[1] Born M, Wolf E[M]. Principles of optics(1999).

[2] Bykov V P, Vainshtein L A. Geometric optics of open resonators[J]. Soviet Physics JETP, 20, 338-344(1965).

[3] Jiang K L, Han X G, Ren K F. Scattering of a Gaussian beam by an elliptical cylinder using the vectorial complex ray model[J]. Journal of the Optical Society of America A, 30, 1548-1556(2013).

[4] Yang P, Liou K N. Light scattering by hexagonal ice crystals: solutions by a ray-by-ray integration algorithm[J]. Journal of the Optical Society of America A, 14, 2278-2289(1997). http://www.opticsinfobase.org/abstract.cfm?uri=josaa-14-9-2278

[5] Li X Z. Geometrical-optics approximation of light scattering by particles Xi'an:[D]. Xidian University(2009).

[6] Arnaud J. Representation of Gaussian beams by complex rays[J]. Applied Optics, 24, 538-543(1985). http://www.ncbi.nlm.nih.gov/pubmed/18216983

[7] Zhang L W. Simulation and analysis of nonlinear effect in high power laser system based on ray-tracing[D]. Hangzhou: Zhejiang University(2014).

[8] Zhu J. Study of characterizing optical free-form surface and ray-tracing model[D]. Nanjing: Nanjing University of Science and Technology(2012).

[9] Alonso M A, Bandres M A. Generation of nonparaxial accelerating fields through mirrors I: two dimensions[J]. Optics Express, 22, 7124-7132(2014). http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-22-12-14738

[10] Alonso M A, Bandres M A. Generation of nonparaxial accelerating fields through mirrors II: three dimensions[J]. Optics Express, 22, 14738-14749(2014). http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-22-12-14738

[11] McNamara D A, Pistorius C W I, Malherbe J A G. Introduction to the uniform geometrical theory of diffraction[M]. London: Artech House(1990).

[12] Vainshtein L A. Open resonators with spherical mirrors[J]. Soviet Physics JETP, 18, 471-479(1964).

[13] 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, 45, 8185-8189(1992).

[14] Durnin J, Miceli J J, Eberly J H. Diffraction-free beams[J]. Physical Review Letters, 58, 1499-1501(1987).

[15] Gutiérrez-Vega J C, Bandres M A. Helmholtz-Gauss waves[J]. Journal of the Optical Society of America A, 22, 289-298(2005).

[16] Berry M V, Balazs N L. Nonspreading wave packets[J]. American Journal of Physics, 47, 264-267(1979).

[17] Siviloglou G A, Broky J, Dogariu A et al. Observation of accelerating airy beams[J]. Physical Review Letters, 99, 213901(2007). http://europepmc.org/abstract/MED/18233219

[18] Zhang P, Hu Y, Li T C et al. Nonparaxial Mathieu and Weber accelerating beams[J]. Physical Review Letters, 109, 193901(2012). http://www.ncbi.nlm.nih.gov/pubmed/23215384

[19] Bandres M A, Alonso M A, Kaminer I et al. Three-dimensional accelerating electromagnetic waves[J]. Optics Express, 21, 13917-13929(2013). http://www.ncbi.nlm.nih.gov/pubmed/23787581

[20] Chen Z G, Xu J J, Hu Y et al. Control and novel applications of self-accelerating beams[J]. Acta Optica Sinica, 36, 1026009(2016).

[21] Efremidis N K, Christodoulides D N. Abruptly autofocusing waves[J]. Optics Letters, 35, 4045-4047(2010).

[22] Froehly L, Courvoisier F, Mathis A et al. Arbitrary accelerating micron-scale caustic beams in two and three dimensions[J]. Optics Express, 19, 16455-16465(2011). http://www.onacademic.com/detail/journal_1000035235807510_6570.html

[23] Chremmos I D, Chen Z G, Christodoulides D N et al. Abruptly autofocusing and autodefocusing optical beams with arbitrary caustics[J]. Physical Review A, 85, 023828(2012). http://adsabs.harvard.edu/abs/2012PhRvA..85b3828C

[24] Davis J A, Cottrell D M, Sand D. Abruptly autofocusing vortex beams[J]. Optics Express, 20, 13302-13310(2012). http://www.ncbi.nlm.nih.gov/pubmed/22714358

[25] Penciu R S, Makris K G, Efremidis N K. Nonparaxial abruptly autofocusing beams[J]. Optics Letters, 41, 1042-1045(2016).

