[1] Snitzer E. Cylindrical dielectric waveguide modes[J]. Journal of the Optical Society of America, 1961, 51(5): 491-498.

[2] Pohl D. Operation of a ruby laser in the purely transverse electric mode TE01[J]. Applied Physics Letters, 1972, 20(7): 266-267.

[3] Mushiake Y, Matsumura K, Nakajima N. Generation of radially polarized optical beam mode by laser oscillation[J]. Proceedings of the IEEE, 1972, 60(9): 1107-1109.

[4] Zhan Q W. Cylindrical vector beams: From mathematical concepts to applications[J]. Advances in Optics and Photonics, 2009, 1(1): 1-57.

[5] Marhic M E, Garmire E. Low-order TE0q operation of a CO2 laser for transmission through circular metallic waveguides[J]. Applied Physics Letters, 1981, 38(10): 743-745.

[6] Tidwell S C, Ford D H, Kimura W D. Generating radially polarized beams interferometrically[J]. Applied Optics, 1990, 29(15): 2234-2239.

[7] Churin E G, Hoβfeld J, Tschudi T. Polarization configurations with singular point formed by computer generated holograms[J]. Optics Communications, 1993, 99(1/2): 13-17.

[8] Tidwell S C, Kim G H, Kimura W D. Efficient radially polarized laser beam generation with a double interferometer[J]. Applied Optics, 1993, 32(27): 5222-5229.

[9] Stalder M, Schadt M. Linearly polarized light with axial symmetry generated by liquid-crystal polarization converters[J]. Optics Letters, 1996, 21(23): 1948-1950.

[10] Jordan R H, Hall D G. Free-space azimuthal paraxial wave equation: The azimuthal Bessel-Gauss beam solution[J]. Optics Letters, 1994, 19(7): 427-429.

[11] Greene P L, Hall D G. Diffraction characteristics of the azimuthal Bessel-Gauss beam[J]. Journal of the Optical Society of America A, 1996, 13(5): 962-966.

[12] Hall D G. Vector-beam solutions of Maxwell’s wave equation[J]. Optics Letters, 1996, 21(1): 9-11.

[13] Greene P L, Hall D G. Focal shift in vector beams[J]. Optics Express, 1999, 4(10): 411-419.

[14] Youngworth K S, Brown T G. Focusing of high numerical aperture cylindrical-vector beams[J]. Optics Express, 2000, 7(2): 77-87.

[15] Richards B, Wolf E. Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system[J]. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 1959, 253(1274): 358-379.

[16] Dorn R, Quabis S, Leuchs G. Sharper focus for a radially polarized light beam[J]. Physical Review Letters, 2003, 91(23): 233901.

[17] Hao X, Kuang C F, Wang T T, et al. Phase encoding for sharper focus of the azimuthally polarized beam[J]. Optics Letters, 2010, 35(23): 3928-3930.

[18] Wang H F, Shi L P, Lukyanchuk B, et al. Creation of a needle of longitudinally polarized light in vacuum using binary optics[J]. Nature Photonics, 2008, 2(8): 501-505.

[19] Kozawa Y, Sato S. Focusing property of a double-ring-shaped radially polarized beam[J]. Optics Letters, 2006, 31(6): 820-822.

[20] Wang X L, Ding J P, Qin J Q, et al. Configurable three-dimensional optical cage generated from cylindrical vector beams[J]. Optics Communications, 2009, 282(17): 3421-3425.

[21] Zhao Y Q, Zhan Q W, Zhang Y L, et al. Creation of a three-dimensional optical chain for controllable particle delivery[J]. Optics Letters, 2005, 30(8): 848-850.

[22] Gabriel C, Aiello A, Zhong W, et al. Entangling different degrees of freedom by quadrature squeezing cylindrically polarized modes[J]. Physical Review Letters, 2011, 106(6): 060502.

[23] Varin C, Piche M. Acceleration of ultra-relativistic electrons using high-intensity TM01 laser beams[J]. Applied Physics B, 2002, 74(1): s83-s88.

