HTML
-
回顾光学史,从早期的时域强度(振幅)到近代光学的频率(波长)、相位、偏振等信息[1-3],人们对光的认识、研究、开发通常都发端于、也依赖于对物理自由度的探索。近年来,随着研究人员对于光的空间结构的理解不断加深、控制能力不断提高,具有特殊振幅、相位和偏振分布的空间结构光场(如图1所示)受到学术界的广泛关注[4-5]。1992年,Allen等人指出光场的螺旋相位 (Spiral phase) 结构与光子的光学轨道角动量 (Orbital angular momentum, OAM) 有关,当光场相位含有可表示为
$\exp \left(i l_{1} \varphi\right)$ 的螺旋相位因子时,光场内每个光子的OAM为$l\hbar $ ,其中$\varphi $ 为空间方位角[6-9]。这一发现引发了结构光领域的研究热潮。具有特定强度、相位和偏振分布的结构光场被广泛应用于光通信、光学探测、显微成像、量子纠缠、材料加工等领域[9-11]。特别地,OAM提供了一个新的高维可调谐自由度,对经典和量子通信技术的进一步发展具有重要意义[12-15]。OAM模式的空间正交性使得共轴传播的不同模式原则上可以被解复用,因此,基于光场空间模式的模分复用技术(Mode division multiplexing,MDM)或高维空间模式编码都可以与现有的波分复用技术(WDM)、时分复用技术相兼容,提高量子通信和经典通信的数据传输速率[10, 16-18]。涡旋光束的产生方法和探测手段是涡旋光束应用开发和技术突破的关键[19-20]。涡旋光产生方面,有谐振腔调控、数字化定制和超构表面调制等方法[21-25],涡旋场的研究对象也突破了光学涡旋范畴,迅速拓展至电子涡旋、太赫兹涡旋、声学涡旋等领域[18, 26-30]。涡旋光探测方面,结构光的识别和分类仍是一个很大的挑战。目前常用方法有干涉、衍射、模式投影测量等技术,探测手段逐渐向高效、集成化方向发展[31-37]。利用涡旋光特殊的相位分布,可通过孔径衍射和光束干涉的方法测量光束拓扑荷,具体的方案包括三角孔径衍射、圆形孔径衍射、椭圆形孔径衍射、同轴干涉和离轴干涉等[23, 38-40]。根据此类方法得到的远场衍射光斑阵列和干涉条纹,可以判断涡旋光OAM的大小和正负,但仅适用于探测具有单一OAM的光束,无法应用于多个OAM模式叠加的光束,也无法实现灵活、高精度的测量[34-35]。光场空间模式的探测可视为模式产生的逆过程,因此相位调制器件可以通过显示共轭全息图来检测空间模式,被称为投影测量[41-43]。例如,对于入射的OAM模式
$\exp \left(i l_{1} \varphi\right)$ ,当空间光调制器(Spatial light modulator, SLM)加载的全息图对光场施加$\exp \left(-i l_{2} \varphi\right)$ 的相位调制时,输出的OAM模式为$\exp \left[i\left(l_{1}-l_{2}\right) \varphi\right]$ 。若满足$l_{1}=l_{2}$ ,螺旋相位结构会被抵消,因此光束可以被耦合进入单模光纤中[44]。尽管投影测量的操作过程简单,但对于N维希尔伯特空间而言,该方法的检测效率在机理上被限定为$1/N$ [45]。与之相比,基于几何坐标变换原理的OAM模式分类器可以并行、无能量损耗地对OAM模式进行空间分离的投影测量[46-47]。近年来,涡旋光的几何坐标变换技术作为新兴的涡旋光探测方法,展现出器件无源、无能量损耗、结构紧凑、价格低廉等诸多优点,成为涡旋光的空间分离和解复用的高效有力工具,为涡旋光的识别和应用提供了全新的研究平台,具有广阔的发展前景。文中围绕这一主题,详细介绍涡旋光的几何坐标变换及其应用技术的基本原理、技术路径和优势特点。
[1] | Webb W T, Hanzo L. Modern Quadrature Amplitude Modulation: Principles and Applications for Fixed and Wireless Channels: One[M]. US: IEEE Press-John Wiley, 1994. |
[2] | Mukherjee B. Optical WDM Networks[M]. Berlin: Springer Science & Business Media, 2006. |
[3] | Hanzo L, Ng S X, Keller T, et al. Quadrature Amplitude Modulation[M]. Chichester, UK: Wiley, 2004. |
[4] | Rubinsztein-Dunlop H, Forbes A, Berry M V, et al. Roadmap on structured light [J]. Journal of Optics, 2016, 19(1): 013001. |
[5] | Forbes A, Oliveira M, Dennis M R. Structured light [J]. Nature Photonics, 2021, 15(4): 253-262. |
[6] | Beijersbergen M W, Allen L, Veen H E L O, et al. Astigmatic laser mode converters and transfer of orbital angular momentum [J]. Optics Communications, 1993, 96(1-3): 123-132. |
[7] | Enk S J, Nienhuis G. Eigenfunction description of laser beams and orbital angular momentum of light [J]. Optics Communications, 1992, 94(1-3): 147-158. |
[8] | Allen L, Beijersbergen M W, Spreeuw R, et al. Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes [J]. Physical Review A, 1992, 45(11): 8185. |
[9] | Shen Y, Wang X, Xie Z, et al. Optical vortices 30 years on: OAM manipulation from topological charge to multiple singularities [J]. Light: Science & Applications, 2019, 8: 90. |
[10] | Willner A E, Huang H, Yan Y, et al. Optical communications using orbital angular momentum beams [J]. Advances in Optics and Photonics, 2015, 7(1): 66-106. |
