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Pattern fluctuations and revivals in complex structured light from unitary transformation
preprintposted on 2024-02-07, 17:00 authored by Zheng-Xiao Cao, Ting-Ting Liu, Bo-Zhao, Carmelo Rosales-Guzmán, Jun Liu, Zhi-Han Zhu
Astigmatic unitary transformations allow for the adiabatic connections of all feasible states of paraxial Gaussian beams on the same modal sphere, i.e., Hermite-Laguerre-Gaussian (HLG) modes. Here, we present a comprehensive investigation into the unitary modal evolution of complex structured Gaussian beams, comprised by HLG modes from disparate modal spheres, via astigmatic transformation. The non-synchronized higher-order geometric phases in cyclic transformations originates pattern fluctuations in the superposition state of these HLG modes, as well as possible pattern revivals in transformations with specific geodesic loops. Using Ince-Gaussian modes as an illustrative example, we systematically analyze and experimentally corroborate the beamforming mechanism behind the pattern evolution. Our results outline a generic modal conversion theory of structured Gaussian beams via astigmatic unitary transformation, offering a new approach for shaping spatial modal structure. These findings may inspire a wide variety of applications based on structured light.