[1] Q. Zhan. Cylindrical vector beams: from mathematical concepts to applications. Adv. Opt. Photon., 1, 1-57(2009).

[2] U. Levy, Y. Silberberg, N. Davidson. Mathematics of vectorial Gaussian beams. Adv. Opt. Photon., 11, 828-891(2019).

[3] K. S. Youngworth, T. G. Brown. Focusing of high numerical aperture cylindrical-vector beams. Opt. Express, 7, 77-87(2000).

[4] R. Dorn, S. Quabis, G. Leuchs. Sharper focus for a radially polarized light beam. Phys. Rev. Lett., 91, 233901(2003).

[5] C. Ping, C. Liang, F. Wang, Y. Cai. Radially polarized multi-Gaussian Schell-model beam and its tight focusing properties. Opt. Express, 25, 32475-32490(2017).

[6] W. Chen, Q. Zhan. Three-dimensional focus shaping with cylindrical vector beams. Opt. Commun., 265, 411-417(2006).

[7] E. Otte, K. Tekce, C. Denz. Tailored intensity landscapes by tight focusing of singular vector beams. Opt. Express, 25, 20194-20201(2017).

[8] H.-F. Xu, Y. Zhou, H.-W. Wu, H.-J. Chen, Z.-Q. Sheng, J. Qu. Focus shaping of the radially polarized Laguerre-Gaussian-correlated Schell-model vortex beams. Opt. Express, 26, 20076-20088(2018).

[9] H.-F. Xu, R. Zhang, Z.-Q. Sheng, J. Qu. Focus shaping of partially coherent radially polarized vortex beam with tunable topological charge. Opt. Express, 27, 23959-23969(2019).

[10] C. Varin, M. Piché. Acceleration of ultra-relativistic electrons using high-intensity TM₀₁ laser beams. Appl. Phys. B, 74, s83-s88(2002).

[11] Q. Zhan. Trapping metallic Rayleigh particles with radial polarization. Opt. Express, 12, 3377-3382(2004).

[12] Y. Kozawa, S. Sato. Optical trapping of micrometer-sized dielectric particles by cylindrical vector beams. Opt. Express, 18, 10828-10833(2010).

[13] B. J. Roxworthy, K. C. Toussaint. Optical trapping with π-phase cylindrical vector beams. New J. Phys., 12, 073012(2010).

[14] O. M. Maragò, P. H. Jones, P. G. Gucciardi, G. Volpe, A. C. Ferrari. Optical trapping and manipulation of nanostructures. Nat. Nanotechnol., 8, 807-819(2013).

[15] V. G. Niziev, A. V. Nesterov. Influence of beam polarization on laser cutting efficiency. J. Phys. D, 32, 1455-1461(1999).

[16] M. Meier, V. Romano, T. Feurer. Material processing with pulsed radially and azimuthally polarized laser radiation. Appl. Phys. A, 86, 329-334(2007).

[17] M.-Q. Cai, P.-P. Li, D. Feng, Y. Pan, S.-X. Qian, Y. Li, C. Tu, H.-T. Wang. Microstructures fabricated by dynamically controlled femtosecond patterned vector optical fields. Opt. Lett., 41, 1474-1477(2016).

[18] P. Török, P. Munro. The use of Gauss-Laguerre vector beams in STED microscopy. Opt. Express, 12, 3605-3617(2004).

[19] S. Segawa, Y. Kozawa, S. Sato. Resolution enhancement of confocal microscopy by subtraction method with vector beams. Opt. Lett., 39, 3118-3121(2014).

[20] Y. Kozawa, S. Sato. Numerical analysis of resolution enhancement in laser scanning microscopy using a radially polarized beam. Opt. Express, 23, 2076-2084(2015).

[21] S. Berg-Johansen, F. Töppel, B. Stiller, P. Banzer, M. Ornigotti, E. Giacobino, G. Leuchs, A. Aiello, C. Marquardt. Classically entangled optical beams for high-speed kinematic sensing. Optica, 2, 864-868(2015).

[22] S. Roy, K. Ushakova, Q. van den Berg, S. F. Pereira, H. P. Urbach. Radially polarized light for detection and nanolocalization of dielectric particles on a planar substrate. Phys. Rev. Lett., 114, 103903(2015).

[23] M. Neugebauer, P. Woźniak, A. Bag, G. Leuchs, P. Banzer. Polarization-controlled directional scattering for nanoscopic position sensing. Nat. Commun., 7, 11286(2016).

