阵列光学涡旋的轨道角动量分析
|
摘要
涡旋光束是指相位为连续的螺旋状的光束,因其具有特殊的波前相位在近些年来受到科学界很大的重视和广泛的研究。光学涡旋的特殊的波前结构和确定的光子轨道角动量,在原子光学、非线性光学、光学微操纵、光信息数据编码和通信等很多方面都有很重要的应用,随着研究的深入,光学涡旋将会应用在越来越多的领域中去。
本文的研究内容主要包括涡旋光束的基本原理;涡旋光束及阵列涡旋光束的几种产生方法;涡旋光束的轨道角动量特性,并以此为出发点重点研究了阵列涡旋光束的轨道角动量,对其进行数学分析和相关计算。
全文共分为四章:
第一章:概述了光学涡旋及阵列涡旋光束的研究背景、国内外对光学涡旋的研究历史和现状,并简单介绍了本文的研究目的和意义;
第二章:论述了光学涡旋的基本原理,对光学涡旋的定义和描述进行了数学上的确定,从经典的麦克斯韦电磁理论出发分析了光学涡旋的轨道角动量特性,证明光学涡旋轨道角动量的确是确定的。简单介绍了产生涡旋光束的几种方法并阐述了其利弊,并介绍了传统的拓扑荷为整数时的光束特性,即螺旋相位板为产生涡旋光束的仪器时,如何输出最大轨道角动量。这些研究对光学涡旋的深入了解和产生高质量涡旋奠定了基础;
第三章:本章介绍了产生阵列涡旋光束的方法,并从光学涡旋的基本原理和轨道角动量特性分析的基础上着重对矩形对称的严格周期性阵列光学涡旋光束的轨道角动量进行了数学分析和计算,得每单元格的轨道角动量是确定的,取决于单元格的选择,甚至,单元格的平移也会影响到轨道角动量的符号。每个单元格上的轨道角动量是本证固有的,并不与测量轴有关。虽然任意选择的晶格所携带的角动量与测量轴的位置没有关系,但是参数光束轨道角动量密度w与函数r导致所选择单元格内轨道角动量的不同。文章还分析由三束平面波干涉而得的涡旋阵列光子的轨道角动量,并验证了结论。此研究的结果适合于X,Y分量在x-y面上具有周期性的角动量的沿z轴的分量,也适合其他的周期光束或旋转的固体或液体。
第四章:光子是信息传递的重要载体,对光子的能量、动量和偏振态进行分析解码就可以得到光子所携带的大量的光信息,所以对其的研究在光信息数据编码和通信等方面有着重要的应用。另外,光学涡旋在粒子的微操纵、非线性光学等方面也有着重要的应用。文章还介绍了研究阵列涡旋光场的意义所在,说明了阵列涡旋光场的应用研究。本部分就讨论了光学涡旋、阵列涡旋光束在微操纵、原子光学、光信息数据编码和通信等方面的可能应用。
Optical vortex beams means the phase as continuous and spiral beam of light, because it has special plane wave’s phase to be subjected to very great respect of science field and far-ranging search in the nearer in the last years. The special plane wave structure of the optical whirlpool and the photon orbit of the assurance angular momentum, At atom optics and nonlinear optics, the optical micro drive, optics the information data encode and correspondence etc. have a very important application all very in many ways,Along with search of thorough, the optical vortex will apply in more and more realms to go.
The textual search contents mainly includes the radical principle of vortex beam of light; A few creation methods of vortex beam of light and array vortex beam of light;The orbit angular momentum of the vortex beam of light characteristic, and took this as a starting point to particularly study the orbit angular momentum of array vortex beam of light, as to it's carry on mathematics analysis and related computing.
The whole paper is divided into five chapters.