[24] Novotny L, Beversluis M R, Youngworth K S, et al. Longitudinal field modes probed by single molecules[J]. Physical Review Letters, 2001, 86(23): 5251-5254.

[25] Ciattoni A, Crosignani B, Di Porto P, et al. Azimuthally polarized spatial dark solitons: Exact solutions of Maxwell's equations in a Kerr medium[J]. Physical Review Letters, 2005, 94(7): 073902.

[26] Meier M, Romano V, Feurer T. Material processing with pulsed radially and azimuthally polarized laser radiation[J]. Applied Physics A, 2007, 86(3): 329-334.

[27] Lou K, Qian S X, Wang X L, et al. Two-dimensional microstructures induced by femtosecond vector light fields on silicon[J]. Optics Express, 2012, 20(1): 120-127.

[28] Kawauchi H, Yonezawa K, Kozawa Y, et al. Calculation of optical trapping forces on a dielectric sphere in the ray optics regime produced by a radially polarized laser beam[J]. Optics Letters, 2007, 32(13): 1839-1841.

[29] Zhan Q W. Trapping metallic Rayleigh particles with radial polarization[J]. Optics Express, 2004, 12(15): 3377-3382.

[30] Wang X L, Li Y N, Chen J, et al. A new type of vector fields with hybrid states of polarization[J]. Optics Express, 2010, 18(10): 10786-10795.

[31] Lerman G M, Stern L, Levy U. Generation and tight focusing of hybridly polarized vector beams[J]. Optics Express, 2010, 18(26): 27650-27657.

[32] Beckley A M, Brown T G, Alonso M A. Full Poincare beams[J]. Optics Express, 2010, 18(10): 10777-10785.

[33] Beckley A M, Brown T G, Alonso M A. Full Poincare beams II: Partial polarization[J]. Optics Express, 2012, 20(9): 9357-9362.

[34] Milione G, Sztul H I, Nolan D A, et al. Higher-order Poincare sphere, Stokes parameters, and the angular momentum of light[J]. Physical Review Letters, 2011, 107(5): 053601.

[35] Yi X N, Liu Y C, Ling X H, et al. Hybrid-order Poincare sphere[J]. Physical Review A, 2015, 91(2): 023801.

[36] Ren Z C, Kong L J, Li S M, et al. Generalized Poincare sphere[J]. Optics Express, 2015, 23(20): 26586-26595.

[37] Lou K, Qian S X, Ren Z C, et al. Femtosecond laser processing by using patterned vector optical fields[J]. Scientific Reports, 2013, 3: 2281.

[38] Cai M Q, Tu C H, Zhang H H, et al. Subwavelength multiple focal spots produced by tight focusing the patterned vector optical fields[J]. Optics Express, 2013, 21(25): 31469-31482.

[39] Pan Y, Gao X Z, Cai M Q, et al. Fractal vector optical fields[J]. Optics Letters, 2016, 41(14): 3161-3164.

[40] Gao X Z, Pan Y, Zhao M D, et al. Focusing behavior of the fractal vector optical fields designed by fractal lattice growth model[J]. Optics Express, 2018, 26(2): 1597-1614.

[41] Yu R L, Xin Y, Zhao Q, et al. Array of polarization singularities in interference of three waves[J]. Journal of the Optical Society of America A, 2013, 30(12): 2556-2560.

[42] Pan Y, Li S M, Mao L, et al. Vector optical fields with polarization distributions similar to electric and magnetic field lines[J]. Optics Express, 2013, 21(13): 16200-16209.

[43] Han L, Liu S, Li P, et al. Managing focal fields of vector beams with multiple polarization singularities[J]. Applied Optics, 2016, 55(32): 9049-9053.

[44] Pan Y, Li Y N, Ren Z C, et al. Parabolic-symmetry vector optical fields and their tightly focusing properties[J]. Physical Review A, 2014, 89(3): 035801.

[45] Pan Y, Li Y N, Li S M, et al. Elliptic-symmetry vector optical fields[J]. Optics Express, 2014, 22(16): 19302-19313.

[46] Pan Y, Li Y N, Li S M, et al. Vector optical fields with bipolar symmetry of linear polarization[J]. Optics Letters, 2013, 38(18): 3700-3703.

