(41-4) 16 * << * >> * Russian * English * Content * All Issues

Vortex-free laser beam with an orbital angular momentum
Kotlyar V.V.
, Kovalev A.A.

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

 PDF 369 kB

DOI: 10.18287/2412-6179-2017-41-4-573-576

Pages: 573-576.

We show that if one cylindrical lens is placed in the Gaussian beam waist and another cylindrical lens is placed at some distance from the first one and rotated by some angle, then the laser beam after the second lens has an orbital angular momentum (OAM). An explicit analytical expression for the OAM of such a beam is obtained. Depending on the inter-lens distance, the OAM can be positive, negative, or zero. Such a laser beam has no isolated intensity nulls with a singular phase and it is not an optical vortex, but has an OAM. By choosing the radius of the beam waist of the source Gaussian beam, the focal lengths of the lenses and the distance between them, it is possible to generate a vortex-free laser beam equivalent to an optical vortex with a topological charge of several hundreds.

elliptic Gaussian beam, cylindrical lens, orbital angular momentum.

Kotlyar VV, Kovalev AA. Vortex-free laser beam with an orbital angular momentum. Computer Optics 2017; 41(4): 573-576. DOI: 10.18287/2412-6179-2017-41-4-


  1. Grier D. A revolution in optical manipulation. Nature 2003; 424: 810-816. DOI: 10.1038/nature01935.
  2. Kuga T, Torii Y, Shiokawa N, Hirano T, Shimizu Y, Sasada H. Novel optical trap of atoms with a doughnut beam. Phys Rev Lett 1997; 78(25): 4713-4716. DOI: 10.1103/PhysRevLett.78.4713.
  3. Bernet S, Jesacher A, Furhapter S, Maurer C, Ritsch-Marte M. Quantitative imaging of complex samples by spiral phase contrast microscopy. Opt Express 2006; 14(9): 3792-3805. DOI: 10.1364/OE.14.003792.
  4. Willig KI, Rizzoli SO, Westphal V, Jahn R, Hell SW. STED microscopy reveals that synaptotagmin remains clustered after synaptic vesicle exocytosis. Nature 2006; 440: 935-939. DOI: 10.1038/nature04592.
  5. Wang J, Yang J, Fazal IM, Ahmed N, Yan Y, Huang H, Ren Y, Yue Y, Dolinar S, Tur M, Willner AE. Terabit free-space data transmission employing orbital angular momentum multiplexing. Nat Phot 2012; 6(7): 488-496. DOI: 10.1038/nphoton.2012.138.
  6. 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.
  7. Courtial J, Dholakia K, Allen L, Padgett MJ. Gaussian beams with very high orbital angular momentum. Opt Commun 1997; 144(4-6): 210-213. DOI: 10.1016/S0030-4018(97)00376-3.
  8. Abramochkin EG, Volostnikov VG. Beam transformations and nontransformed beams. Opt Commun 1991; 83(1-2): 123-135. DOI: 10.1016/0030-4018(91)90534-K.
  9. Izdebskaya Y, Fadeyeva T, Shvedov V, Volyar A. Vortex-bearing array of singular beams with very high orbital angular momentum. Opt Lett 2006; 31(17): 2523-2525. DOI: 10.1364/OL.31.002523.
  10. Fickler R, Lapkiewicz R, Plick WN, Krenn M, Schaeff C, Ramelow S, Zeilinger A. Quantum entanglement of high angular momenta. Science 2012; 338(6107): 640-643. DOI: 10.1126/science.1227193.
  11. Shen Y, Campbell GT, Hage B, Zou H, Buchler BC, Lam PK. Generation and interferometric analysis of high charge optical vortices. J Opt 2013; 15(4): 044005. DOI: 10.1088/2040-8978/15/4/044005.
  12. Fickler R, Campbell G, Buchler B, Lam PK, Zeilinger A. Quantum entanglement of angular momentum states with quantum number up to 10010. Proc Natl Acad Sci USA 2016; 113(48): 13642-13647. DOI: 10.1073/pnas.1616889113.

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