[1] Allen, L. et al. Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes. Phys. Rev. A 45, 8185-8189 (1992). doi: 10.1103/PhysRevA.45.8185
[2] Padgett, M. J. Orbital angular momentum 25 years on. Opt. Express 25, 11265-11274 (2017). doi: 10.1364/OE.25.011265
[3] Padgett, M. & Bowman, R. Tweezers with a twist. Nat. Photonics 5, 343-348 (2011). doi: 10.1038/nphoton.2011.81
[4] Ritsch-Marte, M. Orbital angular momentum light in microscopy. Philos. Trans. R. Soc. A: Math., Phys. Eng. Sci. 375, 20150437 (2017). doi: 10.1098/rsta.2015.0437
[5] Vicidomini, G., Bianchini, P. & Diaspro, A. STED super-resolved microscopy. Nat. Methods 15, 173-182 (2018). doi: 10.1038/nmeth.4593
[6] Mari, E. et al. Sub-Rayleigh optical vortex coronagraphy. Opt. Express 20, 2445-2451 (2012). doi: 10.1364/OE.20.002445
[7] Wang, J. Twisted optical communications using orbital angular momentum. Science China Physics, Mechanics & . Astronomy 62, 34201 (2019). doi: 10.1007/s11433-018-9260-8
[8] Mirhosseini, M. et al. High-dimensional quantum cryptography with twisted light. N. J. Phys. 17, 033033 (2015). doi: 10.1088/1367-2630/17/3/033033
[9] Ruffato, G. et al. Design, fabrication and characterization of computer generated holograms for anti-counterfeiting applications using OAM beams as light decoders. Sci. Rep. 7, 18011 (2017). doi: 10.1038/s41598-017-18147-7
[10] Khonina, S. N. et al. The phase rotor filter. J. Mod. Opt. 39, 1147-1154 (1992). doi: 10.1080/09500349214551151
[11] Massari, M. et al. Fabrication and characterization of high-quality spiral phase plates for optical applications. Appl. Opt. 54, 4077-4083 (2015). doi: 10.1364/AO.54.004077
[12] Sacks, Z. S., Rozas, D. & Swartzlander, G. A. Holographic formation of optical-vortex filaments. J. Optical Soc. Am. B 15, 2226-2234 (1998). doi: 10.1364/JOSAB.15.002226
[13] Lei, T. et al. Massive individual orbital angular momentum channels for multiplexing enabled by Dammann gratings. Light Sci. Appl. 4, e257 (2015). doi: 10.1038/lsa.2015.30
[14] Marrucci, L., Manzo, C. & Paparo, P. Pancharatnam-Berry phase optical elements for wave front shaping in the visible domain: switchable helical mode generation. Appl. Phys. Lett. 88, 221102 (2006). doi: 10.1063/1.2207993
[15] Fickler, R. et al. Interface between path and orbital angular momentum entanglement for high-dimensional photonic quantum information. Nat. Commun. 5, 4502 (2014). doi: 10.1038/ncomms5502
[16] Li, W. Z. et al. Rapidly tunable orbital angular momentum (OAM) system for higher order Bessel beams integrated in time (HOBBIT). Opt. Express 27, 3920-3934 (2019). doi: 10.1364/OE.27.003920
[17] Chen, M. L. N., Jiang, L. J. & Sha, W. E. I. Orbital angular momentum generation and detection by geometric-phase based metasurfaces. Appl. Sci. 8, 362 (2018). doi: 10.3390/app8030362
[18] Hell, S. W. & Wichmann, J. Breaking the diffraction resolution limit by stimulated emission: stimulated-emission-depletion fluorescence microscopy. Opt. Lett. 19, 780-782 (1994). doi: 10.1364/OL.19.000780
[19] Yu, S. Y. Potentials and challenges of using orbital angular momentum communications in optical interconnects. Opt. Express 23, 3075-3087 (2015). doi: 10.1364/OE.23.003075
[20] Wang, J. et al. Terabit free-space data transmission employing orbital angular momentum multiplexing. Nat. Photonics 6, 488-496 (2012). doi: 10.1038/nphoton.2012.138
[21] Bozinovic, N. et al. Terabit-scale orbital angular momentum mode division multiplexing in fibers. Science 340, 1545-1548 (2013). doi: 10.1126/science.1237861
[22] Scaffardi, M. et al. Interconnection network architectures based on integrated orbital angular momentum emitters. Opt. Commun. 408, 63-67 (2018). doi: 10.1016/j.optcom.2017.08.024
[23] Ruffato, G. et al. Electrically activated spin-controlled orbital angular momentum multiplexer. Appl. Phys. Lett. 113, 011109 (2018). doi: 10.1063/1.5030844
[24] Willner, A. E. et al. Orbital-angular-momentum-based reconfigurable optical switching and routing. Photonics Res. 4, B5-B8 (2016). doi: 10.1364/PRJ.4.0000B5