[47] Gao X Z, Pan Y, Cai M Q, et al. Hyperbolic-symmetry vector fields[J]. Optics Express, 2015, 23(25): 32238-32252.

[48] Chen H, Zheng Z, Zhang B F, et al. Polarization structuring of focused field through polarization-only modulation of incident beam[J]. Optics Letters, 2010, 35(16): 2825-2827.

[49] Chen Z Z, Zeng T T, Ding J P. Reverse engineering approach to focus shaping[J]. Optics Letters, 2016, 41(9): 1929-1932.

[50] Lerman G M, Levy U. Tight focusing of spatially variant vector optical fields with elliptical symmetry of linear polarization[J]. Optics Letters, 2007, 32(15): 2194-2196.

[51] Lerman G M, Lilach Y, Levy U. Demonstration of spatially inhomogeneous vector beams with elliptical symmetry[J]. Optics Letters, 2009, 34(11): 1669-1671.

[52] Wang X L, Ding J P, Ni W J, et al. Generation of arbitrary vector beams with a spatial light modulator and a common path interferometric arrangement[J]. Optics Letters, 2007, 32(24): 3549-3551.

[53] Couairon A, Mysyrowicz A. Femtosecond filamentation in transparent media[J]. Physics Reports, 2007, 441: 47-189.

[54] Bespalov V I, Talanov V I. Filamentary structure of light beams in nonlinear liquids[J]. ZhETF Pisma Redaktsiiu, 1966, 3(11): 471-476.

[55] Li S M, Li Y N, Wang X L, et al. Taming the collapse of optical fields[J]. Scientific Reports, 2012, 2: 1007.

[56] Gao X Z, Pan Y, Zhang G L, et al. Redistributing the energy flow of tightly focused ellipticity-variant vector optical fields[J]. Photonics Research, 2017, 5(6): 640-648.

[57] Xu D F, Gu B, Rui G H, et al. Generation of arbitrary vector fields based on a pair of orthogonal elliptically polarized base vectors[J]. Optics Express, 2016, 24(4): 4177-4186.

[58] Gu B, Wen B, Rui G H, et al. Nonlinear polarization evolution of hybridly polarized vector beams through isotropic Kerr nonlinearities[J]. Optics Express, 2016, 24(22): 25867-25875.

[59] Chen R P, Chew K H, Dai C Q, et al. Optical spin-to-orbital angular momentum conversion in the near field of a highly nonparaxial optical field with hybrid states of polarization[J]. Physical Review A, 2017, 96(5): 053862.

[60] Chen R P, Zhong L X, Chew K H, et al. Effect of a spiral phase on a vector optical field with hybrid polarization states[J]. Journal of Optics, 2015, 17(6): 065605.

[61] Chen R P, Chew K H, Zhou G Q, et al. Vectorial effect of hybrid polarization states on the collapse dynamics of a structured optical field[J]. Optics Express, 2016, 24(24): 28143-28153.

[62] Hu H W, Xiao P P. The tight focusing properties of spatial hybrid polarization vector beam[J]. Optik - International Journal for Light and Electron Optics, 2013, 124(16): 2406-2410.

[63] Gu B, Pan Y, Rui G H, et al. Polarization evolution characteristics of focused hybridly polarized vector fields[J]. Applied Physics B, 2014, 117(3): 915-926.

[64] Li S M, Ren Z C, Kong L J, et al. Unveiling stability of multiple filamentation caused by axial symmetry breaking of polarization[J]. Photonics Research, 2016, 4(5): B29-B34.

[65] Si Y, Kong L J, Zhang Y, et al. Spatial-variant geometric phase of hybrid-polarized vector optical fields[J]. Chinese Physics Letters, 2017, 34(4): 044204.

[66] Chen R P, Gao T Y, Chew K H, et al. Near-field characteristics of highly non-paraxial subwavelength optical fields with hybrid states of polarization[J]. Chinese Physics B, 2017, 26(10): 104202.