Chapter 1: Outlined search back ground, search history and present condition of optical vortex and array vortex beam of light, and in brief introduced textual search purpose and meaning
Chapter 2: Discussed the radical principle of optical vortex, carried on a mathematical assurance to definition and present of optical vortex. From classic Maxwell’s electromagnetic theory analyzing the orbit angular momentum of optical vortex characteristic from the theory,Simply introduces several methods of produce vortex beam and expounds its advantages and disadvantages, and introduces the traditional topology for integer beams of Hollywood when characteristics. Namely spiral phase board for generate the instrument of vortex beam of light, how output the biggest orbit angular momentum. These searches lay foundation to thorough understand and creation higher - mass vortex of optical vortex;
Chapter 3: This chapter introduced the method of generating the array vortex beam of light, According to the basic theory of the orbital angular momentum (OAM) of light under paraxial condition, analyzing for the OAM of the beam. we investigate the OAM of strictly periodic arrays of optical vortices with rectangular symmetry. We find that the OAM per unit cell depends on the choice of unit cell and can even change sign when the unit cell is translated. This is the case even if the OAM in each unit cell is intrinsic, that is independent of the choice of measurement axis. We show that spin-like OAM can be found only if the OAM per unit cell vanishes. Although arbitrarily choose the lattice carried by the angular momentum and measurement of shaft, but no relationship position parameter beam orbital angular momentum density of w and function r lead to choose within the cell different orbital angular momentum .And then we analyze the photon’s OAM of vortex array derived form three-beam interference of the plane waves to verify the conclusions .Our results are applicable to the z component of the angular momentum of any x- and y-periodic momentum distribution in the xy plane, and can also be applied to other periodic light beams and arrays of rotating solids or liquids.
Chapter 4: The photon is the importance that the information delivers to carry a body, Vs the energy, momentum of photon and be partial to flap state progress an analysis decrypt and then can receive the optics information of mass that the photon takes, So as to it's of the search has an important application in the optics information data encode and correspondence etc.. Moreover, the optical vortex also has an important application in the tiny operate, and nonlinear optics. The paper also introduces the array of vortex light field study of meaning, and explains the application of optical field array vortex The deli of headquarter talked about optical whirlpool, array whirlpool the beam of light drives in the micro, atom optics, optics the possible application of the information data encode and correspondence etc..
本文的研究内容主要包括涡旋光束的基本原理;涡旋光束及阵列涡旋光束的几种产生方法;涡旋光束的轨道角动量特性,并以此为出发点重点研究了阵列涡旋光束的轨道角动量,对其进行数学分析和相关计算。
全文共分为四章:
第一章:概述了光学涡旋及阵列涡旋光束的研究背景、国内外对光学涡旋的研究历史和现状,并简单介绍了本文的研究目的和意义;
第二章:论述了光学涡旋的基本原理,对光学涡旋的定义和描述进行了数学上的确定,从经典的麦克斯韦电磁理论出发分析了光学涡旋的轨道角动量特性,证明光学涡旋轨道角动量的确是确定的。简单介绍了产生涡旋光束的几种方法并阐述了其利弊,并介绍了传统的拓扑荷为整数时的光束特性,即螺旋相位板为产生涡旋光束的仪器时,如何输出最大轨道角动量。这些研究对光学涡旋的深入了解和产生高质量涡旋奠定了基础;
第三章:本章介绍了产生阵列涡旋光束的方法,并从光学涡旋的基本原理和轨道角动量特性分析的基础上着重对矩形对称的严格周期性阵列光学涡旋光束的轨道角动量进行了数学分析和计算,得每单元格的轨道角动量是确定的,取决于单元格的选择,甚至,单元格的平移也会影响到轨道角动量的符号。每个单元格上的轨道角动量是本证固有的,并不与测量轴有关。虽然任意选择的晶格所携带的角动量与测量轴的位置没有关系,但是参数光束轨道角动量密度w与函数r导致所选择单元格内轨道角动量的不同。文章还分析由三束平面波干涉而得的涡旋阵列光子的轨道角动量,并验证了结论。此研究的结果适合于X,Y分量在x-y面上具有周期性的角动量的沿z轴的分量,也适合其他的周期光束或旋转的固体或液体。
第四章:光子是信息传递的重要载体,对光子的能量、动量和偏振态进行分析解码就可以得到光子所携带的大量的光信息,所以对其的研究在光信息数据编码和通信等方面有着重要的应用。另外,光学涡旋在粒子的微操纵、非线性光学等方面也有着重要的应用。文章还介绍了研究阵列涡旋光场的意义所在,说明了阵列涡旋光场的应用研究。本部分就讨论了光学涡旋、阵列涡旋光束在微操纵、原子光学、光信息数据编码和通信等方面的可能应用。
Optical vortex beams means the phase as continuous and spiral beam of light, because it has special plane wave’s phase to be subjected to very great respect of science field and far-ranging search in the nearer in the last years. The special plane wave structure of the optical whirlpool and the photon orbit of the assurance angular momentum, At atom optics and nonlinear optics, the optical micro drive, optics the information data encode and correspondence etc. have a very important application all very in many ways,Along with search of thorough, the optical vortex will apply in more and more realms to go.