[11] | Geng J. Structured-light 3D surface imaging: a tutorial [J]. Advances in Optics and Photonics, 2011, 3(2): 128-160. |
[12] | Mair A, Vaziri A, Weihs G, et al. Entanglement of the orbital angular momentum states of photons [J]. Nature, 2001, 412(6844): 313-316. |
[13] | Otte E, Nape I, Rosales-Guzmán C, et al. High-dimensional cryptography with spatial modes of light: tutorial [J]. Journal of the Optical Society of America B, 2020, 37(11): A309-A323. |
[14] | Fang X, Ren H, Gu M. Orbital angular momentum holography for high-security encryption [J]. Nature Photonics, 2020, 14(2): 102-108. |
[15] | Erhard M, Fickler R, Krenn M, et al. Twisted photons: new quantum perspectives in high dimensions [J]. Light: Science & Applications, 2018, 7(3): 17146. |
[16] | Wang J. Advances in communications using optical vortices [J]. Photonics Research, 2016, 4(5): B14-B28. |
[17] | Bozinovic N, Yue Y, Ren Y, et al. Orbital angular momentum (OAM) based mode division multiplexing (MDM) over a Km-length fiber [C]//Optical Society of America, 2012: Th.3.C.6. |
[18] | Bozinovic N, Yue Y, Ren Y, et al. Terabit-scale orbital angular momentum mode division multiplexing in fibers [J]. Science, 2013, 340(6140): 1545-1548. |
[19] | Ndagano B, Nape I, Cox M A, et al. Creation and detection of vector vortex modes for classical and quantum communication [J]. Journal of Lightwave Technology, 2018, 36(2): 292-301. |
[20] | Chen R, Zhou H, Moretti M, et al. Orbital angular momentum waves: generation, detection, and emerging applications [J]. IEEE Communications Surveys & Tutorials, 2019, 22(2): 840-868. |
[21] | Qin F, Wan L, Li L, et al. A transmission metasurface for generating OAM beams [J]. IEEE Antennas and Wireless Propagation Letters, 2018, 17(10): 1793-1796. |
[22] | Rosales-Guzmán C, Forbes A. How to Shape Light with Spatial Light Modulators[M]. US: SPIE Press, 2017. |
[23] | Shen Y, Meng Y, Fu X, et al. Wavelength-tunable Hermite–Gaussian modes and an orbital-angular-momentum-tunable vortex beam in a dual-off-axis pumped Yb: CALGO laser [J]. Optics Letters, 2018, 43(2): 291-294. |
[24] | Song R, Gao C, Zhou H, et al. Resonantly pumped Er: YAG vector laser with selective polarization states at 1.6 µm [J]. Optics Letters, 2020, 45(16): 4626-4629. |
[25] | Wang H, Fu S, Gao C. Tailoring a complex perfect optical vortex array with multiple selective degrees of freedom [J]. Optics Express, 2021, 29(7): 10811-10824. |
[26] | Anhäuser A, Wunenburger R, Brasselet E. Acoustic rotational manipulation using orbital angular momentum transfer [J]. Physical Review Letters, 2012, 109(3): 034301. |
[27] | Jiang X, Li Y, Liang B, et al. Convert acoustic resonances to orbital angular momentum [J]. Physical Review Letters, 2016, 117(3): 034301. |
[28] | Li H, Ren G, Zhu B, et al. Guiding terahertz orbital angular momentum beams in multimode Kagome hollow-core fibers [J]. Optics Letters, 2017, 42(2): 179-182. |
[29] | Verbeeck J, Tian H, Schattschneider P. Production and application of electron vortex beams [J]. Nature, 2010, 467(7313): 301-304. |
[30] | Liu C, Liu J, Niu L, et al. Terahertz circular Airy vortex beams [J]. Scientific Reports, 2017, 7(1): 1-8. |