[24] G. Milione, T. A. Nguyen, J. Leach, D. A. Nolan, R. R. Alfano. Using the nonseparability of vector beams to encode information for optical communication. Opt. Lett., 40, 4887-4890(2015).

[25] G. Milione, M. P. J. Lavery, H. Huang, Y. Ren, G. Xie, T. A. Nguyen, E. Karimi, L. Marrucci, D. A. Nolan, R. R. Alfano, A. E. Willner. 4 × 20  gbit/s mode division multiplexing over free space using vector modes and a q-plate mode (de)multiplexer. Opt. Lett., 40, 1980-1983(2015).

[26] Y. Zhao, J. Wang. High-base vector beam encoding/decoding for visible-light communications. Opt. Lett., 40, 4843-4846(2015).

[27] X.-L. Wang, X.-D. Cai, Z.-E. Su, M.-C. Chen, D. Wu, L. Li, N.-L. Liu, C.-Y. Lu, J.-W. Pan. Quantum teleportation of multiple degrees of freedom of a single photon. Nature, 518, 516-519(2015).

[28] P. Li, B. Wang, X. Zhang. High-dimensional encoding based on classical nonseparability. Opt. Express, 24, 15143-15159(2016).

[29] A. Sit, F. Bouchard, R. Fickler, J. Gagnon-Bischoff, H. Larocque, K. Heshami, D. Elser, C. Peuntinger, K. Günthner, B. Heim, C. Marquardt, G. Leuchs, R. W. Boyd, E. Karimi. High-dimensional intracity quantum cryptography with structured photons. Optica, 4, 1006-1010(2017).

[30] J. Zhu, Y. Chen, Y. Zhang, X. Cai, S. Yu. Spin and orbital angular momentum and their conversion in cylindrical vector vortices. Opt. Lett., 39, 4435-4438(2014).

[31] S. Fu, C. Guo, G. Liu, Y. Li, H. Yin, Z. Li, Z. Chen. Spin-orbit optical Hall effect. Phys. Rev. Lett., 123, 243904(2019).

[32] P. Shi, L. Du, X. Yuan. Structured spin angular momentum in highly focused cylindrical vector vortex beams for optical manipulation. Opt. Express, 26, 23449-23459(2018).

[33] Y. Han, L. Chen, Y.-G. Liu, Z. Wang, H. Zhang, K. Yang, K. C. Chou. Orbital angular momentum transition of light using a cylindrical vector beam. Opt. Lett., 43, 2146-2149(2018).

[34] M. Li, Y. Cai, S. Yan, Y. Liang, P. Zhang, B. Yao. Orbit-induced localized spin angular momentum in strong focusing of optical vectorial vortex beams. Phys. Rev. A, 97, 053842(2018).

[35] S. N. Khonina, A. V. Ustinov, S. A. Degtyarev. Inverse energy flux of focused radially polarized optical beams. Phys. Rev. A, 98, 043823(2018).

[36] S. Degtyarev, D. Savelyev, S. Khonina, N. Kazanskiy. Metasurfaces with continuous ridges for inverse energy flux generation. Opt. Express, 27, 15129-15135(2019).

[37] A. Yanai, M. Grajower, G. M. Lerman, M. Hentschel, H. Giessen, U. Levy. Near- and far-field properties of plasmonic oligomers under radially and azimuthally polarized light excitation. ACS Nano, 8, 4969-4974(2014).

[38] S. A. Syubaev, A. Y. Zhizhchenko, D. V. Pavlov, S. O. Gurbatov, E. V. Pustovalov, A. P. Porfirev, S. N. Khonina, S. A. Kulinich, J. B. B. Rayappan, S. I. Kudryashov, A. A. Kuchmizhak. Plasmonic nanolenses produced by cylindrical vector beam printing for sensing applications. Sci. Rep., 9, 19750(2019).

[39] S. A. Schulz, T. Machula, E. Karimi, R. W. Boyd. Integrated multi vector vortex beam generator. Opt. Express, 21, 16130-16141(2013).

[40] X. Ma, S. Zheng, Q. Chen, S. Tan, P. Zhang, Q. Lu, J. Wang, W. Guo. High-speed directly modulated cylindrical vector beam lasers. ACS Photon., 6, 3261-3270(2019).