The textual search contents mainly includes the radical principle of vortex beam of light; A few creation methods of vortex beam of light and array vortex beam of light;The orbit angular momentum of the vortex beam of light characteristic, and took this as a starting point to particularly study the orbit angular momentum of array vortex beam of light, as to it's carry on mathematics analysis and related computing.
The whole paper is divided into five chapters.
Chapter 1: Outlined search back ground, search history and present condition of optical vortex and array vortex beam of light, and in brief introduced textual search purpose and meaning
Chapter 2: Discussed the radical principle of optical vortex, carried on a mathematical assurance to definition and present of optical vortex. From classic Maxwell’s electromagnetic theory analyzing the orbit angular momentum of optical vortex characteristic from the theory,Simply introduces several methods of produce vortex beam and expounds its advantages and disadvantages, and introduces the traditional topology for integer beams of Hollywood when characteristics. Namely spiral phase board for generate the instrument of vortex beam of light, how output the biggest orbit angular momentum. These searches lay foundation to thorough understand and creation higher - mass vortex of optical vortex;
Chapter 3: This chapter introduced the method of generating the array vortex beam of light, According to the basic theory of the orbital angular momentum (OAM) of light under paraxial condition, analyzing for the OAM of the beam. we investigate the OAM of strictly periodic arrays of optical vortices with rectangular symmetry. We find that the OAM per unit cell depends on the choice of unit cell and can even change sign when the unit cell is translated. This is the case even if the OAM in each unit cell is intrinsic, that is independent of the choice of measurement axis. We show that spin-like OAM can be found only if the OAM per unit cell vanishes. Although arbitrarily choose the lattice carried by the angular momentum and measurement of shaft, but no relationship position parameter beam orbital angular momentum density of w and function r lead to choose within the cell different orbital angular momentum .And then we analyze the photon’s OAM of vortex array derived form three-beam interference of the plane waves to verify the conclusions .Our results are applicable to the z component of the angular momentum of any x- and y-periodic momentum distribution in the xy plane, and can also be applied to other periodic light beams and arrays of rotating solids or liquids.
Chapter 4: The photon is the importance that the information delivers to carry a body, Vs the energy, momentum of photon and be partial to flap state progress an analysis decrypt and then can receive the optics information of mass that the photon takes, So as to it's of the search has an important application in the optics information data encode and correspondence etc.. Moreover, the optical vortex also has an important application in the tiny operate, and nonlinear optics. The paper also introduces the array of vortex light field study of meaning, and explains the application of optical field array vortex The deli of headquarter talked about optical whirlpool, array whirlpool the beam of light drives in the micro, atom optics, optics the possible application of the information data encode and correspondence etc..
引文
[1] A. Ashkin.Acceleration and trapping of particles by radiation pressure [J] .Phys. Rev. Lett. , 24: 156-159 (1970).
[2] A. Ashkin, J. M. Dziedic, J. E. Bjorkholm, et al.Observation of a single-beam gradient force optical trap for dielectric particles [J]. Opt.Lett., 11(5):288-290 (1986).
[3] Karel. Svoboda and Steven. M. Block. Optical Trapping of Metallic Ray- leigh Particles [J]. Opt. Lett., 19 (13): 930–932(1994).
[4] Finer. J. T, Simmons. R. M, Spudich. J. A, et al. Single myosin molecule mechanics: Pico - Newton forces and nanometer steps [J]. Nature, 368(10): 113– 118(1994).
[5] Ishijima. A. Doi. T, Sakurada K, et al. Sub - Pico Newton force fluctuation of act myosin in vitro [J]. Nature, 352 (25):301– 306(1991).
[6] N. B. Simpson, L. Allen, M. J. Padgett. Optical tweezers and optical spanners with Laguerre-Gaussian modes [J]. Journal of Modern Optics. 43:2485-2491(1996).
[7] N. B. Simpson, McGloin. D, Dholakia. K, et al. Optical tweezers with increased axial trapping efficiency [J]. Journal of Modern Optics. 45: 1943-1949(1998).
[8] Kwanil Lee, Jong-An Kim, Kihwan Kim, et al, Cold atoms in hollow optical systems[J], Journal of the Korean Physical Society, 35: 115-121(1999).
[9] A. T. O. Neill and Padgett. M. J. Axial and lateral trapping efficiency of Laguerre-Gaussian modes in inverted optical tweezers [J]. Opt. Commun., 193:45-50(2000).
[10] J. Arlt, T. Hitomi and K. Dholaida, Atom guiding along Laguerre-Gaussian and Bessel light beams [J], Appl. Phy. B 71:549-554 (2000).