[31] | Mirhosseini M, Malik M, Shi Z, et al. Efficient separation of the orbital angular momentum eigenstates of light [J]. Nature Communications, 2013, 4(1): 1-6. |
[32] | Leach J, Padgett M J, Barnett S M, et al. Measuring the orbital angular momentum of a single photon [J]. Physical Review Letters, 2002, 88(25): 257901. |
[33] | Liu Z, Yan S, Liu H, et al. Superhigh-resolution recognition of optical vortex modes assisted by a deep-learning method [J]. Physical Review Letters, 2019, 123(18): 183902. |
[34] | Hickmann J M, Fonseca E, Soares W C, et al. Unveiling a truncated optical lattice associated with a triangular aperture using light’s orbital angular momentum [J]. Physical Review Letters, 2010, 105(5): 053904. |
[35] | Mourka A, Baumgartl J, Shanor C, et al. Visualization of the birth of an optical vortex using diffraction from a triangular aperture [J]. Optics Express, 2011, 19(7): 5760-5771. |
[36] | Fu S, Zhang S, Wang T, et al. Measurement of orbital angular momentum spectra of multiplexing optical vortices [J]. Optics Express, 2016, 24(6): 6240-6248. |
[37] | Fu S, Zhai Y, Zhang J, et al. Universal orbital angular momentum spectrum analyzer for beams [J]. PhotoniX, 2020, 1(1): 1-12. |
[38] | Liu Y, Sun S, Pu J, et al. Propagation of an optical vortex beam through a diamond-shaped aperture [J]. Optics & Laser Technology, 2013, 45: 473-479. |
[39] | Ambuj A, Vyas R, Singh S. Diffraction of orbital angular momentum carrying optical beams by a circular aperture [J]. Optics Letters, 2014, 39(19): 5475-5478. |
[40] | Tao H, Liu Y, Chen Z, et al. Measuring the topological charge of vortex beams by using an annular ellipse aperture [J]. Applied Physics B, 2012, 106(4): 927-932. |
[41] | Qassim H, Miatto F M, Torres J P, et al. Limitations to the determination of a Laguerre–Gauss spectrum via projective, phase-flattening measurement [J]. Journal of the Optical Society of America B, 2014, 31(6): A20-A23. |
[42] | Choudhary S, Sampson R, Miyamoto Y, et al. Measurement of the radial mode spectrum of photons through a phase-retrieval method [J]. Optics Letters, 2018, 43(24): 6101-6104. |
[43] | Bouchard F, Valencia N H, Brandt F, et al. Measuring azimuthal and radial modes of photons [J]. Optics Express, 2018, 26(24): 31925-31941. |
[44] | Wang J, Yang J, Fazal I M, et al. Terabit free-space data transmission employing orbital angular momentum multiplexing [J]. Nature photonics, 2012, 6(7): 488-496. |
[45] | Zhou Y. Optical communication with structured photons propagating through dynamic, aberrating media[D]. Rochester: University of Rochester, 2021. |
[46] | Berkhout G C, Lavery M P, Courtial J, et al. Efficient sorting of orbital angular momentum states of light [J]. Physical Review Letters, 2010, 105(15): 153601. |
[47] | Wen Y, Chremmos I, Chen Y, et al. Spiral transformation for high-resolution and efficient sorting of optical vortex modes [J]. Physical Review Letters, 2018, 120(19): 193904. |
[48] | Hossack W J, Darling A M, Dahdouh A. Coordinate transformations with multiple computer-generated optical elements [J]. Journal of Modern Optics, 1987, 34(9): 1235-1250. |
