Abstract

The emergence of vortex transmutation has opened new ways for vorticity modulation of optical vortices. Although several approaches have been proposed to realize vortex transmutation, fractional optical vortex (FOV) transmutation remains elusive owing to a lack of effective generation and detection methods. Here we report quantitative experimental evidence for a free-space FOV transmutation rule. The key idea is to combine the advantages of a single optical element, termed as fractional spiral polygonal lenses (FSPLs), with a deep learning approach. The desired wavefront is simultaneously generated and manipulated at the focal plane of the FSPL, and the fractional output vorticity is measured by analyzing a single far-field diffraction pattern. Especially, a deep learning scheme using a Bayesian optimization method is developed for output vorticity prediction with a data recovery rate up to 98.2%. The average error of recognized fractional orbital angular momentum modes is as small as 0.02. We clearly observe the intriguing phenomenon that the central vorticity of FOV is changed following a modulo-n transmutation rule in free space. Our results have important implications for fundamental understanding of FOV systems in free space, and offer a technological foundation for potential applications such as quantum information processing and particle manipulation and transportation.

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