Skip to main content
SpringerLink
Log in

Modulation of orbital angular momentum on the propagation dynamics of light fields

  • Review Article
  • Published:
Frontiers of Optoelectronics Aims and scope Submit manuscript

Abstract

Optical vortices carrying orbital angular momentum (OAM) have attracted extensive attention in recent decades because of their interesting applications in optical trapping, optical machining, optical communication, quantum information, and optical microscopy. Intriguing effects induced by OAMs, such as angular momentum conversion, spin Hall effect of light (SHEL), and spin–orbital interaction, have also gained increasing interest. In this article, we provide an overview of the modulations of OAMs on the propagation dynamics of scalar and vector fields in free space. First, we introduce the evolution of canonical and noncanonical optical vortices and analyze the modulations by means of local spatial frequency. Second, we review the Pancharatnam–Berry (PB) phases arising from spin–orbital interaction and reveal the control of beam evolution referring to novel behavior such as spindependent splitting and polarization singularity conversion. Finally, we discuss the propagation and focusing properties of azimuthally broken vector vortex beams.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Poynting J. The wave motion of a revolving shaft, and a suggestion as to the angular momentum in a beam of circularly polarised light. Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, 1909, 82(557): 560–567

    MATH  Google Scholar 

  2. O’Neil A T, MacVicar I, Allen L, Padgett M J. Intrinsic and extrinsic nature of the orbital angular momentum of a light beam. Physical Review Letters, 2002, 88(5): 053601

    Google Scholar 

  3. Barnett S M, Allen L, Cameron R P, Gilson C R, Padgett M J, Speirits F C, Yao A M. On the natures of the spin and orbital parts of optical angular momentum. Journal of Optics, 2016, 18(6): 064004

    Google Scholar 

  4. Allen L, Beijersbergen M W, Spreeuw R J, Woerdman J P. Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes. Physical Review A, Atomic, Molecular, and Optical Physics, 1992, 45(11): 8185

    Google Scholar 

  5. He H, Friese ME, Heckenberg N R, Rubinsztein-Dunlop H. Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity. Physical Review Letters, 1995, 75(5): 826–829

    Google Scholar 

  6. Allen L, Padgett M, BabikerMI V. The orbital angular momentum of light. Progress in Optics, 1999, 39: 291–372

    MathSciNet  Google Scholar 

  7. Padgett M, Allen L. The Poynting vector in Laguerre-Gaussian laser modes. Optics Communications, 1995, 121(1–3): 36–40

    Google Scholar 

  8. Curtis J E, Grier D G. Structure of optical vortices. Physical Review Letters, 2003, 90(13): 133901

    Google Scholar 

  9. Berkhout G C, Lavery M P, Courtial J, Beijersbergen M W, Padgett M J. Efficient sorting of orbital angular momentum states of light. Physical Review Letters, 2010, 105(15): 153601

    Google Scholar 

  10. Franke-Arnold S, Allen L, Padgett M. Advances in optical angular momentum. Laser & Photonics Reviews, 2008, 2(4): 299–313

    Google Scholar 

  11. Onoda M, Murakami S, Nagaosa N. Hall effect of light. Physical Review Letters, 2004, 93(8): 083901

    Google Scholar 

  12. Bliokh K Y, Bliokh Y P. Conservation of angular momentum, transverse shift, and spin Hall effect in reflection and refraction of an electromagnetic wave packet. Physical Review Letters, 2006, 96(7): 073903

    Google Scholar 

  13. Hosten O, Kwiat P. Observation of the spin hall effect of light via weak measurements. Science, 2008, 319(5864): 787–790

    Google Scholar 

  14. Bliokh K Y, Smirnova D, Nori F. Quantum spin Hall effect of light. Science, 2015, 348(6242): 1448–1451

    MathSciNet  MATH  Google Scholar 

  15. Liu Y C, Ke Y G, Luo H L, Wen S C. Photonic spin Hall effect in metasurfaces: a brief review. Nanophotonics, 2017, 6(1): 51–70

    Google Scholar 

  16. Bliokh K Y, Rodríguez-Fortuño F J, Nori F, Zayats A V. Spin-orbit interactions of light. Nature Photonics, 2015, 9(12): 796–808

    Google Scholar 

  17. Bliokh K Y, Shadrivov I V, Kivshar Y S. Goos-Hänchen and Imbert-Fedorov shifts of polarized vortex beams. Optics Letters, 2009, 34(3): 389–391

    Google Scholar 

  18. Kong L J, Wang X L, Li S M, Li Y N, Chen J, Gu B, Wang H T. Spin Hall effect of reflected light from an air-glass interface around the Brewster’s angle. Applied Physics Letters, 2012, 100(7): 071109

    Google Scholar 

  19. Kapitanova P V, Ginzburg P, Rodríguez-Fortuño F J, Filonov D S, Voroshilov P M, Belov P A, Poddubny A N, Kivshar Y S,Wurtz G A, Zayats A V. Photonic spin Hall effect in hyperbolic metamaterials for polarization-controlled routing of subwavelength modes. Nature Communications, 2014, 5: 3226