[49] | Ruffato G, Massari M, Parisi G, et al. Test of mode-division multiplexing and demultiplexing in free-space with diffractive transformation optics [J]. Optics Express, 2017, 25(7): 7859-7868. |
[50] | Yang J, Liu Z, Gao S, et al. Two-dimension and high-resolution demultiplexing of coaxial multiple orbital angular momentum beams [J]. Optics Express, 2019, 27(4): 4338-4345. |
[51] | Li C, Zhao S. Efficient separating orbital angular momentum mode with radial varying phase [J]. Photonics Research, 2017, 5(4): 267-270. |
[52] | Ruffato G, Massari M, Romanato F. Compact sorting of optical vortices by means of diffractive transformation optics [J]. Optics Letters, 2017, 42(3): 551-554. |
[53] | Ruffato G, Massari M, Girardi M, et al. Non-paraxial design and fabrication of a compact OAM sorter in the telecom infrared [J]. Optics Express, 2019, 27(17): 24123-24134. |
[54] | Lightman S, Hurvitz G, Gvishi R, et al. Miniature wide-spectrum mode sorter for vortex beams produced by 3D laser printing [J]. Optica, 2017, 4(6): 605-610. |
[55] | Wan C, Chen J, Zhan Q. Compact and high-resolution optical orbital angular momentum sorter [J]. APL Photonics, 2017, 2(3): 031302. |
[56] | Lightman S, Gvishi R, Hurvitz G, et al. Shaping of light beams by 3D direct laser writing on facets of nonlinear crystals [J]. Optics Letters, 2015, 40(19): 4460-4463. |
[57] | Yan Y, Xie G, Lavery M P, et al. High-capacity millimetre-wave communications with orbital angular momentum multiplexing [J]. Nature Communications, 2014, 5(1): 5876. |
[58] | Lavery M P, Robertson D J, Berkhout G C, et al. Refractive elements for the measurement of the orbital angular momentum of a single photon [J]. Optics Express, 2012, 20(3): 2110-2115. |
[59] | Ruffato G, Girardi M, Massari M, et al. A compact diffractive sorter for high-resolution demultiplexing of orbital angular momentum beams [J]. Scientific Reports, 2018, 8(1): 1-12. |
[60] | Wen Y, Chremmos I, Chen Y, et al. High-resolution and compact vortex mode sorters based on a spiral transformation [C]//2018 Conference on Lasers and Electro-Optics (CLEO), IEEE, 2018: 1-2. |
[61] | Huo Y, Yang G, Gu B. Realization of unitary transform and general linear transformation by optical methods—(I)Possibility analysis [J]. Acta Physica Sinica, 1975, 24(6): 438-447. (in Chinese) |
[62] | Fontaine N K, Ryf R, Chen H, et al. Laguerre-Gaussian mode sorter [J]. Nature Communications, 2019, 10(1): 1-7. |
[63] | He L, Lin Z, Wen Y, et al. An inverse design method combining particle swarm optimization and wavefront matching method for multiplane light conversion [C]//Optical Society of America, 2020: FM7D.5. |
[64] | Lin Z, Wen Y, Chen Y, et al. Transmissive multi-plane light conversion for demultiplexing orbital angular momentum modes [C]//Optical Society of America, 2020: SF1J. 5. |
[65] | Bian Y, Li Y, Li W, et al. Modes multiplexing conversion based on multi-plane light conversion [C]//Optical Society of America, 2020: M4A.252. |
[66] | Zhao Q, Hao S, Wang Y, et al. Orbital angular momentum detection based on diffractive deep neural network [J]. Optics Communications, 2019, 443: 245-249. |