[26] Willner A E, Ren Y X, Xie G D et al. Recent advances in high-capacity free-space optical and radio-frequency communications using orbital angular momentum multiplexing[J]. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 375, 20150439(2017). http://europepmc.org/abstract/MED/28069770

[27] Wang J, Liu J, Zhao Y F. Research progress of structured light coding/decoding communications[J]. Acta Optica Sinica, 39, 0126013(2019).

[28] Simpson N B, Dholakia K, Allen L et al. Mechanical equivalence of spin and orbital angular momentum of light: an optical spanner[J]. Optics Letters, 22, 52-54(1997). http://europepmc.org/abstract/MED/18183100

[29] Fahrbach F O, Simon P, Rohrbach A. Microscopy with self-reconstructing beams[J]. Nature Photonics, 4, 780-785(2010). http://www.nature.com/nphoton/journal/v4/n11/abs/nphoton.2010.204.html

[30] Garcés-Chávez V. McGloin D, Melville H, et al. Simultaneous micromanipulation in multiple planes using a self-reconstructing light beam[J]. Nature, 419, 145-147(2002).

[31] Liang Y S, Yao B L, Lei M et al. Optical micro-manipulation based on spatial modulation of optical fields[J]. Acta Optica Sinica, 36, 1026003(2016).

[32] Olarte O E, Andilla J, Gualda E J et al. Light-sheet microscopy: a tutorial[J]. Advances in Optics and Photonics, 10, 111-179(2018). http://www.onacademic.com/detail/journal_1000040491281910_7a32.html

[33] Li R F, Shi K B. High spatiotemporal imaging based on optical field engineering[J]. Acta Optica Sinica, 39, 0126012(2019).

[34] Baumgartl J, Mazilu M, Dholakia K. Optically mediated particle clearing using Airy wavepackets[J]. Nature Photonics, 2, 675-678(2008). http://www.nature.com/nphoton/journal/v2/n11/abs/nphoton.2008.201.html

[35] Baumgartl J, Hannappel G M, Stevenson D J et al. Optical redistribution of microparticles and cells between microwells[J]. Lab on a Chip, 9, 1334-1336(2009). http://www.ncbi.nlm.nih.gov/pubmed/19417896

[36] Moffitt J R, Chemla Y R, Smith S B et al. Recent advances in optical tweezers[J]. Annual Review of Biochemistry, 77, 205-228(2008). http://www.ncbi.nlm.nih.gov/pubmed/18307407

[37] Woerdemann M, Alpmann C, Esseling M et al. Advanced optical trapping by complex beam shaping[J]. Laser & Photonics Reviews, 7, 839-854(2013). http://onlinelibrary.wiley.com/doi/10.1002/lpor.201200058/full

[38] Papazoglou D G, Efremidis N K, Christodoulides D N et al. Observation of abruptly autofocusing waves[J]. Optics Letters, 36, 1842-1844(2011). http://europepmc.org/abstract/MED/21593909

[39] Zhang P, Prakash J, Zhang Z et al. Trapping and guiding microparticles with morphing autofocusing Airy beams[J]. Optics Letters, 36, 2883-2885(2011). http://europepmc.org/abstract/MED/21808346

[40] Chen J, Zhan Q W. Tailoring laser focal fields with vectorial optical fields[J]. Acta Optica Sinica, 39, 0126002(2019).

[41] Pan Y, Ding J P, Wang H T. Manipulation on novel vector optical fields: introduction, advances and applications[J]. Acta Optica Sinica, 39, 0126003(2019).

[42] Liu S, Li P, Zhang Y et al. Transmission and control of polarization modulation light filed in free space[J]. Acta Optica Sinica, 36, 1026001(2016).