[11] Jason. W. Fleischer, Mordechal Segev, Nikolaos. K. Efremidis and Demetrios N. Christodoulides. Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices [J]. Nature.422, (2003).
[12] Dragomir. N. Neshev, Tristram. J. Alexander, Elena. A. Ostrovskaya, et al, Observation of discrete vortex solitons in optically induced photonic lattices [J]. Phy. Rev. Lett. 92: 123903-123906, (2004).
[13] M. Born and E. Wolf, Principles of Optics, 7th ed. Pergamon, New York, (1999).
[14] V. S. Ignatovskii, Trans. Opt. Inst. Petrograd, 1: IV, (1919).
[15] B. Richards and E. Wolf. Proc. R. Soc. London, Ser. A. 253:358-370, (1957).
[16] A. Boivin, A. J. Dow and E. Wolf. J.Opt Soc. Am. 57:1171, (1967).
[17] W. Braunbek and G. Laukien, Optik, 9:174, (1952).
[18] William H. Carter. Anomalies in the field of a Gaussian beam near focus [J]. Opt. Commun., 7(3):211~218, (1973).
[19] J. F. Nye and M. V. Berry, Pro. R. Soc. London Ser. A 336:165, (1974).
[20] G. P. Karman, M.W.Beijersbergen, A. van Duijl et al. Airy pattern reorganization and subwavelength structure in a focus [J]. J. Opt. Soc. Am. A, 15(4):884~899, (1998).
[21] M. V. Berry. Wave dislocation reactions in non- paraxial Gaussian beams [J]. J. Mod. Opt., 45(9):1845~1858, (1998).
[22] J. F. Nye. Unfolding of higher- order wave dislocations [J]. J. Opt. Soc. Am. A, 15(5):1132~1138, (1998).
[23] A. V. Volyar, V. G. Shvedov and T. A. Fadeeva. The structure of no paraxial Gaussian beam near the focus:Ⅱoptical vortices[J]. Optics and Spectroscopy, 90(1):93~100, (2001).
[24] A. V. Volyar, V. G. Shvedov, T. A. Fadeeva. The structure of no paraxial Gaussian beam near the focus:Ⅲstability,eigenmodes and vortices[J]. Optics and Spectroscopy , 91(2):235~245, (2001).
[25] V. A. Pas'ko, M. S. Soskin, M. V. Vasnetsov. Transversal optical vortex [J]. Opt. Commun., 198(1~3):49~56, (2001).
[26] A. Sommerfeld, Optik (Wiesbaden), (1950).
[27] J. M. Vaughan and D. V. Willetts, Opt. Commun. 30:263, (1979).
[28] P. Cullet, L. Gil and F. Rocca. Optical vortices [J]. Opt. Commun. 73:403-408, (1989).
[29] L. Allen, M. W. Beijersbergen, R. J. Spreeuw and J. P. Woerdman. Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes [J]. Phy. Rev. A. 45(11):8185-8189, (1992).
[30] S. M. Barnett and L. Allen. Orbital angular momentum and nonparaxial light beams [J]. Opt. Commun. 110:679-688, (1994).
[31] F. S. Roux, Dynamical behavior of optical vortices [J], Opt. Soc. Am. B 12, 1215-1221, (1995).
[32] G. Idebetouw, Optical vortices and their propagation [J], Mod. Opt. 40, 73-87,(1993).
[33] Guang-Hoon-Kim et al., An array of phase singularities in a self-defocusing medium [J], Opt. Comm. 147, 131-137, (1998).
[34] D. Rozas, Z. S. Sacks, and G. A. Swartzlander Jr., Experimental Observation of Fluidlike Motion of Optical Vortices [J], Phys. Rev. Lett. 79, 3399-3402, (1997).
[35] D. Rozas and G. A. Swartz Lander Jr., Observed rotational enhancement of nonlinear optical vortices [J], Opt. Lett. 25, 126-128, (2000).
[36] G. A. Swartzlander, Jr. and C. T. Law. Optical vortex solitons observed in Kerr nonlinear media [J]. Phy. Rev. Lett. 69: 2503-2506, (1992).
[37] Jason W. Fleischer, Mordechal Segev, Nikolaos K. Efremidis and Demetrios N. Christodoulides. Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices [J]. Nature, 422, (2003).
[38] H. He, M. E. J. Friese, N. R. Heckenberg and H. Rubinsztein-Dunlop. Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity [J]. Phys. Rev. Lett., 75:826-829,(1995).
