We report on a theoretical and numerical study of a Gaussian beam modulated by several optical vortices (OV) that carry same-sign unity topological charge (TC) and are unevenly arranged on a circle. The TC of such a multi-vortex beam equals the sum of the TCs of all OVs. If the OVs are located evenly along an arbitrary-radius circle, a simple relationship for the normalized orbital angular momentum (OAM) is derived for such a beam. It is shown that in a multi-vortex beam, OAM normalized to power cannot exceed the number of constituent vortices and decreases with increasing distance from the optical axis to the vortex centers. We show that for the OVs to appear at the infinity of such a combined beam, an infinite-energy Gaussian beam is needed. On the contrary, the total TC is independent of said distance, remaining equal to the number of constituent vortices. We show that if TC is evaluated not along the whole circle encompassing the singularity centers, but along any part of this circle, such a quantity is also invariant and conserves on propagation. Besides, a multi-spiral phase plate is studied for the first time to our knowledge, and we obtained the TC and OAM of multi-vortices generated by this plate. When propagated through a random phase screen (diffuser) the TC is unchanged, while the OAM changes by less than 10% if the random phase delay on the diffuser does not exceed half wavelength. Such multi-vortices can be used for data transmission in the turbulent atmosphere.

中文翻译：

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多涡高斯光束的轨道角动量和拓扑电荷

我们报告了由几个光学涡旋（OV）调制的高斯光束的理论和数值研究，这些光学涡旋带有相同符号的统一拓扑电荷（TC），并且不均匀地排列在一个圆上。这种多涡旋光束的TC等于所有OV的TC之和。如果OV沿任意半径的圆均匀分布，则针对此类光束得出归一化轨道角动量（OAM）的简单关系。结果表明，在多涡旋光束中，归一化为功率的OAM不能超过组成涡旋的数量，并且随着从光轴到涡旋中心距离的增加而减小。我们表明，要使OV出现在这种组合光束的无穷远处，就需要一个无限能量的高斯光束。相反，总TC与上述距离无关，保持等于组成涡旋的数量。我们表明，如果不是在包含奇点中心的整个圆上评估TC，而是在该圆的任何部分上评估TC，那么该量也是不变的，并且在传播时会节省。此外，据我们所知，首次对多螺旋相位板进行了研究，并获得了由该板产生的多涡旋的TC和OAM。当通过随机相位屏幕（漫射器）传播时，TC保持不变，而如果漫射器上的随机相位延迟不超过一半波长，则OAM的变化小于10％。这种多涡流可用于湍流环境中的数据传输。这样的数量也是不变的，并且在传播上是保守的。此外，据我们所知，首次对多螺旋相位板进行了研究，并获得了由该板产生的多涡流的TC和OAM。当通过随机相位屏幕（漫射器）传播时，TC保持不变，而如果漫射器上的随机相位延迟不超过一半波长，则OAM的变化小于10％。这种多涡流可用于湍流环境中的数据传输。这样的数量也是不变的，并且在传播上是保守的。此外，据我们所知，首次对多螺旋相位板进行了研究，并获得了由该板产生的多涡旋的TC和OAM。当通过随机相位屏幕（漫射器）传播时，TC保持不变，而如果漫射器上的随机相位延迟不超过一半波长，则OAM的变化小于10％。这种多涡流可用于湍流环境中的数据传输。如果漫射器上的随机相位延迟不超过一半波长，则OAM的变化小于10％。这种多涡流可用于湍流环境中的数据传输。如果漫射器上的随机相位延迟不超过一半波长，则OAM的变化小于10％。这种多涡流可用于湍流环境中的数据传输。