    Google Scholar 

  20. Zhang Y, Li P, Liu S, Han L, Cheng H C, Zhao J L. Optimized weak measurement for spatial spin-dependent shifts at Brewster angle. Applied Physics B, Lasers and Optics, 2016, 122(7): 184

    Google Scholar 

  21. Bliokh K Y. Geometrical optics of beams with vortices: Berry phase and orbital angular momentum Hall effect. Physical Review Letters, 2006, 97(4): 043901

    MathSciNet  Google Scholar 

  22. Merano M, Hermosa N, Woerdman J P, Aiello A. How orbital angular momentum affects beam shifts in optical reflection. Physical Review A, Atomic, Molecular, and Optical Physics, 2010, 82(2): 023817

    Google Scholar 

  23. Dooghin A V, Kundikova N D, Liberman V S, Zel’dovich B Y. Optical Magnus effect. Physical Review A, Atomic, Molecular, and Optical Physics, 1992, 45(11): 8204–8208

    Google Scholar 

  24. Van Enk S J, Nienhuis G. Spin and orbital angular momentum of photons. Europhysics Letters, 1994, 25(7): 497–501

    Google Scholar 

  25. Yao A M, Padgett M J. Orbital angular momentum: origins, behavior and applications. Advances in Optics and Photonics, Fig. 20 Distributions of s3 for fan-shaped beams with angular width of p/2, after propagating 25 cm. (a) m = 2, l = 2; (b) m = 2, l = -1; (c) m = 2, l = 3 [145] 2011, 3(2): 161–204

    Google Scholar 

  26. Allen L, Padgett M J. The Poynting vector in Laguerre–Gaussian beams and the interpretation of their angular momentum density. Optics Communications, 2000, 184(1–4): 67–71

    Google Scholar 

  27. Barnett S M, Allen L. Orbital angular momentum and nonparaxial light beams. Optics Communications, 1994, 110(5–6): 670–678

    Google Scholar 

  28. Babiker M, Power W L, Allen L. Light-induced torque on moving atoms. Physical Review Letters, 1994, 73(9): 1239–1242

    Google Scholar 

  29. Simpson N B, Dholakia K, Allen L, Padgett M J. Mechanical equivalence of spin and orbital angular momentum of light: an optical spanner. Optics Letters, 1997, 22(1): 52–54

    Google Scholar 

  30. Grier D G. A revolution in optical manipulation. Nature, 2003, 424 (6950): 810–816

    Google Scholar 

  31. Padgett M, Allen L. Optical tweezers and spanners. PhysicsWorld, 1997, 10(9): 35–40

    Google Scholar 

  32. Bowman R W, Padgett M J. Optical trapping and binding. Reports on Progress in Physics, 2013, 76(2): 026401

    Google Scholar 

  33. Bozinovic N, Yue Y, Ren Y, Tur M, Kristensen P, Huang H, Willner A E, Ramachandran S. Terabit-scale orbital angular momentum mode division multiplexing in fibers. Science, 2013, 340(6140): 1545–1548

    Google Scholar 

  34. Zhang Y, Djordjevic I B, Gao X. On the quantum-channel capacity for orbital angular momentum-based free-space optical communications. Optics Letters, 2012, 37(15): 3267–3269

    Google Scholar 

  35. Leach J, Jack B, Romero J, Jha A K, Yao A M, Franke-Arnold S, Ireland D G, Boyd R W, Barnett S M, Padgett M J. Quantum correlations in optical angle-orbital angular momentum variables. Science, 2010, 329(5992): 662–665

    Google Scholar 

  36. Wang J. Advances in communications using optical vortices. Photonics Research, 2016, 4(5): B14–B28

    Google Scholar 

  37. Malik M, Mirhosseini M, Lavery M P J, Leach J, Padgett M J, Boyd R W. Direct measurement of a 27-dimensional orbitalangular-momentum state vector. Nature Communications, 2014, 5: 3115

    Google Scholar 

  38. Su T, Scott R P, Djordjevic S S, Fontaine N K, Geisler D J, Cai X, Yoo S J B. Demonstration of free space coherent optical communication using integrated silicon photonic orbital angular momentum devices. Optics Express, 2012, 20(9): 9396–9402

    Google Scholar 

  39. Yan Y, Yue Y, Huang H, Yang J Y, Chitgarha M R, Ahmed N, Tur M, Dolinar S J, Willner A E. Efficient generation and multiplexing of optical orbital angular momentum modes in a ring fiber by using multiple coherent inputs. Optics Letters, 2012, 37(17): 3645–3647

    Google Scholar 

  40. Wang J, Yang J Y, Fazal I M, Ahmed N, Yan Y, Huang H, Ren Y X, Yue Y, Dolinar S, Tur M, Willner A E. Terabit free-space data transmission employing orbital angular momentum multiplexing. Nature Photonics, 2012, 6(7): 488–496