[39] N. B. Simpson, K. Dholakia, L. Allen and M. J. Padgett. Mechanical equivalence of spin and orbital angular momentum of light: an optical spanner [J]. Opt. Lett. 22: 52-54, (1997).
[40] Matthew Pelton, Kosta Ladavac, and David G. Grier, Transport and fractionation in periodic potential-energy landscapes [J]. Phy. Rev. E 70:031108, (2004).
[41] T. Kuga, Y. Torii, N. Shiokawa and T. Hirano. Phys. Rev. Lett. 78: 4713, (1997).
[42] A. Berzanskis, A. Matijosius, A. Piskarkas, et al.,Conversion of topological charge of optical vortices in a parametric frequencyconverter,[J] Opt. Comm. 140, 273-276 (1997).
[43] I. D. Maleev and G. A. Swartzlander Jr., Composite optical vortices[J], Opt. Soc.Am. B 20, 1169-1176 (2003).
[44]高明伟,高春清,何晓燕等,利用具有轨道角动量的光束实现微粒的旋转[J],物理学报,53(2),413-417,(2002).
[45] M. V. Berry, Optical vortices evolving from helicoidal integer and fractional phase steps[J], J. Opt. A: Pure Appl. Opt. 6, 259–268, (2004).
[46] J¨org B. G¨otte, Kevin O’Holleran, Daryl Preece,et al., Light beams with fractionalorbital angular momentum and their vortex structure[J], Vol. 16, No. 2 OPTICS EXPRESS,993-1006,(2008).
[47] Matthew Pelton, Kosta Ladavac, and David G. Grier, Transport and fractionation in periodic potential-energy landscapes [J]. Phy. Rev. E 70:031108, (2004).
[48] L. Marrucci, C. Manzo, and D. Paparo, Optical Spin-to-Orbital Angular Momentum Conversion in Inhomogeneous Anisotropic Media [J], PRL 96, 163905-1-163905-4, (2006).
[49] M. W. Beijersbergen, L. Allen, H. Vanderveen, J. P. Woerdman: Astigmatic Laser Mode Converters and Transfer of Orbital Angular-Momentum [J]. Optics Commun. 96:123-132, (1993).
[50] S. J. Van Enk and G. Nienhuis. Angular momentum in evanescent waves [J]. Opt. Commun., 112:225-234, (1994)
[51] J. Durnin, J. J. Miceli, Jr. and J. H. Eberly. Diffraction– free beams [J], JOSA A 3,128 ,(1986).
[52] J. Durnin. Exact solutions of nondiffraction beams. I. The scarlar teory [J]. JOSA A, 4: 651-654,(1987).
[53] J. Durnin, J. J. Miceli, J. H. Eberly, Diffraction–free beams [J]. Phy. Rev. Lett., 58: 1499-1501, (1987).
[54] C.-S. Guo. Optimal phase steps of multi-level spiral phase plates[J]. Optics Communications 268,235-239,(2006)
[55] N. B. Simpson, L. Allen and M. J. Padgett. Optical spanners. In Inaugural Meeting of the Scottish Chapter of LEOS [J], Glasgow University, Glasgow, (1996).
[56] A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett. Intrinsic and extrinsic nature of the orbital angular momentum of a light beam [J]. Phy. Rev. Lett. 88:053601, (2002).
[57] Yin J P, et al., Doughnut-beam-induced Sisyphus cooling in atomic guiding and collimation [J]. J. Opt. Soc. Am B, 15(8):2235, (1998).
[58] L. Allen, M. J. Padgett and M. Babiker. The orbital angular momentum of light [J]. Progress in Optics, XXXIX:291-372, (1999).
[59] M. S. Soskin and M. V.Vasnetsov. Singular optics [J]. 42:219-276,(2001).
[60] R. A. Beth, Phys. rev. 50,115,(1936).
[61] J. H. Poyning.Proc. R. Soc. London. Sor. A. 82,560 (1909).
[62] H. A. Haus. Waves and Fields in Optoelectronics [J]. Prentice-Hall, EnglewoodCliffs, NJ, (1984).
