Journal of Russian Laser Research

, Volume 37, Issue 3, pp 227–235 | Cite as

Optical Gaussian States Carrying Orbital Angular Momentum

  • Elena D. Zhebrak


Within the framework of the tomographic probability representation, we introduce specific optical Gaussian states, which were recently proved to carry the orbital angular momentum. We obtain the symplectic and optical tomograms defining uniquely both quantum and classical states for the rotating Gaussian states of light. This approach needs to be developed and applied to the mentioned states due to the convenience of using in the state reconstructions and measurements. Having in mind this aim, we obtain the mean values and variances of the amplitude quadratures directly measurable in the homodyne optical-tomography experiments. Also we consider the time evolution of the rotating Gaussian states in terms of the tomograms and obtain the corresponding tomographic propagator.


orbital angular momentum (OAM) states Gaussian packets tomographic probability representation time evolution propagator 


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  1. 1.
    R. Fickler, M. Krenn, R. Lapkiewicz, et al., Sci. Rep., 3, 1914 (2013).ADSCrossRefGoogle Scholar
  2. 2.
    R. Fickler, R. Lapkiewicz, M. Huber, et al., Nature Commun., 5, 28 (2014).CrossRefGoogle Scholar
  3. 3.
    R. Fickler, R. Lapkiewicz, W. N. Plick, et al., Science, 338, 640 (2012).ADSCrossRefGoogle Scholar
  4. 4.
    A. Nicolas, L. Veissier, L. Giner, et al., Nature Photon., 8, 234 (2014).ADSCrossRefGoogle Scholar
  5. 5.
    M. A. Bandres and J. C. Gutierrez-Vega, Opt. Lett., 29, 144 (2004).ADSCrossRefGoogle Scholar
  6. 6.
    M. A. Bandres and J. C. Gutierrez-Vega, J. Opt. Soc. Am. A, 21, 873 (2004).ADSCrossRefGoogle Scholar
  7. 7.
    M. Krenn, R. Fickler, M. Huber, et al., Phys. Rev. A, 87, 012326 (2013).ADSCrossRefGoogle Scholar
  8. 8.
    K. Volke-Sepulveda, V. Garces-Chavez, S. Chavez-Cerda, et al., J. Opt. B: Quantum Semiclass. Opt., 4, S82 (2002).ADSCrossRefGoogle Scholar
  9. 9.
    D. McGloin and K. Dholakia, Contemp. Phys., 46, 15 (2005).ADSCrossRefGoogle Scholar
  10. 10.
    V. V. Dodonov, J. Phys. A: Math. Theor., 48, 435303 (2015).ADSMathSciNetCrossRefGoogle Scholar
  11. 11.
    I. Rigas, L. L. Sanchez-Soto, A. B. Klimov, et al., Phys. Rev. A, 78, 060101 (2008).ADSCrossRefGoogle Scholar
  12. 12.
    S. Mancini, V. I. Man’ko, and P. Tombesi, Phys. Lett. A, 213, 1 (1996).ADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    M. Bellini, A. S. Coelho, S. N. Filippov, et al., Phys. Rev. A, 85, 052129 (2012).ADSCrossRefGoogle Scholar
  14. 14.
    M. Lassen, G. Leuchs, and U. L. Andersen, Phys. Rev. Lett., 102, 163602 (2009).ADSCrossRefGoogle Scholar
  15. 15.
    L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Phys. Rev. A, 45, 8185 (1992).ADSCrossRefGoogle Scholar
  16. 16.
    M. A. Leontovich and V. A. Fock, Zh. Éksp. Teor. Fiz., 16, 557 (1946).Google Scholar
  17. 17.
    D. L. Andrews, Structured Light and Its Applications: An Introduction to Phase-Structured Beams and Nanoscale Optical Forces, Academic Press, New York (2011).Google Scholar
  18. 18.
    A. Ibort, V. I. Man’ko, G. Marmo, et al., Phys. Scr., 79, 065013 (2009).ADSCrossRefGoogle Scholar
  19. 19.
    V. I. Man’ko, M. Moshinsky, and A. Sharma, Phys. Rev. A, 59, 1809 (1999).ADSCrossRefGoogle Scholar
  20. 20.
    M. A. Man’ko, V. I. Man’ko, and R. V. Mendes, Phys. Lett. A, 288, 132 (2001).ADSMathSciNetCrossRefGoogle Scholar
  21. 21.
    S. Chavez-Cerda and J. R. Moya-Cesa, and H. M. Moya-Cesa, J. Opt. Soc. Am. B, 24, 404 (2007).ADSCrossRefGoogle Scholar
  22. 22.
    E. Wigner, Phys. Rev., 40, 749 (1932).ADSCrossRefGoogle Scholar
  23. 23.
    V. I. Man’ko and R. V. Mendes, Phys. Lett. A, 263, 53 (1999).ADSMathSciNetCrossRefGoogle Scholar
  24. 24.
    S. Mancini, V. I. Man’ko, and P. Tombest, Found. Phys., 27, 801 (1997).ADSMathSciNetCrossRefGoogle Scholar
  25. 25.
    V. V. Dodonov, Phys. Rev. A, 93, 022106 (2016).ADSCrossRefGoogle Scholar
  26. 26.
    O. V. Man’ko and V. I. Man’ko, J. Russ. Laser Res., 20, 67 (1999).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Moscow Institute of Physics and Technology (State University)DolgoprudnyiRussia

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