[41] L. Feng, Y. Li, S. Wu, X. Guan, C. Yang, W. Tong, W. Li, J. Qiu, X. Hong, Y. Zuo, H. Guo, E. Chen, J. Wu. All-fiber generation of arbitrary cylindrical vector beams on the first-order Poincaré sphere. Photon. Res., 8, 1268-1277(2020).

[42] Y. Sebbag, U. Levy. Arbitrarily directed emission of integrated cylindrical vector vortex beams by geometric phase engineering. Opt. Lett., 45, 6779-6782(2020).

[43] K. Yonezawa, Y. Kozawa, S. Sato. Generation of a radially polarized laser beam by use of the birefringence of a c-cut Nd:YVO₄ crystal. Opt. Lett., 31, 2151-2153(2006).

[44] G. Machavariani, Y. Lumer, I. Moshe, A. Meir, S. Jackel, N. Davidson. Birefringence-induced bifocusing for selection of radially or azimuthally polarized laser modes. Appl. Opt., 46, 3304-3310(2007).

[45] K. Yonezawa, Y. Kozawa, S. Sato. Compact laser with radial polarization using birefringent laser medium. Jpn. J. Appl. Phys., 46, 5160-5163(2007).

[46] J. F. Bisson, J. Li, K. Ueda, Y. Senatsky. Radially polarized ring and arc beams of a neodymium laser with an intra-cavity axicon. Opt. Express, 14, 3304-3311(2006).

[47] Y. Kozawa, S. Sato. Generation of a radially polarized laser beam by use of a conical Brewster prism. Opt. Lett., 30, 3063-3065(2005).

[48] S. Vyas, Y. Kozawa, S. Sato. Generation of radially polarized Bessel–Gaussian beams from c-cut Nd:YVO₄ laser. Opt. Lett., 39, 1101-1104(2014).

[49] D. Naidoo, F. S. Roux, A. Dudley, I. Litvin, B. Piccirillo, L. Marrucci, A. Forbes. Controlled generation of higher-order Poincaré sphere beams from a laser. Nat. Photonics, 10, 327-332(2016).

[50] G. Machavariani, Y. Lumer, I. Moshe, A. Meir, S. Jackel. Efficient extracavity generation of radially and azimuthally polarized beams. Opt. Lett., 32, 1468-1470(2007).

[51] W. J. Lai, B. C. Lim, P. B. Phua, K. S. Tiaw, H. H. Teo, M. H. Hong. Generation of radially polarized beam with a segmented spiral varying retarder. Opt. Express, 16, 15694-15699(2008).

[52] J. Qi, H. Zhang, B. Pan, H. Deng, J. Yang, B. Shi, H. Wang, A. Du, W. Wang, X. Li. A succinct method to generate multi-type HCV beams with a spatial spiral varying retardation-plate. Europhys. Lett., 121, 54004(2018).

[53] K. J. Moh, X.-C. Yuan, J. Bu, D. K. Y. Low, R. E. Burge. Direct noninterference cylindrical vector beam generation applied in the femtosecond regime. Appl. Phys. Lett., 89, 251114(2006).

[54] S. N. Khonina, A. V. Ustinov, S. A. Fomchenkov, A. P. Porfirev. Formation of hybrid higher-order cylindrical vector beams using binary multi-sector phase plates. Sci. Rep., 8, 14320(2018).

[55] C. Loussert, E. Brasselet. Efficient scalar and vectorial singular beam shaping using homogeneous anisotropic media. Opt. Lett., 35, 7-9(2010).

[56] T. Fadeyeva, V. Shvedov, N. Shostka, C. Alexeyev, A. Volyar. Natural shaping of the cylindrically polarized beams. Opt. Lett., 35, 3787-3789(2010).

[57] S. N. Khonina, S. V. Karpeev, V. D. Paranin, A. A. Morozov. Polarization conversion under focusing of vortex laser beams along the axis of anisotropic crystals. Phys. Lett. A, 381, 2444-2455(2017).

[58] S. N. Khonina, A. P. Porfirev, N. L. Kazanskiy. Variable transformation of singular cylindrical vector beams using anisotropic crystals. Sci. Rep., 10, 5590(2020).

[59] S. N. Khonina, S. V. Karpeev. Generating inhomogeneously polarized higher-order laser beams by use of diffractive optical elements. J. Opt. Soc. Am. A, 28, 2115-2123(2011).

[60] S. N. Khonina, S. V. Karpeev, A. P. Porfirev. Sector sandwich structure: an easy-to-manufacture way towards complex vector beam generation. Opt. Express, 28, 27628-27643(2020).