[63]柯熙政,吕宏,武京治,基于光轨道角动量的光通信数据编码研究进展[J],量子电子学报,2008,27(4)385-392;
[64] Cheng-Shan Guo , Yan Zhang , Yu-Jing Han , Jian-Ping Ding , Hui-Tian Wang , Generation of optical vortices with arbitrary shape and array via helical phase spatial filtering[J], Optics Communications 259 (2006) 449–454;
[65] Gong-Xiang Wei , Lei-Lei Lu , Cheng-Shan Guo, Generation of optical vortex array based on the fractional Talbot effect[J], Optics Communications 282 (2009) 2665–2669;
[66] R M Jenkins, J Banerji and A R Davies,The generation of optical vortices and shape preserving vortex arrays in hollow multimode waveguides[J], J. Opt. A: Pure Appl. Opt. 3 (2001) 527–532;
[67] Jan Masajada, Boguslawa Dubik, Optical vortex generation by three plane wave interference [J],Optics Communication 198(2001)21-27;
[68] Sunil Vyas and P. Senthilkumaran, Vortex array generation by interference of spherical waves, APPLIED OPTICS Vol. 46, No. 32 10 November 2007;
[69] Johannes Courtial, Roberta Zambrini, Mark R Dennis,et al,. Angular momentum of optical vortex Arrays [J], OPTICS EXPRESS, Vol. 14, No. 2, 938-949,(2006).
[70] T. C. Bakker Schut,G. Hesselink, B.G.de Grooth,and J.Greve,“Experimental and theoretical investigations on the validity of the geometrical optics model for calculating the stability of optical traps,”Cytometry 12,479-485(1991)
[71] Graham Milne, Kishan Dholakia and David McGloin etal. Transverse particle dynamics in a Bessel beam..Optics Express, 2007, 15(21):13972-139874.
[2] A. Ashkin, J. M. Dziedic, J. E. Bjorkholm, et al.Observation of a single-beam gradient force optical trap for dielectric particles [J]. Opt.Lett., 11(5):288-290 (1986).
[3] Karel. Svoboda and Steven. M. Block. Optical Trapping of Metallic Ray- leigh Particles [J]. Opt. Lett., 19 (13): 930–932(1994).
[4] Finer. J. T, Simmons. R. M, Spudich. J. A, et al. Single myosin molecule mechanics: Pico - Newton forces and nanometer steps [J]. Nature, 368(10): 113– 118(1994).
[5] Ishijima. A. Doi. T, Sakurada K, et al. Sub - Pico Newton force fluctuation of act myosin in vitro [J]. Nature, 352 (25):301– 306(1991).
[6] N. B. Simpson, L. Allen, M. J. Padgett. Optical tweezers and optical spanners with Laguerre-Gaussian modes [J]. Journal of Modern Optics. 43:2485-2491(1996).
[7] N. B. Simpson, McGloin. D, Dholakia. K, et al. Optical tweezers with increased axial trapping efficiency [J]. Journal of Modern Optics. 45: 1943-1949(1998).
[8] Kwanil Lee, Jong-An Kim, Kihwan Kim, et al, Cold atoms in hollow optical systems[J], Journal of the Korean Physical Society, 35: 115-121(1999).
[9] A. T. O. Neill and Padgett. M. J. Axial and lateral trapping efficiency of Laguerre-Gaussian modes in inverted optical tweezers [J]. Opt. Commun., 193:45-50(2000).
[10] J. Arlt, T. Hitomi and K. Dholaida, Atom guiding along Laguerre-Gaussian and Bessel light beams [J], Appl. Phy. B 71:549-554 (2000).
[11] Jason. W. Fleischer, Mordechal Segev, Nikolaos. K. Efremidis and Demetrios N. Christodoulides. Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices [J]. Nature.422, (2003).
[12] Dragomir. N. Neshev, Tristram. J. Alexander, Elena. A. Ostrovskaya, et al, Observation of discrete vortex solitons in optically induced photonic lattices [J]. Phy. Rev. Lett. 92: 123903-123906, (2004).
[13] M. Born and E. Wolf, Principles of Optics, 7th ed. Pergamon, New York, (1999).
[14] V. S. Ignatovskii, Trans. Opt. Inst. Petrograd, 1: IV, (1919).
[15] B. Richards and E. Wolf. Proc. R. Soc. London, Ser. A. 253:358-370, (1957).
[16] A. Boivin, A. J. Dow and E. Wolf. J.Opt Soc. Am. 57:1171, (1967).
[17] W. Braunbek and G. Laukien, Optik, 9:174, (1952).
[18] William H. Carter. Anomalies in the field of a Gaussian beam near focus [J]. Opt. Commun., 7(3):211~218, (1973).
[19] J. F. Nye and M. V. Berry, Pro. R. Soc. London Ser. A 336:165, (1974).
[20] G. P. Karman, M.W.Beijersbergen, A. van Duijl et al. Airy pattern reorganization and subwavelength structure in a focus [J]. J. Opt. Soc. Am. A, 15(4):884~899, (1998).
