Generation And Characterization Of High-dimensional Orbital Angular Momentum States With Propagation-invariant Structure

Photonic states encoded with transverse structure of paraxial light fields provide a promising platform for high-dimensional quantum information study,and corresponding studies,especially for experimental aspect,have made significant headway recently.However,a technical problem encountered in free-space optical experiments has not yet been resolved.That is,asynchronized diffraction between spatial modes with different orders leads to variations in transverse structure of the modes upon propagation.To address this issue,we proposed an encoding method using all LG modes of order to define a N +1 dimensional space,in which all orbital angular momentum(OAM)states are propagation-invariant and have an identity wavefront curvature.By using time-correlated-single-photon imaging combined with a digital propagation technique,we experimentally demonstrated that,without using an imaging system,all problems due to asynchronized diffraction are smartly evaded.The method provides an accessible way to generate propagation-invariant high-dimensional orbital angular momentum states for quantum optical experiments.First,the analytical solutions of paraxial wave equation in elliptic and cylindrical coordinate systems are introduced respectively,namely,the theoretical models of Ince-Gaussian(IG)mode and LG mode,in order to lay a solid foundation for the preparation and characterization of complex spatial models in the following work.The conversion relationship between LG mode and IG mode is mainly introduced to pave the way for the construction of stable propagation complex spatial mode.Secondly,the mathematical and physical concepts of mutually unbiased orthogonal basis(MUBs)are introduced.Based on the coefficients of high-dimensional MUBs,complex spatial patterns based on LG mode eigenstates and non-eigenstates are constructed.With the help of digital propagation technology and complex amplitude intensity modulation technology,the theoretical prediction and numerical simulation of complex spatial mode are realized.The correlation matrix represented by OAM state of propagating invariable high-dimensional photon is constructed and the propagation drift phenomenon of high-dimensional spatial mode interferometry is analyzed and verified.Finally,holograms based on complex amplitude modulation and digital propagation technology are loaded onto Spatial light modulator(SLM).On the one hand,the preparation,digital propagation and theoretical and experimental characterization analysis of Spatial modes with different modes order are completed.We verify the unavailability of Gouy phase shift asynchronous spatial patterns.On the other hand,through the experimental analysis of the generation and characterization process of the spatial mode of Gouy phase shift synchronization of high-dimensional photon OAM state which depends on the mode order N,the consistency of the experimental results with the theoretical prediction and numerical simulation is verified.