[61] Z. Bomzon, G. Biener, V. Kleiner, E. Hasman. Radially and azimuthally polarized beams generated by space-variant dielectric subwavelength gratings. Opt. Lett., 27, 285-287(2002).

[62] G. M. Lerman, U. Levy. Generation of a radially polarized light beam using space-variant subwavelength gratings at 1064 nm. Opt. Lett., 33, 2782-2784(2008).

[63] C. Zhu, Q. Jiao, X. Tan, W. Wang, . Design of a subwavelength all-metal grating for generating azimuthally polarized beams based on modified particle swarm optimization. Appl. Opt., 58, 4052-4058(2019).

[64] P. Yu, S. Chen, J. Li, H. Cheng, Z. Li, W. Liu, B. Xie, Z. Liu, J. Tian. Generation of vector beams with arbitrary spatial variation of phase and linear polarization using plasmonic metasurfaces. Opt. Lett., 40, 3229-3232(2015).

[65] F. Yue, D. Wen, J. Xin, B. D. Gerardot, J. Li, X. Chen. Vector vortex beam generation with a single plasmonic metasurface. ACS Photon., 3, 1558-1563(2016).

[66] Y. Liu, X. Ling, X. Yi, X. Zhou, H. Luo, S. Wen. Realization of polarization evolution on higher-order Poincaré sphere with metasurface. Appl. Phys. Lett., 104, 191110(2014).

[67] W. Shu, Y. Liu, Y. Ke, X. Ling, Z. Liu, B. Huang, H. Luo, X. Yin. Propagation model for vector beams generated by metasurfaces. Opt. Express, 24, 21177-21189(2016).

[68] V. G. Niziev, R. S. Chang, A. V. Nesterov. Generation of inhomogeneously polarized laser beams by use of a Sagnac interferometer. Appl. Opt., 45, 8393-8399(2006).

[69] S. Liu, P. Li, T. Peng, J. Zhao. Generation of arbitrary spatially variant polarization beams with a trapezoid Sagnac interferometer. Opt. Express, 20, 21715-21721(2012).

[70] P. Li, Y. Zhang, S. Liu, C. Ma, L. Han, H. Cheng, J. Zhao. Generation of perfect vectorial vortex beams. Opt. Lett., 41, 2205-2208(2016).

[71] J. Jia, Z. Chang, H. Yang, Q. Liu, F. Wang, H. Gao, F. Li, P. Zhang. Mode sorter designed for (de)multiplexing vector vortex modes. Appl. Opt., 58, 7094-7099(2019).

[72] X. Xu, Y. Zhou, Y.-S. Yuan, J. Wang, H.-F. Xu, J. Qu. Generation of cylindrical and elliptical symmetrical vector beam on the Mach–Zehnder interferometer. AIP Adv., 8, 125007(2018).

[73] C. Chen, Y. Zhang, L. Ma, Y. Zhang, Z. Li, R. Zhang, X. Zeng, Z. Zhan, C. He, X. Ren, C. Cheng, C. Liu. Flexible generation of higher-order Poincaré beams with high efficiency by manipulating the two eigenstates of polarized optical vortices. Opt. Express, 28, 10618-10632(2020).

[74] S. C. Tidwell, D. H. Ford, W. D. Kimura. Generating radially polarized beams interferometrically. Appl. Opt., 29, 2234-2239(1990).

[75] N. Passilly, R. de Saint Denis, K. Aït-Ameur, F. Treussart, R. Hierle, J.-F. Roch. Simple interferometric technique for generation of a radially polarized light beam. J. Opt. Soc. Am. A, 22, 984-991(2005).

[76] X.-L. Wang, J. Ding, W.-J. Ni, C.-S. Guo, H.-T. Wang. Generation of arbitrary vector beams with a spatial light modulator and a common path interferometric arrangement. Opt. Lett., 32, 3549-3551(2007).

[77] Z. Chen, T. Zeng, B. Qian, J. Ding. Complete shaping of optical vector beams. Opt. Express, 23, 17701-17710(2015).

[78] J. Mendoza-Hernández, M. F. Ferrer-Garcia, J. A. Rojas-Santana, D. Lopez-Mago. Cylindrical vector beam generator using a two-element interferometer. Opt. Express, 27, 31810-31819(2019).

[79] W. Han, Y. Yang, W. Cheng, Q. Zhan. Vectorial optical field generator for the creation of arbitrarily complex fields. Opt. Express, 21, 20692-20706(2013).

