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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 17, Iss. 1 — Jan. 1, 2000
  • pp: 84–94

Effect of holes and vortices on beam quality

S. Ramee and R. Simon  »View Author Affiliations

JOSA A, Vol. 17, Issue 1, pp. 84-94 (2000)

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The effect of a vortex on the invariant quality factors of a light beam is studied. It is shown that a vortex degrades beam quality. The beam intensity at the eye of the vortex necessarily vanishes, creating a hole in the intensity distribution. The degradation in the beam quality is shown to be due partly to the vortex phase and partly to the hole. The results are illustrated graphically. An important inequality to be obeyed by the beam-quality parameters is exhibited.

© 2000 Optical Society of America

OCIS Codes
(030.1640) Coherence and statistical optics : Coherence
(030.6600) Coherence and statistical optics : Statistical optics
(260.0260) Physical optics : Physical optics
(350.5500) Other areas of optics : Propagation

Original Manuscript: January 13, 1999
Revised Manuscript: August 30, 1999
Manuscript Accepted: September 24, 1999
Published: January 1, 2000

S. Ramee and R. Simon, "Effect of holes and vortices on beam quality," J. Opt. Soc. Am. A 17, 84-94 (2000)

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  1. J. F. Nye, M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London, Ser. A 336, 165–190 (1974). [CrossRef]
  2. G. Indebetouw, “Optical vortices and their propagation,” J. Mod. Opt. 40, 73–87 (1993). [CrossRef]
  3. E. Abramochkin, N. Losevsky, V. Volostnikov, “Generation of spiral-type laser beams,” Opt. Commun. 141, 59–64 (1997). [CrossRef]
  4. F. S. Roux, “Dynamical behavior of optical vortices,” J. Opt. Soc. Am. B 12, 1215–1221 (1995). [CrossRef]
  5. D. Rozas, C. T. Law, G. A. Swartzlander, “Propagation dynamics of optical vortices,” J. Opt. Soc. Am. B 14, 3054–3065 (1997) and references therein. [CrossRef]
  6. G. S. Agarwal, R. R. Puri, R. P. Singh, “Vortex states for the quantized radiation field,” Phys. Rev. A 56, 4207–4215 (1997). [CrossRef]
  7. M. Vaupel, C. O. Weiss, “Circling optical vortices,” Phys. Rev. A 51, 4078–4085 (1995). [CrossRef] [PubMed]
  8. G. Nienhuis, “Doppler effect induced by rotating lenses,” Opt. Commun. 132, 8–14 (1996). [CrossRef]
  9. P. Di Trapani, A. Berzanskis, S. Minardi, S. Sapone, W. Chinaglia, “Observation of optical vortices and J0 Bessel-like beams in quantum-noise parametric amplification,” Phys. Rev. Lett. 81, 5133–5136 (1998). [CrossRef]
  10. R. Piestun, J. Shamir, “Generalized propagation-invariant wave fields,” J. Opt. Soc. Am. A 15, 3039–3044 (1998). [CrossRef]
  11. M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phase plate,” Opt. Commun. 112, 321–327 (1994). [CrossRef]
  12. G. A. Turnbull, D. A. Robertson, G. M. Smith, L. Allen, M. J. Padgett, “The generation of free-space Laguerre–Gaussian modes at millimetre-wave frequencies by use of a spiral phase plate,” Opt. Commun. 127, 183–188 (1996). [CrossRef]
  13. M. W. Beijersbergen, L. Allen, H. E. L. O. Van der Veen, J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993). [CrossRef]
  14. L. V. Kreminskaya, M. S. Soskin, A. I. Khizhnyak, “The Gaussian lenses give birth to optical vortices in laser beams,” Opt. Commun. 145, 377–384 (1998). [CrossRef]
  15. N. R. Heckenberg, R. McDuff, C. P. Smith, A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17, 221–223 (1992). [CrossRef] [PubMed]
  16. V. Yu. Bazhenov, M. S. Soskin, M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39, 985–990 (1992). [CrossRef]
  17. J. Courtial, K. Dholakia, D. A. Robertson, L. Allen, M. J. Padgett, “Measurement of the rotational frequency shift imparted to a rotating light beam possessing orbital angular momentum,” Phys. Rev. Lett. 80, 3217–3219 (1998). [CrossRef]
  18. L. Allen, M. W. Beijerbergen, R. J. C. Spreeuw, J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992). [CrossRef] [PubMed]
  19. L. Allen, M. Babiker, W. L. Power, “Azimuthal Doppler shift in light beams with orbital angular momentum,” Opt. Commun. 112, 141–144 (1994). [CrossRef]
  20. I. Bialynicki-Birula, Z. Bialynicka-Birula, “Rotational frequency shift,” Phys. Rev. Lett. 78, 2539–2542 (1997). [CrossRef]
  21. J. Courtial, K. Dholakia, L. Allen, M. J. Padgett, “Gaussian beams with very high orbital angular momentum,” Opt. Commun. 144, 210–213 (1997). [CrossRef]
  22. S. J. Van Enk, “Geometric phase, transformations of Gaussian light beams and angular momentum transfer,” Opt. Commun. 102, 59–64 (1993). [CrossRef]