[21] M. V. Berry. Wave dislocation reactions in non- paraxial Gaussian beams [J]. J. Mod. Opt., 45(9):1845~1858, (1998).
[22] J. F. Nye. Unfolding of higher- order wave dislocations [J]. J. Opt. Soc. Am. A, 15(5):1132~1138, (1998).
[23] A. V. Volyar, V. G. Shvedov and T. A. Fadeeva. The structure of no paraxial Gaussian beam near the focus:Ⅱoptical vortices[J]. Optics and Spectroscopy, 90(1):93~100, (2001).
[24] A. V. Volyar, V. G. Shvedov, T. A. Fadeeva. The structure of no paraxial Gaussian beam near the focus:Ⅲstability,eigenmodes and vortices[J]. Optics and Spectroscopy , 91(2):235~245, (2001).
[25] V. A. Pas'ko, M. S. Soskin, M. V. Vasnetsov. Transversal optical vortex [J]. Opt. Commun., 198(1~3):49~56, (2001).
[26] A. Sommerfeld, Optik (Wiesbaden), (1950).
[27] J. M. Vaughan and D. V. Willetts, Opt. Commun. 30:263, (1979).
[28] P. Cullet, L. Gil and F. Rocca. Optical vortices [J]. Opt. Commun. 73:403-408, (1989).
[29] L. Allen, M. W. Beijersbergen, R. J. Spreeuw and J. P. Woerdman. Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes [J]. Phy. Rev. A. 45(11):8185-8189, (1992).
[30] S. M. Barnett and L. Allen. Orbital angular momentum and nonparaxial light beams [J]. Opt. Commun. 110:679-688, (1994).
[31] F. S. Roux, Dynamical behavior of optical vortices [J], Opt. Soc. Am. B 12, 1215-1221, (1995).
[32] G. Idebetouw, Optical vortices and their propagation [J], Mod. Opt. 40, 73-87,(1993).
[33] Guang-Hoon-Kim et al., An array of phase singularities in a self-defocusing medium [J], Opt. Comm. 147, 131-137, (1998).
[34] D. Rozas, Z. S. Sacks, and G. A. Swartzlander Jr., Experimental Observation of Fluidlike Motion of Optical Vortices [J], Phys. Rev. Lett. 79, 3399-3402, (1997).
[35] D. Rozas and G. A. Swartz Lander Jr., Observed rotational enhancement of nonlinear optical vortices [J], Opt. Lett. 25, 126-128, (2000).
[36] G. A. Swartzlander, Jr. and C. T. Law. Optical vortex solitons observed in Kerr nonlinear media [J]. Phy. Rev. Lett. 69: 2503-2506, (1992).
[37] Jason W. Fleischer, Mordechal Segev, Nikolaos K. Efremidis and Demetrios N. Christodoulides. Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices [J]. Nature, 422, (2003).
[38] H. He, M. E. J. Friese, N. R. Heckenberg and H. Rubinsztein-Dunlop. Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity [J]. Phys. Rev. Lett., 75:826-829,(1995).
[39] N. B. Simpson, K. Dholakia, L. Allen and M. J. Padgett. Mechanical equivalence of spin and orbital angular momentum of light: an optical spanner [J]. Opt. Lett. 22: 52-54, (1997).
[40] Matthew Pelton, Kosta Ladavac, and David G. Grier, Transport and fractionation in periodic potential-energy landscapes [J]. Phy. Rev. E 70:031108, (2004).
[41] T. Kuga, Y. Torii, N. Shiokawa and T. Hirano. Phys. Rev. Lett. 78: 4713, (1997).
[42] A. Berzanskis, A. Matijosius, A. Piskarkas, et al.,Conversion of topological charge of optical vortices in a parametric frequencyconverter,[J] Opt. Comm. 140, 273-276 (1997).
[43] I. D. Maleev and G. A. Swartzlander Jr., Composite optical vortices[J], Opt. Soc.Am. B 20, 1169-1176 (2003).
[44]高明伟,高春清,何晓燕等,利用具有轨道角动量的光束实现微粒的旋转[J],物理学报,53(2),413-417,(2002).
[45] M. V. Berry, Optical vortices evolving from helicoidal integer and fractional phase steps[J], J. Opt. A: Pure Appl. Opt. 6, 259–268, (2004).
