[1] Allen L, Beijersbergen M W, Spreeuw R J et al. Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes[J]. Physical Review A, 45, 8185-8189(1992).

[2] Wang J, Yang J Y, Fazal I M et al. Terabit free-space data transmission employing orbital angular momentum multiplexing[J]. Nature Photonics, 6, 488-496(2012).

[3] Bozinovic N, Yue Y, Ren Y X et al. Terabit-scale orbital angular momentum mode division multiplexing in fibers[J]. Science, 340, 1545-1548(2013).

[4] Yan Y, Xie G D, Lavery M P J et al. High-capacity millimetre-wave communications with orbital angular momentum multiplexing[J]. Nature Communications, 5, 4876(2014).

[5] Nan J H, Han Y P. Dual-channel multiband vortex optical communication[J]. Acta Optica Sinica, 41, 1206001(2021).

[6] Vallone G, D’Ambrosio V, Sponselli A et al. Free-space quantum key distribution by rotation-invariant twisted photons[J]. Physical Review Letters, 113, 060503(2014).

[7] Wang X L, Cai X D, Su Z E et al. Quantum teleportation of multiple degrees of freedom of a single photon[J]. Nature, 518, 516-519(2015).

[8] Sit A, Bouchard F, Fickler R et al. High-dimensional intracity quantum cryptography with structured photons[J]. Optica, 4, 1006-1010(2017).

[9] Xie Z W, Gao S C, Lei T et al. Integrated (de)multiplexer for orbital angular momentum fiber communication[J]. Photonics Research, 6, 743-749(2018).

[10] Willig K I, Rizzoli S O, Westphal V et al. STED microscopy reveals that synaptotagmin remains clustered after synaptic vesicle exocytosis[J]. Nature, 440, 935-939(2006).

[11] Xie X S, Chen Y Z, Yang K et al. Harnessing the point-spread function for high-resolution far-field optical microscopy[J]. Physical Review Letters, 113, 263901(2014).

[12] Kozawa Y, Matsunaga D, Sato S. Superresolution imaging via superoscillation focusing of a radially polarized beam[J]. Optica, 5, 86-92(2018).

[13] Lavery M P J, Speirits F C, Barnett S M et al. Detection of a spinning object using light’s orbital angular momentum[J]. Science, 341, 537-540(2013).

[14] Kravets V G, Schedin F, Jalil R et al. Singular phase nano-optics in plasmonic metamaterials for label-free single-molecule detection[J]. Nature Materials, 12, 304-309(2013).

[15] Li Y, Yu L, Zhang Y X. Influence of anisotropic turbulence on the orbital angular momentum modes of Hermite-Gaussian vortex beam in the ocean[J]. Optics Express, 25, 12203-12215(2017).

[16] Baghdady J, Miller K, Morgan K et al. Multi-gigabit/s underwater optical communication link using orbital angular momentum multiplexing[J]. Optics Express, 24, 9794-9805(2016).

[17] Ren Y X, Li L, Wang Z et al. Orbital angular momentum-based space division multiplexing for high-capacity underwater optical communications[J]. Scientific Reports, 6, 33306(2016).

[18] Wang W, Wang P, Cao T et al. Performance investigation of underwater wireless optical communication system using M-ary OAMSK modulation over oceanic turbulence[J]. IEEE Photonics Journal, 9, 7905315(2017).

[19] Wang A D, Zhu L, Zhao Y F et al. Adaptive water-air-water data information transfer using orbital angular momentum[J]. Optics Express, 26, 8669-8678(2018).

[20] Zhao S M, Zhang W H, Wang L et al. Propagation and self-healing properties of Bessel-Gaussian beam carrying orbital angular momentum in an underwater environment[J]. Scientific Reports, 9, 2025(2019).

[21] Zhang J R, Fan F, Zeng J W et al. Prototype system for underwater wireless optical communications employing orbital angular momentum multiplexing[J]. Optics Express, 29, 35570-35578(2021).

[22] Bolduc E, Bent N, Santamato E et al. Exact solution to simultaneous intensity and phase encryption with a single phase-only hologram[J]. Optics Letters, 38, 3546-3549(2013).

[23] Ma W Q, Lu H M, Wang J P et al. Vortex beam generation based on spatial light modulator and deep learning[J]. Acta Optica Sinica, 41, 1107001(2021).

[24] Shi C Y, Wei H Y, Jia P et al. Detect the orbital angular momentum of vortex beams after phase distortion based on machine learning[J]. Acta Photonica Sinica, 51, 0151123(2022).

[25] Xiao Y, Liu H D, Song Y W et al. Accurately quantifying the superposition state of two different Laguerre-Gaussian modes with single intensity distribution measurement[J]. Quantum Information Processing, 21, 90(2022).

[26] Nielsen M A, Chuang I L[M]. Quantum computation and quantum information(2000).

[27] Pratt V. Direct least-squares fitting of algebraic surfaces[J]. ACM SIGGRAPH Computer Graphics, 21, 145-152(1987).

[28] Jerlov N G[M]. Marine optics(1976).

[29] Zhao Y F, Xu J, Wang A D et al. Demonstration of data-carrying orbital angular momentum-based underwater wireless optical multicasting link[J]. Optics Express, 25, 28743-28751(2017).