[67] Allen L, Beijersbergen M W. Spreeuw R J C, et al. Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes[J]. Physical Review A, 1992, 45(11): 8185-8189.

[68] Grier D G. A revolution in optical manipulation[J]. Nature, 2003, 424(6950): 810-816.

[69] Molina-Terriza G, Torres J P, Torner L. Twisted photons[J]. Nature Physics, 2007, 3(5): 305-310.

[70] Wang X L, Chen J, Li Y N, et al. Optical orbital angular momentum from the curl of polarization[J]. Physical Review Letters, 2010, 105(25): 253602.

[71] Yan S H, Yao B L, Lei M. Comment on “optical orbital angular momentum from the curl of polarization”[J]. Physical Review Letters, 2011, 106(18): 189301.

[72] Wang X L, Chen J, Li Y N, et al. A reply to the comment on “optical orbital angular momentum from the curl of polarization”[J]. Physical Review Letters, 2011, 106(18): 189302.

[73] Hu K L, Chen Z Y, Pu J X. Tight focusing properties of hybridly polarized vector beams[J]. Journal of the Optical Society of America A, 2012, 29(6): 1099-1104.

[74] Li J, Wu P H, Chang L P. Analysis of the far-field characteristics of hybridly polarized vector beams from the vectorial structure[J]. Journal of Quantitative Spectroscopy and Radiative Transfer, 2016, 169: 127-134.

[75] Ling X H, Yi X N, Dai Z P, et al. Characterization and manipulation of full Poincare beams on the hybrid Poincare sphere[J]. Journal of the Optical Society of America B, 2016, 33(11): 2172-2176.

[76] Wei C, Wu D, Liang C H, et al. Experimental verification of significant reduction of turbulence-induced scintillation in a full Poincare beam[J]. Optics Express, 2015, 23(19): 24331-24341.

[77] Zhang L, Qiu X D, Li F S, et al. Second harmonic generation with full Poincare beams[J]. Optics Express, 2018, 26(9): 11678-11684.

[78] Pan Y, Ren Z C, Qian S X, et al. Uniformly elliptically-polarized vector optical fields[J]. Journal of Optics, 2015, 17(3): 035616.

[79] Milione G, Evans S, Nolan D A, et al. Higher order Pancharatnam-Berry phase and the angular momentum of light[J]. Physical Review Letters, 2012, 108(19): 190401.

[80] Liu Y C, Ling X H, Yi X N, et al. Realization of polarization evolution on higher-order Poincare sphere with metasurface[J]. Applied Physics Letters, 2014, 104(19): 191110.

[81] Naidoo D, Roux F S, Dudley A, et al. Controlled generation of higher-order Poincare sphere beams from a laser[J]. Nature Photonics, 2016, 10(5): 327-332.

[82] Liu Z X, Liu Y Y, Ke Y G, et al. Generation of arbitrary vector vortex beams on hybrid-order Poincare sphere[J]. Photonics Research, 2017, 5(1): 15-21.

[83] Liu Y Y, Liu Z X, Zhou J X, et al. Measurements of Pancharatnam-Berry phase in mode transfor-mations on hybrid-order Poincare sphere[J]. Optics Letters, 2017, 42(17): 3447-3450.

[84] Pan Y, Gao X Z, Ren Z C, et al. Arbitrarily tunable orbital angular momentum of photons[J]. Scientific Reports, 2016, 6: 29212.

[85] Man Z S, Bai Z D, Li J J, et al. Focus shaping by tailoring arbitrary hybrid polarization states that have a combination of orthogonal linear polarization bases[J]. Applied Optics, 2018, 57(12): 3047-3055.

[86] Mu T K, Chen Z Y, Pacheco S, et al. Generation of a controllable multifocal array from a modulated azimuthally polarized beam[J]. Optics Letters, 2016, 41(2): 261-264.

[87] Zhu L W, Sun M Y, Zhang D W, et al. Multifocal array with controllable polarization in each focal spot[J]. Optics Express, 2015, 23(19): 24688-24698.

[88] Zeng T T, Chang C L, Chen Z Z, et al. Three-dimensional vectorial multifocal arrays created by pseudo-period encoding[J]. Journal of Optics, 2018, 20(6): 065605.

