分数阶和整数阶光学涡旋的相互转换
The mutual transformations of fractional-order and integer-order optical vortices
摘要：
我们认为光学中的奇异光束问题是物理学中，特别是流体力学和量子力学中具有分数拓扑荷的涡旋态的相互作用、成形和变换的一般问题的一部分。从分数阶涡旋态表示为无穷多个具有不同能量分布的整数阶涡旋的叠加出发，（涡旋谱）我们表明分数涡旋光束的平滑波前可以衰减成整数阶涡旋的非对称阵列，反之亦然，光学涡旋阵列可以聚集在一起，形成在自由空间中传播时具有螺旋形相位分布的平滑波前。我们发现，一个简单的叠加的分数阶涡旋光束的有限数量，使我们能够形成对称的奇异光束与所需的拓扑电荷的整数阶涡旋。
英文摘要：
We consider the problem of singular beams in optics as a part of the general questions of interactions, shaping and transformations of vortex states with fractional topological charges in physics, in particular, in hydrodynamic and quantum mechanic. Starting from the representation of the fractional-order vortex states as a superposition of infinite number of integer-order vortices with distinctive energy distributions (the vortex spectra) we showed that the smooth wave front of the fractional vortex beam can either decay into an asymmetric array of integer-order vortices or, vice versa, the array of optical vortices can be gathered together forming a smooth wave front with a helicoid-shaped phase distribution under propagation in free space. We revealed that a simple superposition of a finite number of the fractional-order vortex beams enables us to shape symmetric singular beams with the integer-order vortices of the desired topological charges.
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