    Google Scholar 

  41. Willner A E, Huang H, Yan Y, Ren Y, Ahmed N, Xie G, Bao C, Li L, Cao Y, Zhao Z,Wang J, LaveryMP J, TurM, Ramachandran S, Molisch A F, Ashrafi N, Ashrafi S. Optical communications using orbital angular momentum beams. Advances in Optics and Photonics, 2015, 7(1): 66–106

    Google Scholar 

  42. Mair A, Vaziri A, Weihs G, Zeilinger A. Entanglement of the orbital angular momentum states of photons. Nature, 2001, 412 (6844): 313–316

    Google Scholar 

  43. Oemrawsingh S S, Ma X, Voigt D, Aiello A, Eliel E R,’ t Hooft G W, Woerdman J P. Experimental demonstration of fractional orbital angular momentum entanglement of two photons. Physical Review Letters, 2005, 95(24): 240501

    Google Scholar 

  44. Karimi E, Marrucci L, de Lisio C, Santamato E. Time-division multiplexing of the orbital angular momentum of light. Optics Letters, 2012, 37(2): 127–129

    Google Scholar 

  45. Müller M, Bounouar S, Jöns K D, Glässl M, Michler P. Ondemand generation of indistinguishable polarization-entangled photon pairs. Nature Photonics, 2014, 8(3): 224–228

    Google Scholar 

  46. Wang X L, Cai X D, Su Z E, Chen M C, Wu D, Li L, Liu N L, Lu C Y, Pan J W. Quantum teleportation of multiple degrees of freedom of a single photon. Nature, 2015, 518(7540): 516–519

    Google Scholar 

  47. Lavery M P J, Speirits F C, Barnett S M, Padgett M J. Detection of a spinning object using light’s orbital angular momentum. Science, 2013, 341(6145): 537–540

    Google Scholar 

  48. Löffler W, Aiello A,Woerdman J P. Observation of orbital angular momentum sidebands due to optical reflection. Physical Review Letters, 2012, 109(11): 113602

    Google Scholar 

  49. Chen R P, Chen Z, Chew K H, Li P G, Yu Z, Ding J, He S. Structured caustic vector vortex optical field: manipulating optical angular momentum flux and polarization rotation. Scientific Reports, 2015, 5(1): 10628

    Google Scholar 

  50. Pan Y, Gao X Z, Ren Z C, Wang X L, Tu C, Li Y, Wang H T. Arbitrarily tunable orbital angular momentum of photons. Scientific Reports, 2016, 6(1): 29212

    Google Scholar 

  51. Beijersbergen M W, Allen L, Van der Veen H, Woerdman J P. Astigmatic laser mode converters and transfer of orbital angular momentum. Optics Communications, 1993, 96(1-3): 123–132

    Google Scholar 

  52. Indebetouw G. Optical vortices and their propagation. Journal of Modern Optics, 1993, 40(1): 73–87

    Google Scholar 

  53. Roux F S. Dynamical behavior of optical vortices. Journal of the Optical Society of America B, Optical Physics, 1995, 12(7): 1215–1221

    Google Scholar 

  54. Zhao X Y, Zhang J C, Pang X Y, Wan G B. Properties of a strongly focused Gaussian beam with an off-axis vortex. Optics Communications, 2017, 389: 275–282

    Google Scholar 

  55. Rozas D, Law C T, Swartzlander G A Jr. Propagation dynamics of optical vortices. Journal of the Optical Society of America B, Optical Physics, 1997, 14(11): 3054–3065

    Google Scholar 

  56. Gan X T, Zhao J L, Liu S, Fang L. Generation and motion control of optical multi-vortex. Chinese Optics Letters, 2009, 7(12): 1142–1145

    Google Scholar 

  57. Peng Y, Gan X T, Ju P, Wang Y D, Zhao J L. Measuring topological charges of optical vortices with multi-singularity using a cylindrical lens. Chinese Physics Letters, 2015, 32(2): 024201

    Google Scholar 

  58. Padgett M J, Miatto F M, Lavery M P J, Zeilinger A, Boyd R W. Divergence of an orbital-angular-momentum-carrying beam upon propagation. New Journal of Physics, 2015, 17(2): 023011

    Google Scholar 

  59. Porras M A, Borghi R, Santarsiero M. Relationship between elegant Laguerre-Gauss and Bessel-Gauss beams. Journal of the Optical Society of America A, Optics, Image Science, and Vision, 2001, 18(1): 177–184

    Google Scholar 

  60. Mendoza-Hernández J, Arroyo-Carrasco M L, Iturbe-Castillo M D, Chávez-Cerda S. Laguerre-Gauss beams versus Bessel beams showdown: peer comparison. Optics Letters, 2015, 40(16): 3739–3742

    Google Scholar 

  61. Bencheikh A, Fromager M, Ameur K A. Generation of Laguerre-Gaussian LGp0 beams using binary phase diffractive optical elements. Applied Optics, 2014, 53(21): 4761–4767

