Orbital angular momentum of an elliptic optical vortex embedded into the Gaussian beam
V.V. Kotlyar, A.A. Kovalev, A.P. Porfirev

 

Image Processing Systems Institute of RAS – Branch of the FSRC “Crystallography and Photonics” RAS Samara, Russia,
Samara National Research University, Samara, Russia

Full text of article: Russian language.

Abstract:
We consider an elliptic optical vortex embedded into a Gaussian beam. For such a beam, explicit closed-form expressions are derived for the complex amplitude and the normalized orbital angular momentum (OAM). It is shown that the elliptic Gaussian vortex (EGV) has a fractional OAM. The maximal OAM value equal to the vortex topological charge n is achieved at zero ellipticity of the vortex. The major axis of the intensity ellipse in the beam cross section rotates in propagation, turning by a 90-degree angle from the initial plane to the focal plane of a spherical lens. There are n intensity nulls on the major axis of the EGV intensity ellipse. The distance between the nulls varies during the beam propagation and with changing degree of ellipticity. At a fixed degree of ellipticity, the distance between the intensity nulls is maximal in the focal plane. At zero ellipticity, all nulls are "gathering" into a single on-axis n-times degenerate intensity null. The experimental results are consistent with the theory.

Keywords:
orbital angular momentum, optical vortex, Gaussian beam, elliptic optical vortex.

Citation:
Kotlyar VV, Kovalev AA, Porfirev AP. Orbital angular momentum of an elliptic optical vortex embedded into the Gaussian beam. Computer Optics 2017; 41(3): 330-337. DOI: 10.18287/2412-6179-2017-41-3-330-337.

References:

  1. Mair A, Vaziri A, Weihs G, Zeilinger A. Entanglement of the orbital angular momentum states of photons. Nature 2001; 412: 313-316. DOI: 10.1038/35085529.
  2. Vaziri A, Weihs G, Zeilinger A. Superpositions of the orbital angular momentum for applications in quantum experiments. J Opt B: Quant Semicl Opt 2002; 4(2): S47-S51. DOI: 10.1088/1464-4266/4/2/367.
  3. Chen Q, Shi B, Zhang Y, Guo G. Entanglement of the orbital angular momentum states of the photon pairs generated in a hot atomic ensemble. Phys Rev A 2008; 78(5): 053810. DOI: 10.1103/PhysRevA.78.053810.
  4. Kotlyar VV, Kovalev AA, Porfirev AP. Asymmetric Gaussian optical vortex. Opt Lett 2017; 42(1): 139-142. DOI: 10.1364/OL.42.000139.
  5. Kotlyar VV, Kovalev AA, Porfirev AP, Abramochkin EG. Fractional orbital angular momentum of a Gaussian beam with an embedded off-axis optical vortex. Computer Optics 2017; 41(1): 22-29. DOI: 10.18287/2412-6179-2017-41-1-22-29.
  6. Kotlyar VV, Kovalev AA, Soifer VA. Asymmetric Bessel modes. Opt Lett 2014; 39(8): 2395-2398. DOI: 10.1364/OL.39.002395.
  7. Kovalev AA, Kotlyar VV, Porirev AP. Asymmetric Laguerre-Gaussian beams. Phys Rev A 2016; 93(6): 063858. DOI: 10.1103/PhysRevA.93.063858.
  8. Kumar A, Vaity P, Singh RP. Crafting the core asymmetry to lift the degeneracy of optical vortices. Opt Express 2011; 19(7): 6182-6190. DOI: 10.1364/OE.19.006182.
  9. Dennis MR. Rows of optical vortices from elliptically perturbing a high-order beam. Opt Lett 2006; 31(9): 1325-1327. DOI: 10.1364/OL.31.001325.
  10. Kotlyar VV, Khonina SN, Almazov AA, Soifer VA, Jefimovs K, Turunen J. Elliptic Laguerre-Gaussian beams. J Opt Soc Am A 2006; 23(1): 43-56. DOI: 10.1364/JOSA­A.23.000043.
  11. Kotlyar VV, Kovalev AA, Porfirev AP. Vortex Hermite-Gaussian laser beams. Opt Lett 2015; 40(5): 701-704. DOI: 10.1364/OL.40.000701.
  12. Prudnikov AP, Brychkov YA, Marichev OI. Integrals and Series, Special Functions. New York: Gordon and Breach; 1986.

© 2009, IPSI RAS
Institution of Russian Academy of Sciences, Image Processing Systems Institute of RAS, Russia, 443001, Samara, Molodogvardeyskaya Street 151; e-mail: ko@smr.ru; Phones: +7 (846 2) 332-56-22, Fax: +7 (846 2) 332-56-20