Skip to main content
SpringerLink
Log in

Orbital Angular Momentum of Light

  • Chapter
Quantum Imaging

Abstract

The study of the mechanical effects of light, including angular momentum, has a long history. The recent rapid growth of interest, however, can be traced to the observation that the Laguerre–Gaussian modes, familiar from laser physics, carry a well-defined quantity of orbital angular momentum [1]. To be specific, the mode u LG pℓ (Eq. (12.21)) propagating in the z-direction, with azimuthal dependence exp(iℓø), carries a z-component of orbital angular momentum of ℓħ per photon. This idea is strongly suggested by the powerful analogy between paraxial optics and the Schrödinger equation, together with the operator corresponding to the z-component of orbital angular momentum L z = -iħ∂/∂ø [2]. A convincing demonstration follows from an analysis of the Poynting vector and the associated angular momentum density [1, 3] as briefly described in Section 12.2.

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

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A 45, 8185 (1992).

    Article  ADS  Google Scholar 

  2. D. Marcuse, Light Transmission Optics (Van Nostrand, New York, 1972).

    Google Scholar 

  3. L. Allen, M. J. Padgett, Opt. Commun. 184, 67 (2000).

    Article  ADS  Google Scholar 

  4. L. Allen, M. J. Padgett, and M. Babiker, in Progress in Optics, vol. XXXIX, 291 (1999).

    Article  MathSciNet  Google Scholar 

  5. L. Allen, S. M. Barnett, and M. J. Padgett, Optical Angular Momentum (Institute of Physics Publishing, Bristol, 2003).

    Google Scholar 

  6. J. D. Jackson, Classical Electrodynamics, 3rd edn. (Wiley, New York, 1999).

    MATH  Google Scholar 

  7. C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Photons and Atoms: Introduction to Quantum Electrodynamics (Wiley, New York, 1997).

    Google Scholar 

  8. S. J. van Enk and G. Nienhuis, Opt. Commun. 94, 147 (1992).

    Article  ADS  Google Scholar 

  9. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, Cambridge, 1995).