    Google Scholar 

  62. Haddadi S, Louhibi D, Hasnaoui A, Harfouche A, Aït-Ameur K. Spatial properties of a diffracted high-order radial Laguerre–Gauss LGp0 beam. Laser Physics, 2015, 25(12): 125002

    Google Scholar 

  63. Li L, Xie G D, Yan Y, Ren Y X, Liao P C, Zhao Z, Ahmed N, Wang Z, Bao C J, Willner A J, Ashrafi S, Tur M, Willner A E. Power loss mitigation of orbital-angular-momentum-multiplexed free-space optical links using nonzero radial index Laguerre–Gaussian beams. Journal of the Optical Society of America B, Optical Physics, 2017, 34(1): 1–6

    Google Scholar 

  64. Hamazaki J, Mineta Y, Oka K, Morita R. Direct observation of Gouy phase shift in a propagating optical vortex. Optics Express, 2006, 14(18): 8382–8392

    Google Scholar 

  65. Amaral A M, Falcão-Filho E L, de Araújo C B. Shaping optical beams with topological charge. Optics Letters, 2013, 38(9): 1579–1581

    Google Scholar 

  66. Hermosa N P II, Manaois C O. Phase structure of helico-conical optical beams. Optics Communications, 2007, 271(1): 178–183

    Google Scholar 

  67. Alonzo C, Rodrigo P J, Glückstad J. Helico-conical optical beams: a product of helical and conical phase fronts. Optics Express, 2005, 13(5): 1749–1760

    Google Scholar 

  68. Daria V R, Palima D Z, Glückstad J. Optical twists in phase and amplitude. Optics Express, 2011, 19(2): 476–481

    Google Scholar 

  69. Götte J B, O’Holleran K, Preece D, Flossmann F, Franke-Arnold S, Barnett S M, Padgett M J. Light beams with fractional orbital angular momentum and their vortex structure. Optics Express, 2008, 16(2): 993–1006

    Google Scholar 

  70. Nugrowati A M, StamW G, Woerdman J P. Position measurement of non-integer OAM beams with structurally invariant propagation. Optics Express, 2012, 20(25): 27429–27441

    Google Scholar 

  71. Maji S, Brundavanam M M. Controlled noncanonical vortices from higher-order fractional screw dislocations. Optics Letters, 2017, 42(12): 2322–2325

    Google Scholar 

  72. Dai H T, Liu Y J, Luo D, Sun X W. Propagation properties of an optical vortex carried by an Airy beam: experimental implementation. Optics Letters, 2011, 36(9): 1617–1619

    Google Scholar 

  73. Chu X. Propagation of an Airy beam with a spiral phase. Optics Letters, 2012, 37(24): 5202–5204

    Google Scholar 

  74. Rosales-Guzmán C, Mazilu M, Baumgartl J, Rodríguez-Fajardo V, Ramos-García R, Dholakia K. Collision of propagating vortices embedded within Airy beams. Journal of Optics, 2013, 15(4): 044001

    Google Scholar 

  75. Kim G H, Lee H J, Kim L U, Suk H. Propagation dynamics of optical vortices with anisotropic phase profiles. Journal of the Optical Society of America B, Optical Physics, 2003, 20(2): 351–359

    Google Scholar 

  76. Curtis J E, Grier D G. Modulated optical vortices. Optics Letters, 2003, 28(11): 872–874

    Google Scholar 

  77. Rodrigo J A, Alieva T, Abramochkin E, Castro I. Shaping of light beams along curves in three dimensions. Optics Express, 2013, 21 (18): 20544–20555

    Google Scholar 

  78. Rodrigo J A, Alieva T. Freestyle 3D laser traps: tools for studying light-driven particle dynamics and beyond. Optica, 2015, 2(9): 812–815

    Google Scholar 

  79. Li P, Liu S, Peng T, Xie G, Gan X, Zhao J. Spiral autofocusing Airy beams carrying power-exponent-phase vortices. Optics Express, 2014, 22(7): 7598–7606

    Google Scholar 

  80. Chremmos I, Efremidis N K, Christodoulides D N. Pre-engineered abruptly autofocusing beams. Optics Letters, 2011, 36(10): 1890–1892

    Google Scholar 

  81. Papazoglou D G, Efremidis N K, Christodoulides D N, Tzortzakis S. Observation of abruptly autofocusing waves. Optics Letters, 2011, 36(10): 1842–1844

    Google Scholar 

  82. Jiang Y, Huang K, Lu X. Propagation dynamics of abruptly autofocusing Airy beams with optical vortices. Optics Express, 2012, 20(17): 18579–18584

    Google Scholar 

  83. Chen B, Chen C, Peng X, Peng Y, Zhou M, Deng D. Propagation of sharply autofocused ring Airy Gaussian vortex beams. Optics Express, 2015, 23(15): 19288–19298

    Google Scholar 

  84. Zhang Y, Li P, Liu S, Han L, Cheng H, Zhao J. Manipulating spindependent splitting of vector abruptly autofocusing beam by encoding cosine-azimuthal variant phases. Optics Express, 2016, 24(25): 28409–28418

