(27) * << * >> * Russian * English * Content * All Issues

Optical pure vortices and hypergeometrical modes

V.V. Kotlyar 1, 2, S.N. Khonina 1, 2, A.A. Almazov 1, 2, V.A. Soifer 1, 2
1Image Processing Systems Institute of RAS
2Samara State Aerospace University(SSAU)

 PDF, 125 kB

Pages: 21-27.

Full text of article: Russian language.

Abstract:
A countable set of linearly independent solutions of a paraxial wave equation (such as the Schrödinger equation), which are called hypergeometric modes, is obtained. These solutions describe pure optical vortices and can be formed by illumination of a spiral phase plate by a plane wave. These modes differ from the known paraxial modes in that their radius increases as a square root of the distance covered, and that they all propagate with the same phase velocity.

Keywords:
hypergeometrical mode, paraxial wave equation, Schrödinger equation, optical vortex.

Citation:
Kotlyar VV, Khonina SN, Almazov AA, Soifer VA. Optical pure vortices and hypergeometrical modes. Computer Optics 2005; 27: 21-27.

Acknowledgements:
This work was financially supported by the Russian-American program “Basic Research and Higher Education” (grant CRDF REC-SA-014-02) and a grant from the President of the Russian Federation NSh1007.2003.01, as well as a grant from the Russian Foundation for Basic Research 05-01-96505.

References:
  1. Siegman AE. Lasers. Sausalito, CA, University Science Books; 1986. ISBN: 0-935702-11-3. 
  2. Miller W Jr. Symmetry and separation of variables. Reading, Massachusetts: Addison-Wesley Pub; 1977. 
  3. Durnin J, Miceli JJ, Eberly JH. Diffraction-free beams. Phys Rev Lett 1987; 58: 1499-1501. DOI: 10.1103/PhysRevLett.58.1499. 
  4. Bandres MA, Gutiérrez-Vega JC. Ince-Gaussian beams. Opt Lett 2004; 29(2): 144-146. DOI: 10.1364/OL.29.000144. 
  5. Bandres MA, Gutiérrez-Vega JC. Ince-Gaussian modes of the paraxial wave equation and stable resonators. J Opt Soc Am A 2004; 21(5): 873-880. DOI: 10.1364/JOSAA.21.000873. 
  6. Bandres MA. Elegant Ince-Gaussian beams. Opt Lett 2004; 29(15): 1724-1726. DOI: 10.1364/OL.29.001724. 
  7. Bandres MA, Gutiérrez-Vega JC. Higher-order complex source for elegant Laguerre-Gaussian waves. Opt Lett 2004; 29(19): 2213-2215. DOI: 10.1364/OL.29.002213. 
  8. Schwarz UT, Bandres MA, Gutiérrez-Vega JC. Observation of Ince-Gaussian modes in stable resonators. Opt Lett 2004; 29(16): 1870-1872. DOI: 10.1364/OL.29.001870. 
  9. Abramochkin EG, Volostnikov VG. Generalized Gaussian beams. J Opt A: Pure Appl Opt 2004; 6: S157-S161. DOI: 10.1088/1464-4258/6/5/001. 
  10. Khonina SN, Kotlyar VV, Shinkaryev MV, Soifer VA, Uspleniev GV. The phase rotor filter. J Mod Opt 1992; 39(5): 1147-1154. DOI: 10.1080/09500349214551151. 
  11. Beijersbergen MW, Coerwinkel RPC, Kristiensen M, Woerdman JP. Helical-wave front laser beams produced with a spiral phase plate. Opt Commun 1994; 112(5-6): 321-327. DOI: 10.1016/0030-4018(94)90638-6. 
  12. Oemrawsingh SSR, Van Houwelingen JAM, Eliel ER, Woerdman JP, Verstegen EJK, Kloosterboer JG, Hooft GW. Production and characterization of spiral phase plates for optical wavelengths. Appl Opt 2004; 43(3): 688-694. DOI: 10.1364/AO.43.000688. 
  13. Soskin MS, Gorshkov UN, Vasnetsov MV. Topological charge and angular momentum of light beams carrying optical vortices. Phys Rev A 1997; 56(5): 4064-4075. DOI: 10.1103/PhysRevA.56.4064. 
  14. Kotlyar VV, Almazov AA, Khonina SN, Soifer VA, Elfstrom H, Turunen J. Generation of phase singularity through diffracting a plane or Gaussian beam by a spiral phase plate. J Opt Soc Am A 2005; 22(5): 849-861. DOI: 10.1364/JOSAA.22.000849. 
  15. Allen L, Beijersbergen MV, Spreeuw RJC, Woerdman JP. Orbital angular-momentum of light and the transformation of Laguerre-Gaussian laser modes. Phys Rev A 1992; 45: 8185-8189. DOI: 10.1103/physreva.45.8185. 
  16. Khonina SN, Kotlyar VV, Soifer VA, Pääkkönen P, Simonen J, Turunen J. An analysis of the angular momentum of a light field in terms of angular harmonics. J Mod Opt 2001; 48(10): 1543-1557. DOI: 10.1080/09500340108231783. 
  17. Khonina SN, Kotlyar VV, Soifer VA, Paakkonen P, Turunen J. Measuring the light field orbital angular momentum using DOE. Optical Memory and Neural Networks 2001; 10(4): 241-255. 
  18. Wright EM, Arlt J, Dholakia K. Toroidal optical dipole traps for atomic Bose-Einstein condensates using Laguerre-Gaussian beams. Phys Rev A 2000; 63: 013608. DOI: 10.1103/PhysRevA.63.013608.

© 2009, IPSI RAS
151, Molodogvardeiskaya str., Samara, 443001, Russia; E-mail: ko@smr.ru ; Tel: +7 (846) 242-41-24 (Executive secretary), +7 (846) 332-56-22 (Issuing editor), Fax: +7 (846) 332-56-20