[43] Liu H L, Hu Z H, Xia J et al. Generation and applications of non-diffraction beam[J]. Acta Physica Sinica, 67, 214204(2018).

[44] Yu X H, Yao B L, Lei M et al. Generation and three-dimensional characterization of complex nondiffracting optical beams[J]. Acta Physica Sinica, 64, 244203(2015).

[45] Sidick E, Collins S D, Knoesen A. Trapping forces in a multiple-beam fiber-optic trap[J]. Applied Optics, 36, 6423-6433(1997). http://www.ncbi.nlm.nih.gov/pubmed/18259500

[46] Kline M. An asymptotic solution of Maxwell's equations[J]. Communications on Pure and Applied Mathematics, 4, 225-262(1951).

[47] Luneburg R K[M]. Mathematical theory of optics(1966).

[48] Keller J B, Streifer W. Complex rays with an application to Gaussian beams[J]. Journal of the Optical Society of America, 61, 40-43(1971).

[49] Deschamps G A. Gaussian beam as a bundle of complex rays[J]. Electronics Letters, 7, 684-685(1971).

[50] Kravtsov Y A, Forbes G W, Asatryan A A. I theory and applications of complex rays[M]. ∥Wolf E. Progress in optics. New York: Elsevier, 39, 1-62(1999).

[51] Herloski R, Marshall S, Antos R. Gaussian beam ray-equivalent modeling and optical design[J]. Applied Optics, 22, 1168-1174(1983).

[52] Landesman B T, Barrett H H. Gaussian amplitude functions that are exact solutions to the scalar Helmholtz equation[J]. Journal of the Optical Society of America A, 5, 1610-1619(1988).

[53] Landesman B T. Geometrical representation of the fundamental mode of a Gaussian beam in oblate spheroidal coordinates[J]. Journal of the Optical Society of America A, 6, 5-17(1989).

[54] Tycho A, Jørgensen T M, Yura H T et al. Derivation of a Monte Carlo method for modeling heterodyne detection in optical coherence tomography systems[J]. Applied Optics, 41, 6676-6691(2002). http://www.ncbi.nlm.nih.gov/pubmed/12412659

[55] Zhang S H, Zhou J H, Gong L. Skew line ray model of nonparaxial Gaussian beam[J]. Optics Express, 26, 3381-3393(2018). http://www.ncbi.nlm.nih.gov/pubmed/29401866

[56] Kay I, Keller J B. Asymptotic evaluation of the field at a caustic[J]. Journal of Applied Physics, 25, 876-883(1954).

[57] Ludwig D. Wave propagation near a smooth caustic[J]. Bulletin of the American Mathematical Society, 71, 776-780(1965). http://www.sciencedirect.com/science/article/pii/B9780080119229500440

[58] Berry M V, Upstill C. IV catastrophe optics: morphologies of caustics and their diffraction patterns[M]. ∥Wolf E. Progress in optics. New York: Elsevier, 18, 257-346(1980).

[59] Forbes G W, Alonso M A. Using rays better. I. Theory for smoothly varying media[J]. Journal of the Optical Society of America A, 18, 1132-1145(2001). http://www.ncbi.nlm.nih.gov/pubmed/11336216

[60] Ouellette P É. Geometric optics of a refringent sphere illuminated by a point source: caustics, wavefronts, and zero phase-fronts for every rainbow “k” order[J]. Journal of the Optical Society of America A, 35, 1-11(2018). http://europepmc.org/abstract/MED/29328086

[61] Berry M V. Uniform approximation a new concept in wave theory[J]. Science Progress, 57, 43-64(1969).

[62] Ludwig D. Wave propagation near a smooth caustic[M]. ∥Brown J. Electromagnetic wave theory. New York: Elsevier, 915-917(1967).

[63] Anguiano-Morales M, Martínez A. Iturbe-Castillo M D, et al. Self-healing property of a caustic optical beam[J]. Applied Optics, 46, 8284-8290(2007).

[64] Kaganovsky Y, Heyman E. Wave analysis of Airy beams[J]. Optics Express, 18, 8440-8452(2010). http://europepmc.org/abstract/MED/20588690

[65] Popov M M. A new method of computation of wave fields using Gaussian beams[J]. Wave Motion, 4, 85-97(1982).