    Google Scholar 

  85. Wang F, Zhao C L, Dong Y, Dong Y M, Cai Y J. Generation and tight-focusing properties of cylindrical vector circular Airy beams. Applied Physics B, Lasers and Optics, 2014, 117(3): 905–913

    Google Scholar 

  86. Wang X L, Ding J, Ni W J, Guo C S, Wang H T. Generation of arbitrary vector beams with a spatial light modulator and a common path interferometric arrangement. Optics Letters, 2007, 32(24): 3549–3551

    Google Scholar 

  87. Wang X L, Chen J, Li Y, Ding J, Guo C S, Wang H T. Optical orbital angular momentum from the curl of polarization. Physical Review Letters, 2010, 105(25): 253602

    Google Scholar 

  88. Liu S, Li P, Peng T, Zhao J. Generation of arbitrary spatially variant polarization beams with a trapezoid Sagnac interferometer. Optics Express, 2012, 20(19): 21715–21721

    Google Scholar 

  89. Marrucci L, Manzo C, Paparo D. Optical spin-to-orbital angular momentum conversion in inhomogeneous anisotropic media. Physical Review Letters, 2006, 96(16): 163905

    Google Scholar 

  90. Biener G, Niv A, Kleiner V, Hasman E. Formation of helical beams by use of Pancharatnam-Berry phase optical elements. Optics Letters, 2002, 27(21): 1875–1877

    Google Scholar 

  91. Yu N, Genevet P, Kats M A, Aieta F, Tetienne J P, Capasso F, Gaburro Z. Light propagation with phase discontinuities: generalized laws of reflection and refraction. Science, 2011, 334(6054): 333–337

    Google Scholar 

  92. Yu N, Capasso F. Flat optics with designer metasurfaces. Nature Materials, 2014, 13(2): 139–150

    Google Scholar 

  93. Zhang L, Mei S T, Huang K, Qiu C W. Advances in full control of electromagnetic waves with metasurfaces. Advanced Optical Materials, 2016, 4(6): 818–833

    Google Scholar 

  94. Estakhri N M, Alù A. Recent progress in gradient metasurfaces. Journal of the Optical Society of America B, Optical Physics, 2016, 33(2): A21–A30

    Google Scholar 

  95. Epstein A, Eleftheriades G V. Huygens’ metasurfaces via the equivalence principle: design and applications. Journal of the Optical Society of America B, Optical Physics, 2016, 33(2): A31–A50

    Google Scholar 

  96. Marrucci L, Karimi E, Slussarenko S, Piccirillo B, Santamato E, Nagali E, Sciarrino F. Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications. Journal of Optics, 2011, 13(6): 064001

    Google Scholar 

  97. Cardano F, Marrucci L. Spin-orbit photonics. Nature Photonics, 2015, 9(12): 776–778

    Google Scholar 

  98. Berry M V. The adiabatic phase and Pancharatnam phase for polarized light. Journal of Modern Optics, 1987, 34(11): 1401–1407

    MathSciNet  MATH  Google Scholar 

  99. Liu S, Li P, Zhang Y, Gan X, Wang M, Zhao J. Longitudinal spin separation of light and its performance in three-dimensionally controllable spin-dependent focal shift. Scientific Reports, 2016, 6 (1): 20774

    Google Scholar 

  100. Milione G, Sztul H I, Nolan D A, Alfano R R. Higher-order Poincaré sphere, stokes parameters, and the angular momentum of light. Physical Review Letters, 2011, 107(5): 053601

    Google Scholar 

  101. Wang X L, Li Y, Chen J, Guo C S, Ding J, Wang H T. A new type of vector fields with hybrid states of polarization. Optics Express, 2010, 18(10): 10786–10795

    Google Scholar 

  102. Yi X N, Liu Y C, Ling X H, Zhou X X, Ke Y G, Luo H L, Wen S C, Fan D Y. Hybrid-order Poincaré sphere. Physical Review A, Atomic, molecular, and optical physics, 2015, 91: 023801

    Google Scholar 

  103. Ren Z C, Kong L J, Li S M, Qian S X, Li Y, Tu C, Wang H T. Generalized Poincaré sphere. Optics Express, 2015, 23(20): 26586–26595

    Google Scholar 

  104. Gorodetski Y, Biener G, Niv A, Kleiner V, Hasman E. Spacevariant polarization manipulation for far-field polarimetry by use of subwavelength dielectric gratings. Optics Letters, 2005, 30(17): 2245–2247

    Google Scholar 

  105. Niv A, Biener G, Kleiner V, Hasman E. Rotating vectorial vortices produced by space-variant subwavelength gratings. Optics Letters, 2005, 30(21): 2933–2935

    Google Scholar 

  106. Biener G, Gorodetski Y, Niv A, Kleiner V, Hasman E. Manipulation of polarization-dependent multivortices with quasiperiodic subwavelength structures. Optics Letters, 2006, 31(11): 1594–1596