    Google Scholar 

  10. S. J. van Enk and G. Nienhuis, Europhys. Lett. 25, 497 (1994).

    Article  ADS  Google Scholar 

  11. S. J. van Enk and G. Nienhuis, J. Mod. Opt. 41, 963 (1994).

    Article  ADS  Google Scholar 

  12. S. M. Barnett, J. Opt. B: Quantum Semiclass. Opt. 4, S7 (2002).

    Article  ADS  MathSciNet  Google Scholar 

  13. C. N. Alexeyev, Y. A. Fridman, and A. N. Alexeyev: Ukr. Phys. J. 46, 43 (2001).

    Google Scholar 

  14. H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, NJ, 1984).

    Google Scholar 

  15. R. A. Beth, Phys. Rev. 50, 115 (1936).

    Article  ADS  Google Scholar 

  16. N. He, M. E. J. Friese, N. R. Hechenberg, and H. Rubinstein-Dunlop, Phys. Rev. Lett. 75, 826 (1995).

    Article  ADS  Google Scholar 

  17. M. E. J. Friese, J. Enger, H. Rubinstein-Dunlop, and N. R. Heckenberg, Phys. Rev. A 54, 1593 (1996).

    Article  ADS  Google Scholar 

  18. N. B. Simpson, K. Dholakia, L. Allen, and M. J. Padgett, Opt. Lett. 22, 52 (1997).

    ADS  Google Scholar 

  19. A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, Phys. Rev. Lett. 88, 053601 (2002).

    Article  ADS  Google Scholar 

  20. R. Zambrini and S. M. Barnett, J. Mod. Opt. 52, 1045 (2005).

    Article  ADS  Google Scholar 

  21. J. F. Nye, Natural Focusing and Fine Structure of Light (Institute of Physics Publishing, Bristol, 1999).

    MATH  Google Scholar 

  22. M. S. Soskin and M. V. Vasnetsov, in Progress in Optics, vol. 42, ed. by E. Wolf (Elsevier, Amsterdam, 2001).

    Google Scholar 

  23. J. Leach, PhD Thesis, University of Glasgow, Glasgow (2005).

    Google Scholar 

  24. A E. Siegman, Lasers (University Science Books, Mill Valley, CA, 1986).

    Google Scholar 

  25. J. Durnin, J. J. Miceli, and J. H. Eberly, Phys. Rev. Lett. 58, 1499 (1987).

    Article  ADS  Google Scholar 

  26. L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, Opt. Commun. 96, 123 (1993).

    Article  ADS  Google Scholar 

  27. M. J. Padgett, J. Arlt, N. Simpson, and L. Allen, Am. J. Phys. 64, 77 (1996).

    Article  ADS  Google Scholar 

  28. M. J. Padgett and L. Allen, J. Opt. B: Quantum Semiclass. Opt. 4, S17 (2002).

    Article  ADS  Google Scholar 

  29. L. Allen, J. Courtial, and M. J. Padgett, Phys. Rev. E 60, 7497 (1999).

    Article  ADS  Google Scholar 

  30. M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, Opt. Commun. 112 321 (1994).

    Article  ADS  Google Scholar 

  31. G. A. Turnbull, D. A. Robertson, G. M. Smith, L. Allen, and M. J. Padgett, Opt. Commun. 127, 183 (1996).

    Article  ADS  Google Scholar 

  32. S. S. R, Oemrawsingh, A. Aiello, E. R. Eliel, G. Nienhuis, and J. P. Woerdman, Phys. Rev. Lett. 92, 217901 (2004).

    Article  ADS  Google Scholar 

  33. V. Y. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, JEPT Lett. 52, 429 (1990).

    ADS  Google Scholar 

  34. N. R. Heckenberg, R, McDuff, C. P. Smith, H. Rubinsztein-Dunlop, and M. J. Wegener, Opt. Quantum Electron. 24, S951 (1992).

    Article  Google Scholar 

  35. G. Molina-Terriza, J. Recolons, J. P. Torres, L. Torner, and E. M. Wright, Phys. Rev. Lett. 87, 023902 (2001).

    Article  ADS  Google Scholar 

  36. J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, Opt. Commun. 144, 210 (1997).

    Article  ADS  Google Scholar 

  37. J. Visser and G. Nienhuis, Phys. Rev. A 70, 013809 (2004).

    Article  ADS  Google Scholar 

  38. M. V. Berry, J. Opt. A 6, 259 (2004).

    ADS  Google Scholar 

  39. J. Leach, E. Yao, and M. J. Padgett, New J. Phys. 6, 71 (2004).

    Article  ADS  Google Scholar 

  40. A. Mair, A. Vaziri, G. Weihs, and A. Zeilinger, Nature 412, 313 (2001).

    Article  ADS  Google Scholar 

  41. J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, Phys. Rev. Lett. 65, 033823 (2002).

    Google Scholar 

  42. N. K. Langford, R. B. Dalton, M. D. Harvey, J. L. O’Brien, G. J. Pryde, A. Gilchrist, S. D. Bartlett, and A. G. White, Phys. Rev. Lett. 93, 053601 (2004).

    Article  ADS  Google Scholar 

  43. A. R. Altman, K. G. Köprülü, E. Corndorf, P. Kumar, and G. A. Barbosa, Phys. Rev. Lett. 94, 123601 (2005).

    Article  ADS  Google Scholar 

  44. M. Harris, C. A. Hill, P. R. Tapster, and J. M. Vaughan, Phys. Rev. A 49, 3119 (1994).

    Article  ADS  Google Scholar 

  45. G. Weihs and A. Zeilinger, Nature 412, 313 (2001).

    Article  ADS  Google Scholar 

  46. V. V. Kotlyar, V. A. Soifer, and S. N. Khonina, J. Mod. Opt. 44, 1409 (1997).

    ADS  Google Scholar 

  47. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000).

    MATH  Google Scholar 

  48. S. J. D. Phoenix and P. D. Townsend, Contemp. Phys. 36, 165 (1995).

    Article  ADS  Google Scholar 

  49. G. Gibson, J. Courtial, M. J. Padgett, M. Vasnetsov, V. Pas’ko, S. M. Barnett, and S. Franke-Arnold, Opt. Express 12, 5448 (2004).

    Article  ADS  Google Scholar 

  50. A. Gatti, H. Wiedemann, L. A. Lugiato, I. Marzoli, G. L. Oppo, and S. M. Barnett, Phys. Rev. A 56, 877 (1997).

    Article  ADS  Google Scholar 

  51. H. Wei, X. Xue, J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, E. Yao, and J. Courtial, Opt. Commun. 223, 117 (2003).

    Article  ADS  Google Scholar 

  52. J. Leach, J. Courtial, K. Skeldon, S. M. Barnett, S. Franke-Arnold, and M. J. Padgett, Phys. Rev. Lett. 92, 013601 (2004).