[66] White B S, Norris A, Bayliss A et al. Some remarks on the Gaussian beam summation method[J]. Geophysical Journal International, 89, 579-636(1987).

[67] Norris A N. Complex point-source representation of real point sources and the Gaussian beam summation method[J]. Journal of the Optical Society of America A, 3, 2005-2010(1986). http://www.opticsinfobase.org/josaa/abstract.cfm?uri=josaa-3-12-2005

[68] Goodman J W. Introduction to Fourier optics[M]. New York: McGraw-Hill(1968).

[69] Berry M V. Semi-classical mechanics in phase space: a study of Wigner's function[J]. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 287, 237-271(1977).

[70] Alonso M A. Wigner functions in optics: describing beams as ray bundles and pulses as particle ensembles[J]. Advances in Optics and Photonics, 3, 272-365(2011). http://www.opticsinfobase.org/abstract.cfm?uri=aop-3-4-272

[71] Forbes G W, Alonso M A. What on earth is a ray and how can we use them best?[J]. Proceedings of SPIE, 3482, 22-31(1998). http://proceedings.spiedigitallibrary.org/proceeding.aspx?articleid=961182

[72] Alonso M A, Forbes G W. Phase-space distributions for high-frequency fields[J]. Journal of the Optical Society of America A, 17, 2288-2300(2000). http://www.ncbi.nlm.nih.gov/pubmed/11140489

[73] de Bruijn N G. Uncertainty principles in Fourier analysis[J]. Inequalities, 2, 57-71(1967). http://www.ams.org/mathscinet-getitem?mr=219977

[74] Alonso M A, Forbes G W. Stable aggregates of flexible elements give a stronger link between rays and waves[J]. Optics Express, 10, 728-739(2002). http://www.opticsinfobase.org/oe/abstract.cfm?uri=oe-10-16-728

[75] Alonso M A, Forbes G W. Using rays better. II. Ray families to match prescribed wave fields[J]. Journal of the Optical Society of America A, 18, 1146-1159(2001). http://www.ncbi.nlm.nih.gov/pubmed/11336217

[76] Alonso M A, Forbes G W. Using rays better. III. Error estimates and illustrative applications in smooth media[J]. Journal of the Optical Society of America A, 18, 1357-1370(2001). http://www.ncbi.nlm.nih.gov/pubmed/11393628

[77] Forbes G W. Using rays better. IV. Theory for refraction and reflection[J]. Journal of the Optical Society of America A, 18, 2557-2564(2001). http://europepmc.org/abstract/MED/11583273

[78] Alonso M A, Dennis M R. Ray-optical Poincaré sphere for structured Gaussian beams[J]. Optica, 4, 476-486(2017).

[79] Bareza N D, Hermosa N. Subluminal group velocity and dispersion of Laguerre Gauss beams in free space[J]. Scientific Reports, 6, 26842(2016). http://pubmedcentralcanada.ca/pmcc/articles/PMC4882591/

[80] Bouchard F, Harris J, Mand H et al. Observation of subluminal twisted light in vacuum[J]. Optica, 3, 351-354(2016). http://arxiv.org/abs/1610.01082

[81] Marcuse D. Light transmission optics[M]. 2nd ed. New York: Van Nostrand Reinhold Company(1972).

[82] Greenfield E, Segev M, Walasik W et al. Accelerating light beams along arbitrary convex trajectories[J]. Physical Review Letters, 106, 213902(2011). http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5951325

[83] Penciu R S, Paltoglou V, Efremidis N K. Closed-form expressions for nonparaxial accelerating beams with pre-engineered trajectories[J]. Optics Letters, 40, 1444-1447(2015).

[84] Epstein I, Arie A. Arbitrary bending plasmonic light waves[J]. Physical Review Letters, 112, 023903(2014). http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.023903

[85] Zhao Z Y, Xie C, Ni D D et al. Scaling the abruptly autofocusing beams in the direct-space[J]. Optics Express, 25, 30598-30605(2017). http://europepmc.org/abstract/MED/29221087

[86] Greynolds A W. Propagation of generally astigmatic Gaussian beams along skew ray paths[J]. Proceedings of SPIE, 560, 33-51(1986).