  23. H. He, M. E. J. Friese, N. R. Heckenberg, H. Rubinsztein-Dunlop, “Direct observation of transfer of angular momentum to absorptive particles from a laser beam with a phase singularity,” Phys. Rev. Lett. 75, 826–829 (1995). [CrossRef] [PubMed]
  24. S. Chavez-Cerda, G. S. McDonald, G. H. C. New, “Nondiffracting beams: traveling, standing, rotating and spiral waves,” Opt. Commun. 123, 225–233 (1996). [CrossRef]
  25. B. Spektor, R. Piestun, J. Shamir, “Dark beams with a constant notch,” Opt. Lett. 21, 456–458 (1996). [CrossRef] [PubMed]
  26. E. C. G. Sudarshan, N. Mukunda, R. Simon, “Realization of first-order optical systems using thin lenses,” Opt. Acta 32, 855–872 (1985). [CrossRef]
  27. R. Simon, E. C. G. Sudarshan, N. Mukunda, “Anisotropic Gaussian Schell-model beams: passage through optical systems and associated invariants,” Phys. Rev. A 31, 2419–2434 (1985). [CrossRef] [PubMed]
  28. R. Simon, E. C. G. Sudarshan, N. Mukunda, “Gaussian Wigner distributions in quantum mechanics and optics,” Phys. Rev. A 36, 3868–3880 (1987). [CrossRef] [PubMed]
  29. A. Siegman, “New developments in laser resonators,” in Optical Resonators, D. A. Holmes, ed., Proc. SPIE1224, 2–10 (1990). [CrossRef]
  30. J. Serna, P. M. Mejias, R. Martinez-Herrero, “Beam quality dependence on the coherence length of Gaussian Schell-model fields propagating through ABCD optical systems,” J. Mod. Opt. 39, 625–635 (1992). [CrossRef]
  31. R. Simon, N. Mukunda, B. Dutta, “Quantum-noise matrix, for multimode systems: U(n) invariance, squeezing, and normal forms,” Phys. Rev. A 49, 1567–1683 (1994). [CrossRef] [PubMed]
  32. R. Simon, E. C. G. Sudarshan, N. Mukunda, “Generalized rays in first order optics: transformation properties of Gaussian Schell-model fields,” Phys. Rev. A 29, 3273–3279 (1984). [CrossRef]
  33. R. Simon, N. Mukunda, E. C. G. Sudarshan, “Partially coherent beams and a generalized abcd-law,” Opt. Commun. 65, 322–328 (1988). [CrossRef]
  34. A. T. Friberg, C. Gao, B. Eppich, H. Weber, “Generation of partially coherent fields with twist,” in 10th Meeting on Optical Engineering in Israel, I. Shladov, S. R. Rotman, eds., Proc. SPIE3110, 317–328 (1997). [CrossRef]
  35. D. Gloge, D. Marcuse, “Formal quantum theory of light rays,” J. Opt. Soc. Am. 59, 1629–1631 (1969). [CrossRef]
  36. M. Nazarathy, J. Shamir, “First-order optics—a canonical operator representation: lossless systems,” J. Opt. Soc. Am. 72, 356–364 (1982). [CrossRef]
  37. J. Williamson, “On the algebraic problem concerning the normal forms of linear dynamical systems,” Am. J. Math. 58, 141–163 (1936). [CrossRef]
  38. G. Nemes, A. E. Siegman, “Measurement of all ten second-order moments of an astigmatic beam by the use of rotating simple astigmatic (anamorphic) optics,” J. Opt. Soc. Am. A 11, 2257–2264 (1994). [CrossRef]
  39. R. Simon, N. Mukunda, “Twisted Gaussian Schell-model beams,” J. Opt. Soc. Am. A 10, 95–109 (1993); A. T. Friberg, E. Tervonen, J. Turunen, “Interpretation and experimental demonstration of twisted Gaussian Schell-model beams,” J. Opt. Soc. Am. A 11, 1818–1826 (1994); D. Ambrosini, V. Bagini, F. Gori, M. Santarsiero, “Twisted Gaussian Schell-model beams: a superposition model,” J. Mod. Opt. 41, 1391–1399 (1994); R. Simon, A. T. Friberg, E. Wolf, “Transfer of radiance by twisted Gaussian Schell-model beams in paraxial systems,” Pure Appl. Opt. 5, 331–343 (1996); R. Simon, N. Mukunda, “Twist phase in Gaussian beam optics,” J. Opt. Soc. Am. A 15, 2373–2382 (1998); R. Simon, N. Mukunda, “Shape-invariant anisotropic Gaussian Schell-model beams: a complete characterization,” J. Opt. Soc. Am. A 15, 1361–1370 (1998); R. Simon, N. Mukunda, “Iwasawa decomposition in first-order optics: universal treatment of shape-invariant propagation for coherent and partially coherent beams,” J. Opt. Soc. Am. A 15, 2146–2155 (1998). [CrossRef]
  40. F. Gori, M. Santarsiero, R. Borghi, S. Vicalvi, “Partially coherent sources with helicoidal modes,” J. Mod. Opt. 45, 539–554 (1998). [CrossRef]
  41. A. E. Siegman, Lasers (Oxford U. Press, Oxford, UK, 1986), Chap. 19.
  42. D. Rozas, Z. S. Sacks, G. A. Swartzlander, “Experimental observation of fluidlike motion of optical vortices,” Phys. Rev. Lett. 79, 3399–3402 (1997). [CrossRef]
  43. I. S. Gradshetyn, I. M. Ryzhik, Table of Integrals, Series, and Products, 5th ed. (Academic, Boston, 1994), Sec. 7.414.7, p. 850.
  44. I. S. Gradshetyn, I. M. Ryzhik, Table of Integrals, Series, and Products, 5th ed. (Academic, Boston, 1994), Sec. 3.551.6, p. 403.

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