[67] | Huang Z, Wang P, Liu J, et al. All-optical signal processing of vortex beams with diffractive deep neural networks [J]. Physical Review Applied, 2021, 15(1): 014037. |
[68] | Khonina S N, Kotlyar V V, Skidanov R V, et al. Gauss–Laguerre modes with different indices in prescribed diffraction orders of a diffractive phase element [J]. Optics Communications, 2000, 175(4-6): 301-308. |
[69] | Gibson G, Courtial J, Padgett M J, et al. Free-space information transfer using light beams carrying orbital angular momentum [J]. Optics Express, 2004, 12(22): 5448-5456. |
[70] | Lavery M P, Berkhout G C, Courtial J, et al. Measurement of the light orbital angular momentum spectrum using an optical geometric transformation [J]. Journal of Optics, 2011, 13(6): 064006. |
[71] | Malik M, Mirhosseini M, Lavery M P, et al. Direct measurement of a 27-dimensional orbital-angular-momentum state vector [J]. Nature Communications, 2014, 5(1): 4115. |
[72] | Potoček V, Miatto F M, Mirhosseini M, et al. Quantum hilbert hotel [J]. Physical Review Letters, 2015, 115(16): 160505. |
[73] | Ruffato G, Massari M, Romanato F. Multiplication and division of the orbital angular momentum of light with diffractive transformation optics [J]. Light: Science & Applications, 2019, 8(1): 1-13. |
[74] | Takashima S, Kobayashi H, Iwashita K. Integer multiplier for the orbital angular momentum of light using a circular-sector transformation [J]. Physical Review A, 2019, 100(6): 063822. |
[75] | Wen Y, Chremmos I, Chen Y, et al. Arbitrary multiplication and division of the orbital angular momentum of light [J]. Physical Review Letters, 2020, 124(21): 213901. |
[76] | Zhou H, Dong J, Wang J, et al. Orbital angular momentum divider of light [J]. IEEE Photonics Journal, 2017, 9(1): 1-8. |
[77] | Zhao Z, Ren Y, Xie G, et al. Invited Article: Division and multiplication of the state order for data-carrying orbital angular momentum beams [J]. APL Photonics, 2016, 1(9): 090802. |
[78] | Ruffato G, Romanato F. Algebra of light: multiplication and division of orbital angular momentum [C]//2020 Italian Conference on Optics and Photonics (ICOP), IEEE, 2020: 1-4. |
[79] | Wen Y, Chremmos I, Chen Y, et al. Compact and high-performance vortex mode sorter for multi-dimensional multiplexed fiber communication systems [J]. Optica, 2020, 7(3): 254-262. |
[80] | Fickler R, Lapkiewicz R, Huber M, et al. Interface between path and orbital angular momentum entanglement for high-dimensional photonic quantum information [J]. Nature Communications, 2014, 5(1): 5502. |
[81] | Walsh G F. Pancharatnam-Berry optical element sorter of full angular momentum eigenstate [J]. Optics Express, 2016, 24(6): 6689-6704. |
[82] | Ruffato G, Brasselet E, Massari M, et al. Electrically activated spin-controlled orbital angular momentum multiplexer [J]. Applied Physics Letters, 2018, 113(1): 011109. |
[83] | Fontaine N K, Ryf R, Chen H, et al. Laguerre-Gaussian mode sorters of high spatial mode count [C]//International Society for Optics and Photonics, 2020: 1120319. |