[25] Liu, J. & Wang, J. Demonstration of reconfigurable joint orbital angular momentum mode and space switching. Sci. Rep. 6, 37331 (2016). doi: 10.1038/srep37331
[26] García-Escartín, J. C. & Chamorro-Posada, P. Quantum multiplexing with the orbital angular momentum of light. Phys. Rev. A 78, 062320 (2008). doi: 10.1103/PhysRevA.78.062320
[27] García-Escartín, J. C. & Chamorro-Posada, P. Universal quantum computation with the orbital angular momentum of a single photon. J. Opt. 13, 064022 (2011). doi: 10.1088/2040-8978/13/6/064022
[28] Potoček, V. et al. Quantum Hilbert hotel. Phys. Rev. Lett. 115, 160505 (2015). doi: 10.1103/PhysRevLett.115.160505
[29] Zhao, Z. et al. Invited article: division and multiplication of the state order for data-carrying orbital angular momentum beams. APL Photonics 1, 090802 (2016). doi: 10.1063/1.4968838
[30] Zhou, H. L. et al. Orbital angular momentum divider of light. IEEE Photon. J. 9, 6500208 (2017). http://ieeexplore.ieee.org/document/7801909/
[31] Berkhout, G. C. G. et al. Efficient sorting of orbital angular momentum states of light. Phys. Rev. Lett. 105, 153601 (2010). doi: 10.1103/PhysRevLett.105.153601
[32] Lavery, M. P. J. et al. Refractive elements for the measurement of the orbital angular momentum of a single photon. Opt. Express 20, 2110-2115 (2012). doi: 10.1364/OE.20.002110
[33] O'Sullivan, M. N. et al. Near-perfect sorting of orbital angular momentum and angular position states of light. Opt. Express 20, 24444-24449 (2012). doi: 10.1364/OE.20.024444
[34] Ruffato, G. et al. Test of mode-division multiplexing and demultiplexing in free-space with diffractive transformation optics. Opt. Express 25, 7859-7868 (2017). doi: 10.1364/OE.25.007859
[35] Ruffato, G. et al. A compact diffractive sorter for high-resolution demultiplexing of orbital angular momentum beams. Sci. Rep. 8, 10248 (2018). doi: 10.1038/s41598-018-28447-1
[36] Takashima, S., Kobayashi, H. & Iwashita, K. Integer multiplier for orbital angular momentum of light using circular-sector transformation. Preprint at https://arxiv.org/abs/1902.10472, https://journals.aps.org/pra/accepted/8d070Y3aOfa19863589627f0451c8001552155743#abstract (2019).
[37] Hossack, W. J., Darling, A. M. & Dahdouh, A. Coordinate transformations with multiple computer-generated optical elements. J. Mod. Opt. 34, 1235-1250 (1987). doi: 10.1080/09500348714551121
[38] Ruffato, G., Massari, M. & Romanato, F. Diffractive optics for combined spatial- and mode- division demultiplexing of optical vortices: design, fabrication and optical characterization. Sci. Rep. 6, 24760 (2016). doi: 10.1038/srep24760
[39] Rosales-Guzmán, C. & Forbes, A. How to shape light with spatial light modulators (SPIE Press, 2017).
[40] Lavery, M. P. J. et al. Efficient measurement of an optical orbital-angular-momentum spectrum comprising more than 50 states. N. J. Phys. 15, 013024 (2013). doi: 10.1088/1367-2630/15/1/013024
[41] Berry, M. V. & McDonald, K. T. Exact and geometrical optics energy trajectories in twisted beams. J. Opt. A 10, 035005 (2008). doi: 10.1088/1464-4258/10/3/035005
[42] Liu, C. M. et al. Discrimination of orbital angular momentum modes of the terahertz vortex beam using a diffractive mode transformer. Opt. Express 24, 12534-12541 (2016). doi: 10.1364/OE.24.012534
[43] McMorran, B. J. et al. Origins and demonstrations of electrons with orbital angular momentum. Philos. Trans. R. Soc. 375, 20150434 (2017). doi: 10.1098/rsta.2015.0434
[44] Harris, J. et al. Structured quantum waves. Nat. Phys. 11, 629-634 (2015). doi: 10.1038/nphys3404
[45] Grillo, V. et al. Measuring the orbital angular momentum spectrum of an electron beam. Nat. Commun. 8, 15536 (2017). doi: 10.1038/ncomms15536
[46] McMorran, B. J., Harvey, T. R. & Lavery, M. P. J. Efficient sorting of free electron orbital angular momentum. N. J. Phys. 19, 023053 (2017). doi: 10.1088/1367-2630/aa5f6f
[47] Li, J. C., Peng, Z. J. & Fu, Y. C. Diffraction transfer function and its calculation of classic diffraction formula. Opt. Commun. 280, 243–248 (2007). doi: 10.1016/j.optcom.2007.08.053