[87] Shi B Y, Meng Z, Wang L Z et al. Monte Carlo modeling of human tooth optical coherence tomography imaging[J]. Journal of Optics, 15, 075304(2013). http://adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2013JOpt...15g5304S&db_key=PHY&link_type=EJOURNAL

[88] Kaganovsky Y, Heyman E. Nonparaxial wave analysis of three-dimensional Airy beams[J]. Journal of the Optical Society of America A, 29, 671-688(2012).

[89] Zhang Z Y, Levoy M. Wigner distributions and how they relate to the light field. [C]∥2009 IEEE International Conference on Computational Photography (ICCP), April 16-17, 2009, San Francisco, CA, USA. New York: IEEE, 11499058(2009).

[90] Poto ek V, Barnett S M. Generalized ray optics and orbital angular momentum carrying beams[J]. New Journal of Physics, 17, 103034(2015).

[91] Zhu Q Z, Wu F T, He X. Generation of hollow beams through focusing J0-correlated schell-model beams with axicon[J]. Acta Optica Sinica, 36, 1026022(2016).

[92] Li D, Wu F T, Xie X X. A novel method of generating qausi-non-diffracting Mathieu beam based on axicon[J]. Acta Physica Sinica, 63, 152401(2014).

[93] Alvarez-Elizondo M B, Rodríguez-Masegosa R, Gutiérrez-Vega J C. Generation of Mathieu-Gauss modes with an axicon-based laser resonator[J]. Optics Express, 16, 18770-18775(2008). http://www.ncbi.nlm.nih.gov/pubmed/19581964

[94] Cižmár T, Zemánek P. High quality quasi-Bessel beam generated by round-tip axicon[J]. Optics Express, 16, 12688-12700(2008). http://europepmc.org/abstract/MED/18711507

[95] Vaveliuk P, Martínez-Matos Ó, Ren Y X et al. Dual behavior of caustic optical beams facing obstacles[J]. Physical Review A, 95, 063838(2017).

[96] Turnbull G A, Robertson D A, Smith G M et al. The generation of free-space Laguerre-Gaussian modes at millimetre-wave frequencies by use of a spiral phaseplate[J]. Optics Communications, 127, 183-188(1996).

[97] Sueda K, Miyaji G, Miyanaga N et al. Laguerre-Gaussian beam generated with a multilevel spiral phase plate for high intensity laser pulses[J]. Optics Express, 12, 3548-3553(2004).

[98] 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, 22, 849-861(2005).

[99] Eggleston M, Godat T, Munro E et al. Ray transfer matrix for a spiral phase plate[J]. Journal of the Optical Society of America A, 30, 2526-2530(2013).

[100] Zhang S H, Shao M, Zhou J H. Structured beam designed by ray-optical Poincaré sphere method and its propagation properties[J]. Acta Physica Sinica, 67, 224204(2018).

[101] Alonso M A. Ray-based diffraction calculations using stable aggregates of flexible elements[J]. Journal of the Optical Society of America A, 30, 1223-1235(2013).

[102] Keller J B. Geometrical theory of diffraction[J]. Journal of the Optical Society of America, 52, 116-130(1962).

[103] Kumar B S, Ranganath S. Geometrical theory of diffraction[J]. Pramana, 37, 457-488(1991).

[104] Felsen L B. Geometrical theory of diffraction, evanescent waves, complex rays and Gaussian beams[J]. Geophysical Journal International, 79, 77-88(1984).

[105] Senior T B A, Uslenghi P L E. Experimental detection of the edge-diffraction cone[J]. Proceedings of the IEEE, 60, 1448(1972).

[106] Sun J G. High-frequency asymptotic scattering theories and their applications in numerical modeling and imaging of geophysical fields: an overview of the research history and the state-of-the-art, and some new developments[J]. Journal of Jilin University(Earth Science Edition), 46, 1231-1259(2016).