    Google Scholar 

  107. Shitrit N, Yulevich I, Maguid E, Ozeri D, Veksler D, Kleiner V, Hasman E. Spin-optical metamaterial route to spin-controlled photonics. Science, 2013, 340(6133): 724–726

    MathSciNet  MATH  Google Scholar 

  108. Yin X, Ye Z, Rho J,Wang Y, Zhang X. Photonic spin Hall effect at metasurfaces. Science, 2013, 339(6126): 1405–1407

    Google Scholar 

  109. Slussarenko S, Alberucci A, Jisha C P, Piccirillo B, Santamato E, Assanto G, Marrucci L. Guiding light via geometric phases. Nature Photonics, 2016, 10(9): 571–575

    Google Scholar 

  110. Philip GM, Kumar V, Milione G, Viswanathan N K. Manifestation of the Gouy phase in vector-vortex beams. Optics Letters, 2012, 37 (13): 2667–2669

    Google Scholar 

  111. Niv A, Biener G, Kleiner V, Hasman E. Manipulation of the Pancharatnam phase in vectorial vortices. Optics Express, 2006, 14 (10): 4208–4220

    Google Scholar 

  112. Shu W X, Ke Y G, Liu Y C, Ling X H, Luo H L, Yin X B. Radial spin Hall effect of light. Physical Review A, Atomic, molecular, and optical physics, 2016, 93(1): 013839

    Google Scholar 

  113. Li P, Zhang Y, Liu S, Ma C, Han L, Cheng H, Zhao J. Generation of perfect vectorial vortex beams. Optics Letters, 2016, 41(10): 2205–2208

    Google Scholar 

  114. Zhang W, Liu S, Li P, Jiao X, Zhao J. Controlling the polarization singularities of the focused azimuthally polarized beams. Optics Express, 2013, 21(1): 974–983

    Google Scholar 

  115. Baumann S M, Kalb D M, MacMillan L H, Galvez E J. Propagation dynamics of optical vortices due to Gouy phase. Optics Express, 2009, 17(12): 9818–9827

    Google Scholar 

  116. Liu S, Wang M, Li P, Zhang P, Zhao J. Abrupt polarization transition of vector autofocusing Airy beams. Optics Letters, 2013, 38(14): 2416–2418

    Google Scholar 

  117. Bomzon Z, Niv A, Biener G, Kleiner V, Hasman E. Nondiffracting periodically space-variant polarization beams with subwavelength gratings. Applied Physics Letters, 2002, 80(20): 3685–3687

    Google Scholar 

  118. Bomzon Z, Biener G, Kleiner V, Hasman E. Space-variant Pancharatnam-Berry phase optical elements with computergenerated subwavelength gratings. Optics Letters, 2002, 27(13): 1141–1143

    Google Scholar 

  119. Ling X H, Zhou X X, Yi X N, ShuWX, Liu Y C, Chen S Z, Luo H L, Wen S C, Fan D Y. Giant photonic spin Hall effect in momentum space in a structured metamaterial with spatially varying birefringence. Light, Science & Applications, 2015, 4(5): e290

    Google Scholar 

  120. Ke Y G, Liu Y C, He Y L, Zhou J X, Luo H L, Wen S C. Realization of spin-dependent splitting with arbitrary intensity patterns based on all-dielectric metasurfaces. Applied Physics Letters, 2015, 107(4): 041107

    Google Scholar 

  121. Gorodetski Y, Biener G, Niv A, Kleiner V, Hasman E. Optical properties of polarization-dependent geometric phase elements with partially polarized light. Optics Communications, 2006, 266 (2): 365–375

    Google Scholar 

  122. Ke Y G, Liu Y C, Zhou J X, Liu Y Y, Luo H L, Wen S C. Optical integration of Pancharatnam-Berry phase lens and dynamical phase lens. Applied Physics Letters, 2016, 108(10): 101102

    Google Scholar 

  123. Hasman E, Kleiner V, Biener G, Niv A. Polarization dependent focusing lens by use of quantized Pancharatnam–Berry phase diffractive optics. Applied Physics Letters, 2003, 82(3): 328–330

    Google Scholar 

  124. Ni X J, Ishii S, Kildishev A V, Shalaev V M. Ultra-thin, planar, Babinet-inverted plasmonic metalenses. Light, Science & Applications, 2013, 2(4): e72

    Google Scholar 

  125. Gao K, Cheng H H, Bhowmik A K, Bos P J. Thin-film Pancharatnam lens with low f-number and high quality. Optics Express, 2015, 23(20): 26086–26094

    Google Scholar 

  126. Ding X, Monticone F, Zhang K, Zhang L, Gao D, Burokur S N, de Lustrac A, Wu Q, Qiu C W, Alù A. Ultrathin pancharatnam-berry metasurface with maximal cross-polarization efficiency. Advanced Materials, 2015, 27(7): 1195–1200

    Google Scholar 

  127. Chen X Z, Chen M, Mehmood M Q, Wen D D, Yue F Y, Qiu CW, Zhang S. Longitudinal multifoci metalens for circularly polarized light. Advanced Optical Matericals, 2015, 3(9): 1201–1206

