋光束创建为具有正交极化的轨道角动量（OAM）模式的叠加，从而将可用自由度（DoFs）限制为2，而由复杂的光学设备（如超表面，液晶和干涉仪）创建的矢量阻碍了它们的多功能性。在这里，我们展示了由四个自由度构成的一类新的矢量涡旋光束，它们是具有波状特性的多条射线状轨迹，是通过在频率简并状态下操作简单的各向异性微芯片激光器而创建的。我们的新结构是通过叠加两个稳定的周期性射线轨迹而获得的，同时完成了空腔中的完整振荡。通过简单的外部调制，我们可以将射线轨迹转换为具有大OAM，多个奇点的涡旋光束，以及奇特的螺旋形星形图案。我们的实验结果得到了这一新型梁的完整理论框架的补充，揭示了与杂化SU（2）相干态的相似之处。我们的方法原则上为矢量结构化光提供了无限制的DoF，并伴随着应用，例如在工程经典纠缠光以及矢量光学陷波和钳夹中。