    Article  ADS  Google Scholar 

  53. S. M. Barnett and D. T. Pegg, Phys. Rev. A 41, 3427 (1990).

    Article  ADS  MathSciNet  Google Scholar 

  54. D. T. Pegg and S. M. Barnett, Phys. Rev. A 39, 1665 (1989).

    Article  ADS  Google Scholar 

  55. S. M. Barnett and D. T. Pegg, J. Mod. Opt. 36, 7 (1989).

    Article  ADS  Google Scholar 

  56. S. Franke-Arnold, S. M. Barnett, E. Yao, J. Leach, J. Courtial, and M. Padgett, New J. Phys. 6, 103 (2004).

    Article  ADS  Google Scholar 

  57. D. T. Pegg, S. M. Barnett, R. Zambrini, S. Franke-Arnold, and M. Padgett, New J. Phys. 7, 62 (2005).

    Article  ADS  MathSciNet  Google Scholar 

  58. C. Aragone, E. Chalbaud, S. Salam, J. Phys. A: Math. Gen. 7, L149 (1974).

    Article  ADS  Google Scholar 

  59. R. Jackiw, J. Math. Phys. 9, 339 (1968).

    Article  MATH  ADS  Google Scholar 

  60. G. S. Summy and D. T. Pegg, Opt. Commun. 77, 75 (1990).

    Article  ADS  Google Scholar 

  61. G. Molina-Terriza, J. P. Torres, and L. Torner, Phys. Rev. Lett. 88, 013601 (2002).

    Article  ADS  Google Scholar 

  62. M. V. Vasnetsov, V. A. Pas’ko, and M. S. Soskin, New J. Phys. 7, 46 (2005).

    Article  ADS  Google Scholar 

  63. N. Treps, U. Andersen, B. Buchler, P. K. Lam, A. Maitre, H.-A. Bachor, and C. Fabre, Phys. Rev. Lett. 88, 203601 (2002).

    Article  ADS  Google Scholar 

  64. C. M. Caves, Phys. Rev. D 23, 1693 (1981).

    Article  ADS  Google Scholar 

  65. M. J. Holland and K. Burnett, Phys. Rev. Lett. 71, 1355 (1993).

    Article  ADS  Google Scholar 

  66. S. M. Barnett and R. Zambrini, J. Mod. Opt., 53, 613 (2006).

    Article  MATH  ADS  Google Scholar 

  67. S. M. Barnett, C. Fabre, and A. Maitre, Eur. Phys. J. D 22, 513 (2003).

    ADS  Google Scholar 

  68. V. L. Ginzburg and L. P. Pitaevskii, Sov. Phys. JETP 34, 858 (1958).

    MathSciNet  Google Scholar 

  69. J F. Nye and M. V. Berry, Proc. R, Soc. London Ser. 336, 165 (1974).

    MATH  ADS  MathSciNet  Google Scholar 

  70. L. Allen, J. Opt. B, Qunantum Semiclass. Opt. 4, S1 (2002).

    Article  ADS  Google Scholar 

  71. Y. S. Kivshar and B. Luther-Davies, Phys. Rep. 298, 81 (1998).

    Article  ADS  Google Scholar 

  72. M. Berry, M. Dennis, and M. Soskin (Guest Editors), J. Opt. A 6, S155 (2004).

    Google Scholar 

  73. J. M. Vaughan and D. V. Willetts, Opt. Commun. 30, 263 (1979).

    Article  ADS  Google Scholar 

  74. P. Coullet, L. Gil, and F. Rocca, Opt. Commun. 73, 403 (1989).

    Article  ADS  Google Scholar 

  75. J. Courtial, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. A 56, 4193 (1997).

    Article  ADS  Google Scholar 

  76. G. Molina-Terriza, J. P. Torres, and L. Torner, Opt. Commun. 228, 155 (2003).

    Article  ADS  Google Scholar 

  77. S. Franke-Arnold, S. M. Barnett, M. J. Padgett, and L. Allen, Phys. Rev. A 65, 033823 (2002).

    Article  ADS  Google Scholar 

  78. H. H. Arnaut and G. A. Barbosa, Phys. Rev. Lett. 85, 286 (2000).

    Article  ADS  Google Scholar 

  79. E. R, Eliel, S. M. Dutra, G. Nienhuis, and J. P. Woerdman, Phys. Rev. Lett. 86, 5208 (2001).

    Article  ADS  Google Scholar 

  80. H. H. Arnaut and G. A. Barbosa, Phys. Rev. Lett. 86, 5209 (2001).

    Article  ADS  Google Scholar 

  81. M. Martinelli, J. A. O. Huguenin, P. Nussenzveig, and A. Z. Khoury, Phys. Rev. A 70, 013812 (2004).

    Article  ADS  Google Scholar 

  82. V. Pyragaite, A. Piskarskas, K. Regelskis, V. Smilgevicius, A. Stabinis, S. Mikalauskas, Opt. Commun. 240, 191 (2004).

