Orbital angular momentum of an elliptically symmetric laser beam after passing an elliptical spiral phase plate
Kovalev A.A.


Samara National Research University, 34, Moskovskoye shosse, Samara, 443086, Samara, Russia,
IPSI RAS – Branch of the FSRC “Crystallography and Photonics” RAS, Molodogvardeyskaya 151, 443001, Samara, Russia

We obtain a simple closed expression for the normalized orbital angular momentum (OAM) (OAM per unit power) of an arbitrary paraxial light beam of an elliptical cross-section, diffracted by an elliptical spiral phase plate (SPP), rotated by an arbitrary angle around the optical axis. Note that the ellipticities of the beam and of the SPP can be different. It is shown that when an elliptical beam illuminates an elliptical SPP, the normalized OAM of the output beam is maximal / minimal if the ellipses of the beam cross-section and the SPP are parallel / orthogonal. The results can be used in optical trapping, e.g. for continuously changing the OAM transferred to a particle by rotating the SPP around the optical axis.

elliptic laser beam, elliptical spiral phase plate, orbital angular momentum.

Kovalev AA. Orbital angular momentum of an elliptically symmetric laser beam after passing an elliptical spiral phase plate. Computer Optics 2018; 42(4): 606-613. DOI: 10.18287/2412-6179-2018-42-4-606-613.


  1. Allen L, Beijersbergen MW, Spreeuw RJC, Woerdman JP. Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes. Phys Rev A 1992; 45(11): 8185-8189. DOI: 10.1103/PhysRevA.45.8185.
  2. 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.
  3. Kotlyar VV, Kovalev AA, Porfirev AP. Astigmatic laser beams with a large orbital angular momentum. Opt Express 2018; 26(1): 141-156. DOI: 10.1364/OE.26.000141.
  4. Serna J, Movilla J. Orbital angular momentum of partially coherent beams. Opt Lett 2001; 26(7): 405-407. DOI: 10.1364/OL.26.000405.
  5. Yang Z. Optical orbital angular momentum of evanescent Bessel waves. Opt Express 2015; 23(10): 12700-12711. DOI: 10.1364/OE.23.012700.
  6. Charnotskii M. Transverse linear and orbital angular momenta of beam waves and propagation in random media. J Opt 2017; 20(2): 025602. DOI: 10.1088/2040-8986/aa9f50.
  7. Martinez-Castellanos I, Gutiérrez-Vega JC. Shaping optical beams with non-integer orbital-angular momentum: a generalized differential operator approach. Opt Lett 2015; 40(8): 1764-1767. DOI: 10.1364/OL.40.001764.
  8. Bekshaev AYa, Soskin MS, Vasnetsov MV. Optical vortex symmetry breakdown and decomposition of the orbital angular momentum of light beams. J Opt Soc Am A 2003; 20(8): 1635-1643. DOI: 10.1364/JOSAA.20.001635.
  9. Bekshaev AYa, Soskin MS, Vasnetsov MV. Transformation of higher-order optical vortices upon focusing by an astigmatic lens. Opt Commun 2004; 241(4-6): 237-247. DOI: 10.1016/j.optcom.2004.07.023.
  10. Kotlyar VV, Kovalev AA, Porfirev AP. Elliptic Gaussian optical vortices. Phys Rev A 2017; 95(5): 053805. DOI: 10.1103/PhysRevA.95.053805.
  11. Kovalev AA, Kotlyar VV, Porfirev AP. A highly efficient element for generating elliptic perfect optical vortices. Appl Phys Lett 2017; 110(26): 261102. DOI: 10.1063/1.4990394.
  12. Tahara T, Kanno T, Arai Y, Ozawa T. Single-shot phase-shifting incoherent digital holography. J Opt 2017; 19(6): 065705. DOI: 10.1088/2040-8986/aa6e82.
  13. Zhang P, Hernandez D, Cannan D, Hu Y, Fardad S, Huang S, Chen J, Christodoulides D, Chen Z. Trapping and rotating microparticles and bacteria with Moiré-based optical propelling beams. Biomed Opt Express 2012; 3(8): 1891-1897. DOI: 10.1364/BOE.3.001891.
  14. De Sio L, Roberts D, Liao Z, Nersisyan S, Uskova O, Wickboldt L, Tabiryan N, Steeves D, Kimball B. Digital polarization holography advancing geometrical phase optics. Opt Express 2016; 24(16): 18297-18306. DOI: 10.1364/OE.24.018297.
  15. Ruffato G, Massari M, Romanato F. Diffractive optics for combined spatial- and mode- division demultiplexing of optical vortices: design, fabrication and optical characterization. Sci Rep 2016; 6: 24760. DOI: 10.1038/srep24760.
  16. Kotlyar VV, Kovalev AA. Controlling orbital angular momentum of an optical vortex by varying its ellipticity. Opt Commun 2018; 410: 202-205. DOI: 10.1016/j.optcom.2017.10.004.
  17. Kogelnik H, Li T. Laser beams and resonators. Appl Opt 1966; 5(10): 1550-1567. DOI: 10.1364/AO.5.001550.

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