[80] S. Fu, C. Gao, T. Wang, S. Zhang, Y. Zhai. Simultaneous generation of multiple perfect polarization vortices with selective spatial states in various diffraction orders. Opt. Lett., 41, 5454-5457(2016).

[81] S. Fu, T. Wang, C. Gao. Generating perfect polarization vortices through encoding liquid-crystal display devices. Appl. Opt., 55, 6501-6505(2016).

[82] S. Fu, C. Gao, T. Wang, Y. Zhai, C. Yin. Anisotropic polarization modulation for the production of arbitrary Poincaré beams. J. Opt. Soc. Am. B, 35, 1-7(2018).

[83] M. Bashkansky, D. Park, F. K. Fatemi. Azimuthally and radially polarized light with a nematic SLM. Opt. Express, 18, 212-217(2010).

[84] J. Qi, W. Sun, J. Liao, Y. Nie, X. Wang, J. Zhang, X. Liu, H. Jia, M. Lu, S. Chen, J. Liu, J. Yang, J. Tan, X. Li. Generation and analysis of both in-phase and out-phase radially polarized femtosecond-pulse beam. Opt. Eng., 45, 024201(2013).

[85] Y. Zhang, P. Li, C. Ma, S. Liu, H. Cheng, L. Han, J. Zhao. Efficient generation of vector beams by calibrating the phase response of a spatial light modulator. Appl. Opt., 56, 4956-4960(2017).

[86] S. Liu, S. Qi, Y. Zhang, P. Li, D. Wu, L. Han, J. Zhao. Highly efficient generation of arbitrary vector beams with tunable polarization, phase, and amplitude. Photon. Res., 6, 228-233(2018).

[87] Y. Zhou, X. Li, Y. Cai, Y. Zhang, S. Yan, M. Zhou, M. Li, B. Yao. Compact optical module to generate arbitrary vector vortex beams. Appl. Opt., 59, 8932-8938(2020).

[88] S. N. Khonina, A. V. Ustinov, A. P. Porfirev. Vector Lissajous laser beams. Opt. Lett., 45, 4112-4115(2020).

[89] M. Rashid, O. M. Maragò, P. H. Jones. Focusing of high order cylindrical vector beams. J. Opt. A, 11, 065204(2009).

[90] S. N. Khonina. Vortex beams with high-order cylindrical polarization: features of focal distributions. Appl. Phys. B, 125, 100(2019).

[91] L. Marrucci, C. Manzo, D. Paparo. Pancharatnam-Berry phase optical elements for wave front shaping in the visible domain: switchable helical mode generation. Appl. Phys. Lett., 88, 221102(2006).

[92] E. Karimi, B. Piccirillo, E. Nagali, L. Marrucci, E. Santamato. Efficient generation and sorting of orbital angular momentum eigenmodes of light by thermally tuned q-plates. Appl. Phys. Lett., 94, 231124(2009).

[93] S. Slussarenko, A. Murauski, T. Du, V. Chigrinov, L. Marrucci, E. Santamato. Tunable liquid crystal q-plates with arbitrary topological charge. Opt. Express, 19, 4085-4090(2011).

[94] A. Rubano, F. Cardano, B. Piccirillo, L. Marrucci. Q-plate technology: a progress review [Invited]. J. Opt. Soc. Am. B, 36, D70-D87(2019).

[95] M. Beresna, M. Gecevicius, P. G. Kazansky, T. Gertus. Radially polarized optical vortex converter created by femtosecond laser nanostructuring of glass. Appl. Phys. Lett., 98, 201101(2011).

[96] M. Beresna, M. Gecevičius, P. G. Kazansky. Polarization sensitive elements fabricated by femtosecond laser nanostructuring of glass [Invited]. Opt. Mater. Express, 1, 783-795(2011).

[97] D. Wu, Y. Li, W. Jia, J. Zhou, Y. Zhao, Y. Fu, J. Wang. Generation of arbitrary vector vortex beams based on the dual-modulation method. Appl. Opt., 58, 1508-1513(2019).

[98] L. Marrucci, C. Manzo, D. Paparo. Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media. Phys. Rev. Lett., 96, 163905(2006).

[99] W. Shu, X. Ling, X. Fu, Y. Liu, Y. Ke, H. Luo. Polarization evolution of vector beams generated by q-plates. Photon. Res., 5, 64-72(2017).