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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Franco Gori
  • Vol. 31, Iss. 2 — Feb. 1, 2014
  • pp: 274–282

Hermite–Gaussian modal laser beams with orbital angular momentum

V. V. Kotlyar and A. A. Kovalev  »View Author Affiliations


JOSA A, Vol. 31, Issue 2, pp. 274-282 (2014)
http://dx.doi.org/10.1364/JOSAA.31.000274


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Abstract

A relationship for the complex amplitude of generalized paraxial Hermite–Gaussian (HG) beams is deduced. We show that under certain parameters, these beams transform into the familiar HG modes and elegant HG beams. The orbital angular momentum (OAM) of a linear combination of two generalized HG beams with a phase shift of π/2, with their double indices composed of adjacent integer numbers taken in direct and inverse order, is calculated. The modulus of the OAM is shown to be an integer number for the combination of two HG modes, always equal to unity for the superposition of two elegant HG beams, and a fractional number for two hybrid HG beams. Interestingly, a linear combination of two such HG modes also presents a mode that is characterized by a nonzero OAM and the lack of radial symmetry but does not rotate during propagation.

© 2014 Optical Society of America

OCIS Codes
(050.1960) Diffraction and gratings : Diffraction theory
(350.5500) Other areas of optics : Propagation

ToC Category:
Diffraction and Gratings

History
Original Manuscript: October 22, 2013
Revised Manuscript: December 5, 2013
Manuscript Accepted: December 8, 2013
Published: January 17, 2014

Citation
V. V. Kotlyar and A. A. Kovalev, "Hermite–Gaussian modal laser beams with orbital angular momentum," J. Opt. Soc. Am. A 31, 274-282 (2014)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-31-2-274


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References

  1. L. Allen, M. W. Beijersergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992). [CrossRef]
  2. M. Berry, J. Nye, and F. Wright, “The elliptic umbilic diffraction catastrophe,” Phil. Trans. R. Soc. Lond. 291, 453–484 (1979). [CrossRef]
  3. J. M. Vaughan and D. Willetts, “Interference properties of a light-beam having a helical wave surface,” Opt. Commun. 30, 263–267 (1979). [CrossRef]
  4. P. Coullet, G. Gil, and F. Rocca, “Optical vortices,” Opt. Commun. 73, 403–408 (1989). [CrossRef]
  5. V. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, “Laser-beam with screw dislocations in the wavefront,” JETP Lett. 52, 429–431 (1990).
  6. S. N. Khonina, V. V. Kotlyar, M. V. Shinkarev, V. A. Soifer, and G. V. Uspleniev, “The rotor phase filter,” J. Mod. Opt. 39, 1147–1154 (1992). [CrossRef]
  7. E. G. Abramochkin and V. G. Volostnikov, “Beam transformation and nontransformed beams,” Opt. Commun. 83, 123–135 (1991). [CrossRef]
  8. M. W. Beijersbergen, L. Allen, H. E. Van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993). [CrossRef]
  9. A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photon. 3, 161–204 (2011). [CrossRef]
  10. V. V. Kotlyar and A. A. Kovalev, Vortex Laser Beams (Novaya Tekhnika, 2012) [in Russian].
  11. S. Vyas and P. Senthilkumaran, “Interferometric optical vortex array generator,” Appl. Opt. 46, 2893–2898 (2007). [CrossRef]
  12. E. Fraczek and G. Budzyn, “An analysis of an optical vortices interferometer with focused beam,” Opt. Appl. 39, 91–99 (2009).
  13. B. K. Singh, G. Singh, P. Senthilkumaran, and D. S. Metha, “Generation of optical vortex array using single-element reversed-wavefront folding interferometer,” Int. J. Opt. 2012, 689612 (2012). [CrossRef]
  14. P. Vaity, A. Aadhi, and R. Singh, “Formation of optical vortices through superposition of two Gaussian beams,” Appl. Opt. 52, 6652–6656 (2013). [CrossRef]
  15. Y. Shen, G. T. Campbell, B. Hage, H. Zou, B. C. Buchler, and P. K. Lam, “Generation and interferometric analysis of high charge optical vortices,” J. Opt. 15, 044005 (2013). [CrossRef]
  16. J. B. Gotte, K. O’Holleran, D. Precce, F. Flossman, S. Franke-Arnold, S. M. Barnett, and M. J. Padgett, “Light beams with fractional orbital angular momentum and their vortex structure,” Opt. Express 16, 993–1006 (2008). [CrossRef]
  17. E. G. Abramochkin and V. G. Volostnikov, “Generalized Gaussian beams,” J. Opt. A 6, S157–S161 (2004). [CrossRef]
  18. D. P. O’Dwyer, C. F. Phelan, Y. P. Rakovich, P. R. Eastham, J. C. Lunney, and J. F. Donegan, “Generation of continuously tunable fractional orbital angular momentum using internal conical diffraction,” Opt. Express 18, 16480–16485 (2010). [CrossRef]
  19. H. Kogelnik and T. Li, “Laser beams and resonators,” Proc. IEEE 54, 1312–1329 (1966). [CrossRef]
  20. A. E. Siegman, “Hermite-Gaussian functions of complex argument as optical beam eigenfunction,” J. Opt. Soc. Am. 63, 1093–1094 (1973). [CrossRef]
  21. F. Gori, “Why is the Fresnel transform so little known?” in Current Trends in Optics, J. C. Dainty, ed. (Academic, 1994), pp. 140–148.
  22. S. N. Khonina, V. V. Kotlyar, V. A. Soifer, P. Paakkonen, J. Simonen, and J. Turunen, “An analysis of the angular momentum of a light field in terms of angular harmonics,” J. Mod. Opt. 48, 1543–1557 (2001).
  23. J. Humblet, “Sur le moment d’impulsion d’une onde electromagnetique,” Physica 10, 585–603 (1943).
  24. A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series. Special Functions (Gordon and Breach Science, 1986).
  25. V. V. Kotlyar, S. N. Khonina, R. V. Skidanov, and V. A. Soifer, “Rotation of laser beams with zero of the orbital angular momentum,” Opt. Commun. 274, 8–14 (2007). [CrossRef]
  26. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Elsevier, 2007).

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