[89] Cai M Q, Li P P, Feng D, et al. Microstructures fabricated by dynamically controlled femtosecond patterned vector optical fields[J]. Optics Letters, 2016, 41(7): 1474-1477.

[90] Berry M. Making waves in physics[J]. Nature, 2000, 403(6765): 21.

[91] Soskin M S, Vasnetsov M V. Singular optics[J]. Progress in Optics, 2001, 42(4): 219-276.

[92] Freund I. Polarization singularity indices in Gaussian laser beams[J]. Optics Communications, 2002, 201: 251-270.

[93] Flossmann F, Schwarz U T, Maier M, et al. Polarization singularities from unfolding an optical vortex through a birefringent crystal[J]. Physical Review Letters, 2005, 95(25): 253901.

[94] Bliokh K Y, Niv A, Kleiner V, et al. Singular polarimetry: evolution of polarization singularities in electromagnetic waves propagating in a weakly anisotropic medium[J]. Optics Express, 2008, 16(2): 695-709.

[95] Pal S K, Senthilkumaran P. Lattice of C points at intensity nulls[J]. Optics Letters, 2018, 43(6): 1259-1262.

[96] Pal S K, Senthilkumaran P. Generation of V-point polarization singularity lattices[J]. Optics Express, 2017, 25(16): 19326-19331.

[97] Pal S K, Senthilkumaran P. Cultivation of lemon fields[J]. Optics Express, 2016, 24(24): 28008-28013.

[98] Pal S K, Senthilkumaran P. C-point and V-point singularity lattice formation and index sign conversion methods[J]. Optics Communications, 2017, 393: 156-168.

[99] Schoonover R W, Visser T D. Creating polarization singularities with an N-pinhole interferometer[J]. Physical Review A, 2009, 79(4): 043809.

[100] Zhang W, Liu S, Li P, et al. Controlling the polarization singularities of the focused azimuthally polarized beams[J]. Optics Express, 2013, 21(1): 974-983.

[101] Freund I, Soskin M S, Mokhun A I. Elliptic critical points in paraxial optical fields[J]. Optics Communications, 2002, 208: 223-253.

[102] Kiselev A D. Singularities in polarization resolved angular patterns: Transmittance of nematic liquid crystal cells[J]. Journal of Physics: Condensed Matter, 2007, 19(24): 246102.

[103] Felde C V, Chernyshov A A, Bogatyryova G V, et al. Polarization singularities in partially coherent combined beams[J]. JETP Letters, 2008, 88(7): 418-422.

[104] Vyas S, Kozawa Y, Sato S. Polarization singularities in superposition of vector beams[J]. Optics Express, 2013, 21(7): 8972-8986.

[105] Chang C L, Gao Y, Xia J P, et al. Shaping of optical vector beams in three dimensions[J]. Optics Letters, 2017, 42(19): 3884-3887.

[106] Chen H, Hao J J, Zhang B F, et al. Generation of vector beam with space-variant distribution of both polarization and phase[J]. Optics Letters, 2011, 36(16): 3179-3181.

[107] Zhang G L, Gao X Z, Pan Y, et al. Inverse method to engineer uniform-intensity focal fields with arbitrary shape[J]. Optics Express, 2018, 26(13): 16782-16796.

[108] Han W, Yang Y F, Cheng W, et al. Vectorial optical field generator for the creation of arbitrarily complex fields[J]. Optics Express, 2013, 21(18): 20692-20706.

[109] Yu Z L, Chen H, Chen Z Z, et al. Simultaneous tailoring of complete polarization, amplitude and phase of vector beams[J]. Optics Communications, 2015, 345: 135-140.

[110] Chen Z Z, Zeng T T, Qian B J, et al. Complete shaping of optical vector beams[J]. Optics Express, 2015, 23(14): 17701-17710.

[111] Rong Z Y, Han Y J, Wang S Z, et al. Generation of arbitrary vector beams with cascaded liquid crystal spatial light modulators[J]. Optics Express, 2014, 22(2): 1636-1644.