[46] J¨org B. G¨otte, Kevin O’Holleran, Daryl Preece,et al., Light beams with fractionalorbital angular momentum and their vortex structure[J], Vol. 16, No. 2 OPTICS EXPRESS,993-1006,(2008).
[47] Matthew Pelton, Kosta Ladavac, and David G. Grier, Transport and fractionation in periodic potential-energy landscapes [J]. Phy. Rev. E 70:031108, (2004).
[48] L. Marrucci, C. Manzo, and D. Paparo, Optical Spin-to-Orbital Angular Momentum Conversion in Inhomogeneous Anisotropic Media [J], PRL 96, 163905-1-163905-4, (2006).
[49] M. W. Beijersbergen, L. Allen, H. Vanderveen, J. P. Woerdman: Astigmatic Laser Mode Converters and Transfer of Orbital Angular-Momentum [J]. Optics Commun. 96:123-132, (1993).
[50] S. J. Van Enk and G. Nienhuis. Angular momentum in evanescent waves [J]. Opt. Commun., 112:225-234, (1994)
[51] J. Durnin, J. J. Miceli, Jr. and J. H. Eberly. Diffraction– free beams [J], JOSA A 3,128 ,(1986).
[52] J. Durnin. Exact solutions of nondiffraction beams. I. The scarlar teory [J]. JOSA A, 4: 651-654,(1987).
[53] J. Durnin, J. J. Miceli, J. H. Eberly, Diffraction–free beams [J]. Phy. Rev. Lett., 58: 1499-1501, (1987).
[54] C.-S. Guo. Optimal phase steps of multi-level spiral phase plates[J]. Optics Communications 268,235-239,(2006)
[55] N. B. Simpson, L. Allen and M. J. Padgett. Optical spanners. In Inaugural Meeting of the Scottish Chapter of LEOS [J], Glasgow University, Glasgow, (1996).
[56] A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett. Intrinsic and extrinsic nature of the orbital angular momentum of a light beam [J]. Phy. Rev. Lett. 88:053601, (2002).
[57] Yin J P, et al., Doughnut-beam-induced Sisyphus cooling in atomic guiding and collimation [J]. J. Opt. Soc. Am B, 15(8):2235, (1998).
[58] L. Allen, M. J. Padgett and M. Babiker. The orbital angular momentum of light [J]. Progress in Optics, XXXIX:291-372, (1999).
[59] M. S. Soskin and M. V.Vasnetsov. Singular optics [J]. 42:219-276,(2001).
[60] R. A. Beth, Phys. rev. 50,115,(1936).
[61] J. H. Poyning.Proc. R. Soc. London. Sor. A. 82,560 (1909).
[62] H. A. Haus. Waves and Fields in Optoelectronics [J]. Prentice-Hall, EnglewoodCliffs, NJ, (1984).
[63]柯熙政,吕宏,武京治,基于光轨道角动量的光通信数据编码研究进展[J],量子电子学报,2008,27(4)385-392;
[64] Cheng-Shan Guo , Yan Zhang , Yu-Jing Han , Jian-Ping Ding , Hui-Tian Wang , Generation of optical vortices with arbitrary shape and array via helical phase spatial filtering[J], Optics Communications 259 (2006) 449–454;
[65] Gong-Xiang Wei , Lei-Lei Lu , Cheng-Shan Guo, Generation of optical vortex array based on the fractional Talbot effect[J], Optics Communications 282 (2009) 2665–2669;
[66] R M Jenkins, J Banerji and A R Davies,The generation of optical vortices and shape preserving vortex arrays in hollow multimode waveguides[J], J. Opt. A: Pure Appl. Opt. 3 (2001) 527–532;
[67] Jan Masajada, Boguslawa Dubik, Optical vortex generation by three plane wave interference [J],Optics Communication 198(2001)21-27;
[68] Sunil Vyas and P. Senthilkumaran, Vortex array generation by interference of spherical waves, APPLIED OPTICS Vol. 46, No. 32 10 November 2007;
[69] Johannes Courtial, Roberta Zambrini, Mark R Dennis,et al,. Angular momentum of optical vortex Arrays [J], OPTICS EXPRESS, Vol. 14, No. 2, 938-949,(2006).
[70] T. C. Bakker Schut,G. Hesselink, B.G.de Grooth,and J.Greve,“Experimental and theoretical investigations on the validity of the geometrical optics model for calculating the stability of optical traps,”Cytometry 12,479-485(1991)
[71] Graham Milne, Kishan Dholakia and David McGloin etal. Transverse particle dynamics in a Bessel beam..Optics Express, 2007, 15(21):13972-139874.