[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, Atomic, Molecular, and Optical Physics, 45, 8185-8189(1992).
[2] Grier D G. A revolution in optical manipulation[J]. Nature, 424, 810-816(2003).
[3] Shvedov V G, Rode A V, Izdebskaya Y V et al. Giant optical manipulation[J]. Physical Review Letters, 105, 118103(2010).
[4] Padgett M, Bowman R. Tweezers with a twist[J]. Nature Photonics, 5, 343-348(2011).
[5] Paterson L, MacDonald M P, Arlt J et al. Controlled rotation of optically trapped microscopic particles[J]. Science, 292, 912-914(2001).
[6] Hell S W, Wichmann J. Breaking the diffraction resolution limit by stimulated emission: stimulated-emission-depletion fluorescence microscopy[J]. Optics Letters, 19, 780-782(1994).
[7] Berning S, Willig K I, Steffens H et al. Nanoscopy in a living mouse brain[J]. Science, 335, 551(2012).
[8] Nan J H, Han Y P. Dual-channel multi-band orbital angular momentum optical communication[J]. Acta Optica Sinica, 41, 1206001(2021).
[9] Sun Y L, Zhang J R, Lu Z Z. Propagation characteristics of Laguerre-Gaussian vortex beams in underwater turbulence[J]. Acta Optica Sinica, 39, 1001005(2019).
[10] Wang J. Advances in communications using optical vortices[J]. Photonics Research, 4, B14-B28(2016).
[11] Qiu S, Ren Y, Liu T et al. Detection of rotational cylinder speed using Doppler effect of optical vortex[J]. Acta Optica Sinica, 40, 2026001(2020).
[12] Fu Z L, Wang Z, Cui C et al. Angular velocity measurement based on rotational Doppler effect of vortex beam[J]. Laser & Optoelectronics Progress, 56, 180501(2019).
[13] Toyoda K, Miyamoto K, Aoki N et al. Using optical vortex to control the chirality of twisted metal nanostructures[J]. Nano Letters, 12, 3645-3649(2012).
[14] Levy U, Derevyanko S, Silberberg Y. Light modes of free space[M]. Visser T D. Progress in optics, 61, 237-281(2016).
[15] Forbes A. Controlling light’s helicity at the source: orbital angular momentum states from lasers[J]. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 375, 20150436(2017).
[16] Zeng B B, Xu D Y, Wang R W. Physical concept and measurement on laser beam quality factor M2[J]. Applied Laser, 14, 104-108(1994).
[17] He Y X. Study of evaluating and measuring laser beam quality[D], 22(2012).
[18] Sasnett M W, Johnston T J. Beam characterization and measurement of propagation attributes[J]. Proceedings of SPIE, 1414, 21-32(1991).
[19] Lü B D[M]. Laser optics: beam description, transmission transformation and optical cavity technology physics(2003).
[20] Lü B D, Kang X P. Some aspects of laser beam quality[J]. Infrared and Laser Engineering, 36, 47-51(2007).
[21] Siegman A E. New developments in laser resonators[J]. Proceedings of SPIE, 1224, 2-14(1990).
[22] Weber H. Laser beam quality[J]. Optical and Quantum Electronics, 24, vii(1992).
[23] Huang S P. A new method for simultaneously measuring waist position and waist radius of Gaussian beam[J]. Physics and Engineering, 27, 30-33(2017).
[24] Li L, Zang J F. Measurement of laser beam quality by means of double-slit scanning method[J]. Laser Technology, 39, 845-849(2015).
[25] Hu L T, Lu X K, Jin J K et al. Laser facula measurement with CCD[J]. Laser Technology, 25, 154-157(2001).
[26] Gao X S, Gao C Q, Yang S Z et al. Experimental study on beam parameter measurement system by using area array CCD[J]. Chinese Journal of Lasers, 32, 993-996(2005).
[27] Diso D, Perrone M R, Protopapa M L. Beam width measurements of asymmetric multi-mode laser beams[J]. Optics & Laser Technology, 31, 411-418(1999).
[28] González-Cardel M, Arguijo P, Díaz-Uribe R. Gaussian beam radius measurement with a knife-edge: a polynomial approximation to the inverse error function[J]. Applied Optics, 52, 3849-3855(2013).
[29] Bilger H R, Habib T. Knife-edge scanning of an astigmatic Gaussian beam[J]. Applied Optics, 24, 686-690(1985).
[30] Khosrofian J M, Garetz B A. Measurement of a Gaussian laser beam diameter through the direct inversion of knife-edge data[J]. Applied Optics, 22, 3406-3410(1983).
[31] Plass W, Maestle R, Wittig K et al. High-resolution knife-edge laser beam profiling[J]. Optics Communications, 134, 21-24(1997).
[32] Yang X D, Shao J X, Liao S H et al. Investigation on measuring beam width of the Gaussian beam by knife-edge method[J]. Laser & Infrared, 39, 829-832(2009).
[33] Bélanger P A, Champagne Y, de Paré C. Beam propagation factor of diffracted laser beams[J]. Optics Communications, 105, 233-242(1994).
[34] Siegman A E. New developments in laser resonators[J]. Proceedings of SPIE, 1224, 2-14(1990).
[35] Yuan B, Gong Z B, Shen S P et al. Effect of measurement methods on beamwidths and M2 factors of Laguerre-Gaussian modes[J]. Applied Laser, 19, 313-315(1999).
[36] Lv Q, Liu H Y, Luo H L et al. The role of dispersion in the propagation of rotating beams in left-handed materials[J]. Optics Express, 17, 5645-5655(2009).
[37] Ma J B, Li P, Zhou Z H et al. Characteristics of fork-shaped fringes formed by off-axis interference of two vortex beams[J]. Journal of the Optical Society of America A-Optics Image Science and Vision, 38, 115-123(2021).
[38] Gong Y T, Liu L Q, Geng Y C et al. Research progress on ultrashort vortex pulse generation methods[J]. Laser & Optoelectronics Progress, 57, 050008(2020).
[39] Beijersbergen M W, Coerwinkel R P C, Kristensen M et al. Helical-wavefront laser beams produced with a spiral phaseplate[J]. Optics Communications, 112, 321-327(1994).
[40] Berry M V. Optical vortices evolving from helicoidal integer and fractional phase steps[J]. Journal of Optics A: Pure and Applied Optics, 6, 259-268(2004).
[41] Kotlyar V V, Almazov A A, Khonina S N et al. Generation of phase singularity through diffracting a plane or Gaussian beam by a spiral phase plate[J]. Journal of the Optical Society of America. A, Optics, Image Science, and Vision, 22, 849-861(2005).
[42] Massari M, Ruffato G, Gintoli M et al. Fabrication and characterization of high-quality spiral phase plates for optical applications[J]. Applied Optics, 54, 4077-4083(2015).
[43] Mawardi A, Hild S, Widera A et al. ABCD-treatment of a propagating doughnut beam generated by a spiral phase plate[J]. Optics Express, 19, 21205-21210(2011).
[44] Janicijevic L, Topuzoski S. Gaussian laser beam transformation into an optical vortex beam by helical lens[J]. Journal of Modern Optics, 63, 164-176(2016).