Abstract

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

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    [CrossRef]
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    [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).
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  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]
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  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]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [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).
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    [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]
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    [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.

1998 (5)

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]

R. Piestun, J. Shamir, “Generalized propagation-invariant wave fields,” J. Opt. Soc. Am. A 15, 3039–3044 (1998).
[CrossRef]

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]

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]

F. Gori, M. Santarsiero, R. Borghi, S. Vicalvi, “Partially coherent sources with helicoidal modes,” J. Mod. Opt. 45, 539–554 (1998).
[CrossRef]

1997 (6)

D. Rozas, Z. S. Sacks, G. A. Swartzlander, “Experimental observation of fluidlike motion of optical vortices,” Phys. Rev. Lett. 79, 3399–3402 (1997).
[CrossRef]

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]

G. S. Agarwal, R. R. Puri, R. P. Singh, “Vortex states for the quantized radiation field,” Phys. Rev. A 56, 4207–4215 (1997).
[CrossRef]

E. Abramochkin, N. Losevsky, V. Volostnikov, “Generation of spiral-type laser beams,” Opt. Commun. 141, 59–64 (1997).
[CrossRef]

I. Bialynicki-Birula, Z. Bialynicka-Birula, “Rotational frequency shift,” Phys. Rev. Lett. 78, 2539–2542 (1997).
[CrossRef]

J. Courtial, K. Dholakia, L. Allen, M. J. Padgett, “Gaussian beams with very high orbital angular momentum,” Opt. Commun. 144, 210–213 (1997).
[CrossRef]

1996 (4)

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]

B. Spektor, R. Piestun, J. Shamir, “Dark beams with a constant notch,” Opt. Lett. 21, 456–458 (1996).
[CrossRef] [PubMed]

G. Nienhuis, “Doppler effect induced by rotating lenses,” Opt. Commun. 132, 8–14 (1996).
[CrossRef]

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]

1995 (3)

F. S. Roux, “Dynamical behavior of optical vortices,” J. Opt. Soc. Am. B 12, 1215–1221 (1995).
[CrossRef]

M. Vaupel, C. O. Weiss, “Circling optical vortices,” Phys. Rev. A 51, 4078–4085 (1995).
[CrossRef] [PubMed]

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]

1994 (4)

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]

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]

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]

L. Allen, M. Babiker, W. L. Power, “Azimuthal Doppler shift in light beams with orbital angular momentum,” Opt. Commun. 112, 141–144 (1994).
[CrossRef]

1993 (4)

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]

G. Indebetouw, “Optical vortices and their propagation,” J. Mod. Opt. 40, 73–87 (1993).
[CrossRef]

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]

S. J. Van Enk, “Geometric phase, transformations of Gaussian light beams and angular momentum transfer,” Opt. Commun. 102, 59–64 (1993).
[CrossRef]

1992 (4)

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]

V. Yu. Bazhenov, M. S. Soskin, M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39, 985–990 (1992).
[CrossRef]

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]

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]

1988 (1)

R. Simon, N. Mukunda, E. C. G. Sudarshan, “Partially coherent beams and a generalized abcd-law,” Opt. Commun. 65, 322–328 (1988).
[CrossRef]

1987 (1)

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]

1985 (2)

E. C. G. Sudarshan, N. Mukunda, R. Simon, “Realization of first-order optical systems using thin lenses,” Opt. Acta 32, 855–872 (1985).
[CrossRef]

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]

1984 (1)

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]

1982 (1)

1974 (1)

J. F. Nye, M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London, Ser. A 336, 165–190 (1974).
[CrossRef]

1969 (1)

1936 (1)

J. Williamson, “On the algebraic problem concerning the normal forms of linear dynamical systems,” Am. J. Math. 58, 141–163 (1936).
[CrossRef]

Abramochkin, E.

E. Abramochkin, N. Losevsky, V. Volostnikov, “Generation of spiral-type laser beams,” Opt. Commun. 141, 59–64 (1997).
[CrossRef]

Agarwal, G. S.

G. S. Agarwal, R. R. Puri, R. P. Singh, “Vortex states for the quantized radiation field,” Phys. Rev. A 56, 4207–4215 (1997).
[CrossRef]

Allen, L.

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]

J. Courtial, K. Dholakia, L. Allen, M. J. Padgett, “Gaussian beams with very high orbital angular momentum,” Opt. Commun. 144, 210–213 (1997).
[CrossRef]

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]

L. Allen, M. Babiker, W. L. Power, “Azimuthal Doppler shift in light beams with orbital angular momentum,” Opt. Commun. 112, 141–144 (1994).
[CrossRef]

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]

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]

Babiker, M.