    Google Scholar 

  128. Li X, Lan T H, Tien C H, Gu M. Three-dimensional orientationunlimited polarization encryption by a single optically configured vectorial beam. Nature Communications, 2012, 3: 998

    Google Scholar 

  129. Zheng G, Mühlenbernd H, Kenney M, Li G, Zentgraf T, Zhang S. Metasurface holograms reaching 80% efficiency. Nature Nanotechnology, 2015, 10(4): 308–312

    Google Scholar 

  130. Cardano F, Karimi E, Marrucci L, de Lisio C, Santamato E. Generation and dynamics of optical beams with polarization singularities. Optics Express, 2013, 21(7): 8815–8820

    Google Scholar 

  131. Moreno I, Davis J A, Sánchez-López M M, Badham K, Cottrell D M. Nondiffracting Bessel beams with polarization state that varies with propagation distance. Optics Letters, 2015, 40(23): 5451–5454

    Google Scholar 

  132. Davis J A, Moreno I, Badham K, Sánchez-López M M, Cottrell D M. Nondiffracting vector beams where the charge and the polarization state vary with propagation distance. Optics Letters, 2016, 41(10): 2270–2273

    Google Scholar 

  133. Li P, Zhang Y, Liu S, Cheng H, Han L, Wu D, Zhao J. Generation and self-healing of vector Bessel-Gauss beams with variant state of polarizations upon propagation. Optics Express, 2017, 25(5): 5821–5831

    Google Scholar 

  134. Gao X Z, Pan Y, Li S M, Wang D, Li Y N, Tu C H, Wang H T. Vector optical fields broken in the spatial frequency domain. Physical Review A, Atomic, molecular, and optical physics, 2016, 93(3): 033834

    Google Scholar 

  135. Davis J A, Bentley J B. Azimuthal prism effect with partially blocked vortex-producing lenses. Optics Letters, 2005, 30(23): 3204–3206

    Google Scholar 

  136. Vyas S, Kozawa Y, Sato S. Self-healing of tightly focused scalar and vector Bessel-Gauss beams at the focal plane. Journal of the Optical Society of America A, Optics, Image Science, and Vision, 2011, 28(5): 837–843

    Google Scholar 

  137. Vyas S, Niwa M, Kozawa Y, Sato S. Diffractive properties of obstructed vector Laguerre-Gaussian beam under tight focusing condition. Journal of the Optical Society of America A, Optics, Image Science, and Vision, 2011, 28(7): 1387–1394

    Google Scholar 

  138. Wang X L, Lou K, Chen J, Gu B, Li Y N, Wang H T. Unveiling locally linearly polarized vector fields with broken axial symmetry. Physical Review A, Atomic, molecular, and optical physics, 2011, 83(6): 063813

    Google Scholar 

  139. Jiao X, Liu S,Wang Q, Gan X, Li P, Zhao J. Redistributing energy flow and polarization of a focused azimuthally polarized beam with rotationally symmetric sector-shaped obstacles. Optics Letters, 2012, 37(6): 1041–1043

    Google Scholar 

  140. Wu G F, Wang F, Cai Y J. Generation and self-healing of a radially polarized Bessel-Gauss beam. Physical Review A, Atomic, molecular, and optical physics, 2014, 89(4): 043807

    Google Scholar 

  141. Franke-Arnold S, Barnett S M, Yao E, Leach J, Courtial J, Padgett M. Uncertainty principle for angular position and angular momentum. New Journal of Physics, 2004, 6: 103

    Google Scholar 

  142. Yao E, Franke-Arnold S, Courtial J, Barnett S, Padgett M. Fourier relationship between angular position and optical orbital angular momentum. Optics Express, 2006, 14(20): 9071–9076

    Google Scholar 

  143. Jack B, Padgett M J, Franke-Arnold S. Angular diffraction. New Journal of Physics, 2008, 10(10): 103013

    Google Scholar 

  144. Li P, Liu S, Xie G, Peng T, Zhao J. Modulation mechanism of multi-azimuthal masks on the redistributions of focused azimuthally polarized beams. Optics Express, 2015, 23(6): 7131–7139

    Google Scholar 

  145. Zhang Y, Li P, Liu S, Zhao J. Unveiling the photonic spin Hall effect of freely propagating fan-shaped cylindrical vector vortex beams. Optics Letters, 2015, 40(19): 4444–4447

    Google Scholar 

  146. Cai Y J, Lü X. Propagation of Bessel and Bessel–Gaussian beams through an unapertured or apertured misaligned paraxial optical systems. Optics Communications, 2007, 274(1): 1–7

    Google Scholar 

  147. Liu X L, Peng X F, Liu L, Wu G F, Zhao C L, Wang F, Cai Y J. Self-reconstruction of the degree of coherence of a partially coherent vortex beam obstructed by an opaque obstacle. Applied Physics Letters, 2017, 110(18): 181104