    Article  ADS  Google Scholar 

  83. S. F. Pereira, M. B. Willemsen, M. P. van Exter, and J. P. Woerdman, Appl. Phys. Lett. 73, 2239 (1998).

    Article  ADS  Google Scholar 

  84. Y. F. Chen and Y. P. Lan, Phys. Rev. A, 63, 063807 (2001).

    Article  ADS  Google Scholar 

  85. S. Barreiro and J. W. R. Tabosa, Phys. Rev. Lett. 90, 133001 (2003).

    Article  ADS  Google Scholar 

  86. D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, Phys. Rev. Lett. 92, 123903 (2004).

    Article  ADS  Google Scholar 

  87. J. W. Fleischer, G. Bartal, O. Cohen, O. Manela, M. Segev, J. Hudock, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123904 (2004).

    Article  ADS  Google Scholar 

  88. K. Dholakia, N. B. Simpson, M. J. Padgett, and L. Allen, Phys. Rev. A 54, R3742 (1996).

    Article  ADS  Google Scholar 

  89. M. J. Padgett and L. Allen, Opt. Commun. 121, 36 (1995).

    Article  ADS  Google Scholar 

  90. A. Berzanskis, A. Matijosius, A. Piskarskas, V. Smilgevicius, and A. Stabinis, Opt. Commun. 140, 273 (1997).

    Article  ADS  Google Scholar 

  91. J. Götte, S. Franke-Arnold, and S. M. Barnett, J. Mod. Opt., 53, 627 (2006).

    Article  MATH  ADS  Google Scholar 

  92. D. McGloin and K. Dholakia, Cont. Phys. 46, 15 (2005).

    Article  ADS  Google Scholar 

  93. L. Torner and D. V. Petrov, J. Opt. Soc. Am. B 14, 2017 (1997).

    Article  ADS  Google Scholar 

  94. A. V. Buryak, P. Di Trapani, D. V. Skryabin, and S. Trillo, Phys. Rep. 370, 63 (2002).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  95. J. Arlt, K. Dholakia, L. Allen, and M. J. Padgett, Phys. Rev. A 59, 3950 (1999).

    Article  ADS  Google Scholar 

  96. S. P. Walborn, A. N. de Oliveira, R. S. Thebaldi, and C. H. Monken, Phys. Rev. A 69, 023811 (2004).

    Article  ADS  Google Scholar 

  97. D. P. Caetano, M. P. Almeida, P. H. Souto Ribeiro, J. A. O. Huguenin, B. Coutinho dos Santos, and A. Z. Khoury, Phys. Rev. A 66, 041801 (R) (2002).

    Article  ADS  Google Scholar 

  98. G-L. Oppo, A. J. Scroggie, and W. J. Firth, Phys. Rev. E 63, 066209 (2001).

    Article  ADS  Google Scholar 

  99. M. Soljacic and M. Segev, Phys. Rev. Lett. 86, 420 (2001).

    Article  ADS  Google Scholar 

  100. V. Pyragaite, K. Regelskis, V. Smilgevicius, and A. Stabinis, Opt. Commun. 198, 459 (2001).

    Article  ADS  Google Scholar 

  101. M. S. Bigelow, P. Zerom, and R. W. Boyd, Phys. Rev. Lett. 92, 083902 (2004).

    Article  ADS  Google Scholar 

  102. Y. S. Kivshar and G. P. Agrawal Optical Solitons: From Fibers to Photonics Crystals (San Diego, CA, Academic, 2003).

    Google Scholar 

  103. V. I. Kruglov and R. A. Vlasov, Phys. Lett. A 111, 401 (1985).

    Article  ADS  Google Scholar 

  104. G. A. Swartzlander and C. T. Law, Phys. Rev. Lett. 69, 2503 (1992).

    Article  ADS  Google Scholar 

  105. V. Tikhonenko, J. Christou, and B. Luther-Davies, Phys. Rev. Lett. 76 2698 (1996).

    Article  ADS  Google Scholar 

  106. D. V. Petrov, L. Torner, J. Martorell, R. Vilaseca, J. P. Torres, and C. Cojocaru, Opt. Lett. 23, 1444 (1998).

    ADS  Google Scholar 

  107. W. J. Firth and D. V. Skryabin, Phys. Rev. Lett. 79, 2450 (1997).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, University of Strathclyde, 107 Rottenrow East, G4 ONG, Glasgow, UK

    Stephen M. Barnett & Roberta Zambrini

Authors
  1. Stephen M. Barnett
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Roberta Zambrini
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Laboratoire PhLAM, Université de Lille 1, Cité Scientifique Bât. P5, Villeneuve d’Ascq Cedex, F-59655, FRANCE

    Mikhail I. Kolobov

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer

About this chapter

Cite this chapter

Barnett, S.M., Zambrini, R. (2007). Orbital Angular Momentum of Light. In: Kolobov, M.I. (eds) Quantum Imaging. Springer, New York, NY. https://doi.org/10.1007/0-387-33988-4_12

Download citation

Publish with us

Policies and ethics

Search

Navigation