L. Allen, M. Babiker, W. L. Power, “Azimuthal Doppler shift in light beams with orbital angular momentum,” Opt. Commun. 112, 141–144 (1994).
[CrossRef]

Bazhenov, V. Yu.

V. Yu. Bazhenov, M. S. Soskin, M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39, 985–990 (1992).
[CrossRef]

Beijerbergen, M. W.

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]

Beijersbergen, M. W.

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]

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]

Berry, M. V.

J. F. Nye, M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London, Ser. A 336, 165–190 (1974).
[CrossRef]

Berzanskis, A.

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]

Bialynicka-Birula, Z.

I. Bialynicki-Birula, Z. Bialynicka-Birula, “Rotational frequency shift,” Phys. Rev. Lett. 78, 2539–2542 (1997).
[CrossRef]

Bialynicki-Birula, I.

I. Bialynicki-Birula, Z. Bialynicka-Birula, “Rotational frequency shift,” Phys. Rev. Lett. 78, 2539–2542 (1997).
[CrossRef]

Borghi, R.

F. Gori, M. Santarsiero, R. Borghi, S. Vicalvi, “Partially coherent sources with helicoidal modes,” J. Mod. Opt. 45, 539–554 (1998).
[CrossRef]

Chavez-Cerda, S.

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]

Chinaglia, W.

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]

Coerwinkel, R. P. C.

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]

Courtial, J.

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]

J. Courtial, K. Dholakia, L. Allen, M. J. Padgett, “Gaussian beams with very high orbital angular momentum,” Opt. Commun. 144, 210–213 (1997).
[CrossRef]

Dholakia, K.

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]

J. Courtial, K. Dholakia, L. Allen, M. J. Padgett, “Gaussian beams with very high orbital angular momentum,” Opt. Commun. 144, 210–213 (1997).
[CrossRef]

Di Trapani, P.

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]

Dutta, B.

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]

Eppich, B.

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]

Friberg, A. T.

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]

Friese, M. E. J.

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]

Gao, C.

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]

Gloge, D.

Gori, F.

F. Gori, M. Santarsiero, R. Borghi, S. Vicalvi, “Partially coherent sources with helicoidal modes,” J. Mod. Opt. 45, 539–554 (1998).
[CrossRef]

Gradshetyn, I. S.

I. S. Gradshetyn, I. M. Ryzhik, Table of Integrals, Series, and Products, 5th ed. (Academic, Boston, 1994), Sec. 7.414.7, p. 850.

I. S. Gradshetyn, I. M. Ryzhik, Table of Integrals, Series, and Products, 5th ed. (Academic, Boston, 1994), Sec. 3.551.6, p. 403.

He, H.

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]

Heckenberg, N. R.

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]

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]

Indebetouw, G.

G. Indebetouw, “Optical vortices and their propagation,” J. Mod. Opt. 40, 73–87 (1993).
[CrossRef]

Khizhnyak, A. I.

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]

Kreminskaya, L. V.

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]

Kristensen, M.

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]

Law, C. T.

Losevsky, N.

E. Abramochkin, N. Losevsky, V. Volostnikov, “Generation of spiral-type laser beams,” Opt. Commun. 141, 59–64 (1997).
[CrossRef]

Marcuse, D.

Martinez-Herrero, R.

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]

McDonald, G. S.

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]

McDuff, R.

Mejias, P. M.

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]

Minardi, S.

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]

Mukunda, N.

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]

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]

R. Simon, N. Mukunda, E. C. G. Sudarshan, “Partially coherent beams and a generalized abcd-law,” Opt. Commun. 65, 322–328 (1988).
[CrossRef]

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]

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]

E. C. G. Sudarshan, N. Mukunda, R. Simon, “Realization of first-order optical systems using thin lenses,” Opt. Acta 32, 855–872 (1985).
[CrossRef]

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]

Nazarathy, M.

Nemes, G.

New, G. H. C.

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]

Nienhuis, G.

G. Nienhuis, “Doppler effect induced by rotating lenses,” Opt. Commun. 132, 8–14 (1996).
[CrossRef]

Nye, J. F.

J. F. Nye, M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London, Ser. A 336, 165–190 (1974).
[CrossRef]

Padgett, M. J.

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]

J. Courtial, K. Dholakia, L. Allen, M. J. Padgett, “Gaussian beams with very high orbital angular momentum,” Opt. Commun. 144, 210–213 (1997).
[CrossRef]

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]

Piestun, R.

Power, W. L.