    Google Scholar 

  148. Ling X H, Yi X N, Zhou X X, Liu Y C, ShuWX, Luo H L,Wen S C. Realization of tunable spin-dependent splitting in intrinsic photonic spin Hall effect. Applied Physics Letters, 2014, 105(15): 151101

    Google Scholar 

  149. Li P, Liu S, Zhang Y, Xie G F, Zhao J L. Experimental realization of focal field engineering of the azimuthally polarized beams modulated by multi-azimuthal masks. Journal of the Optical Society of America B, Optical Physics, 2015, 32(9): 1867–1872

    Google Scholar 

Download references

Acknowledgments

This work was funded by the National Natural Science Foundation of China (NSFC) (Grant Nos. 11634010, 11404262, 61675168, U1630125 and 61377035); Fundamental Research Funds for the Central Universities (No. 3102015ZY057); and Innovation Foundation for Doctor Dissertation of North-western Polytechnical University (No. CX201629).

Author information

Authors and Affiliations

  1. MOE Key Laboratory of Material Physics and Chemistry under Extraordinary Conditions, and Shaanxi Key Laboratory of Optical Information Technology, School of Science, Northwestern Polytechnical University, Xi’an, 710072, China

    Peng Li, Sheng Liu, Yi Zhang, Lei Han, Dongjing Wu, Huachao Cheng, Shuxia Qi, Xuyue Guo & Jianlin Zhao

Authors
  1. Peng Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sheng Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yi Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Lei Han
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Dongjing Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Huachao Cheng
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Shuxia Qi
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Xuyue Guo
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. Jianlin Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Peng Li.

Additional information

Peng Li is currently an Associate Professor at the School of Science, Northwestern Polytechnical University (NPU), Xi’an, China. He received the Ph.D. degree in Optical Engineering from the Department of Applied Physics at NPU in 2013. His research interests include structured optical fields, nanophotonics, and multi-core fibers. He has published more than 30 technical papers in optics related fields.

Sheng Liu received the Ph.D. degree in Optical Engineering from the Department of Applied Physics at Northwestern Polytechnical University (NPU) of China in 2011. He is currently an Associate Professor at the School of Science, NPU, Xi’an, China. His research interests include generation and modulation of optical fields, photonic lattices, and spatial solitons. He has published more than 50 technical papers in optics related fields.

Yi Zhang received the B.S. degree in Optical Information Science and Technology from the Department of Applied Physics at Northwestern Polytechnical University (NPU) of China in 2013. He is currently a Ph.D. student in Optical Engineering at the School of Science, NPU, China. His research interests include complex light fields, optical spin-orbital interaction. He has published 13 technical papers in optics related fields.

Lei Han received the B.S. degree in Optical Information Science and Technology from the Department of Applied Physics at Northwestern Polytechnical University (NPU) of China in 2014. He is currently a Ph.D. student in Optical Engineering at the School of Science, NPU, China. His research work focuses on the focusing properties of spatial structured light fields and its applications. Now he is visiting the National University of Singapore as a joint Ph.D. student funded by China Scholarship Council.

Dongjing Wu received the B.S. degree in Optical Information Science and Technology from the Department of Applied Physics at Northwestern Polytechnical University (NPU) of China in 2016. He is currently working toward the M.S. degree in Optical Engineering in NPU, China. His research work focuses on the construction of spatial structured light fields with longitudinally varying polarization.

Huachao Cheng received the B.S. degree in Optical Information Science and Technology from the Department of Applied Physics at Northwestern Polytechnical University (NPU) of China in 2015. He is now a Ph.D. student at the School of Science, NPU, China. His research interests are mainly in exploring the interaction between structured femtosecond pulses and materials.

Shuxia Qi received the B.S. degree in Applied Physics from Northeastern University of China in 2016. She is currently a master student at the School of Science, Northwestern Polytechnical University, China. Her research interests are mainly in constructing complex light fields, efficiently generating vector beams and exploring its spatial evolution.

Xuyue Guo received the B.S. degree in Optical Information Science and Technology from the Department of Applied Physics at Northwestern Polytechnical University (NPU) of China in 2017. He is currently a Ph.D. student at the School of Science, NPU, China. His research interests are mainly in exploring the focusing properties of vector beams and multifocal array.

Jianlin Zhao is now a Professor at the School of Science, Northwestern Polytechnical University, Xi’an, China. Prof. Zhao received his Ph.D. degree in Optics from the Xi’an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, in 1998. Prof. Zhao is also the director of the Shaanxi Key Laboratory of Optical Information Technology and the MOE Key Laboratory of Material Physics and Chemistry under Extraordinary Conditions. He has published over 480 journal and international conference papers in the fields of digital holography, light field control and information processing, nonlinear optics, micro-nano photonics and optical fiber sensors.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, P., Liu, S., Zhang, Y. et al. Modulation of orbital angular momentum on the propagation dynamics of light fields. Front. Optoelectron. 12, 69–87 (2019). https://doi.org/10.1007/s12200-017-0743-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12200-017-0743-3

Keywords

Search

Navigation