L. Allen, M. Babiker, W. L. Power, “Azimuthal Doppler shift in light beams with orbital angular momentum,” Opt. Commun. 112, 141–144 (1994).
[CrossRef]

Puri, R. R.

G. S. Agarwal, R. R. Puri, R. P. Singh, “Vortex states for the quantized radiation field,” Phys. Rev. A 56, 4207–4215 (1997).
[CrossRef]

Robertson, D. A.

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]

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]

Roux, F. S.

Rozas, D.

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]

D. Rozas, Z. S. Sacks, G. A. Swartzlander, “Experimental observation of fluidlike motion of optical vortices,” Phys. Rev. Lett. 79, 3399–3402 (1997).
[CrossRef]

Rubinsztein-Dunlop, H.

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]

Ryzhik, I. M.

I. S. Gradshetyn, I. M. Ryzhik, Table of Integrals, Series, and Products, 5th ed. (Academic, Boston, 1994), Sec. 3.551.6, p. 403.

I. S. Gradshetyn, I. M. Ryzhik, Table of Integrals, Series, and Products, 5th ed. (Academic, Boston, 1994), Sec. 7.414.7, p. 850.

Sacks, Z. S.

D. Rozas, Z. S. Sacks, G. A. Swartzlander, “Experimental observation of fluidlike motion of optical vortices,” Phys. Rev. Lett. 79, 3399–3402 (1997).
[CrossRef]

Santarsiero, M.

F. Gori, M. Santarsiero, R. Borghi, S. Vicalvi, “Partially coherent sources with helicoidal modes,” J. Mod. Opt. 45, 539–554 (1998).
[CrossRef]

Sapone, S.

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]

Serna, J.

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]

Shamir, J.

Siegman, A.

A. Siegman, “New developments in laser resonators,” in Optical Resonators, D. A. Holmes, ed., Proc. SPIE1224, 2–10 (1990).
[CrossRef]

Siegman, A. E.

Simon, R.

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]

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]

R. Simon, N. Mukunda, E. C. G. Sudarshan, “Partially coherent beams and a generalized abcd-law,” Opt. Commun. 65, 322–328 (1988).
[CrossRef]

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]

E. C. G. Sudarshan, N. Mukunda, R. Simon, “Realization of first-order optical systems using thin lenses,” Opt. Acta 32, 855–872 (1985).
[CrossRef]

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]

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]

Singh, R. P.

G. S. Agarwal, R. R. Puri, R. P. Singh, “Vortex states for the quantized radiation field,” Phys. Rev. A 56, 4207–4215 (1997).
[CrossRef]

Smith, C. P.

Smith, G. M.

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]

Soskin, M. S.

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]

V. Yu. Bazhenov, M. S. Soskin, M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39, 985–990 (1992).
[CrossRef]

Spektor, B.

Spreeuw, R. J. C.

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]

Sudarshan, E. C. G.

R. Simon, N. Mukunda, E. C. G. Sudarshan, “Partially coherent beams and a generalized abcd-law,” Opt. Commun. 65, 322–328 (1988).
[CrossRef]

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]

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]

E. C. G. Sudarshan, N. Mukunda, R. Simon, “Realization of first-order optical systems using thin lenses,” Opt. Acta 32, 855–872 (1985).
[CrossRef]

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]

Swartzlander, G. A.

D. Rozas, Z. S. Sacks, G. A. Swartzlander, “Experimental observation of fluidlike motion of optical vortices,” Phys. Rev. Lett. 79, 3399–3402 (1997).
[CrossRef]

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]

Turnbull, G. A.

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]

Van der Veen, H. E. L. O.

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]

Van Enk, S. J.

S. J. Van Enk, “Geometric phase, transformations of Gaussian light beams and angular momentum transfer,” Opt. Commun. 102, 59–64 (1993).
[CrossRef]

Vasnetsov, M. V.

V. Yu. Bazhenov, M. S. Soskin, M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39, 985–990 (1992).
[CrossRef]

Vaupel, M.

M. Vaupel, C. O. Weiss, “Circling optical vortices,” Phys. Rev. A 51, 4078–4085 (1995).
[CrossRef] [PubMed]

Vicalvi, S.

F. Gori, M. Santarsiero, R. Borghi, S. Vicalvi, “Partially coherent sources with helicoidal modes,” J. Mod. Opt. 45, 539–554 (1998).
[CrossRef]

Volostnikov, V.

E. Abramochkin, N. Losevsky, V. Volostnikov, “Generation of spiral-type laser beams,” Opt. Commun. 141, 59–64 (1997).
[CrossRef]

Weber, H.

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]

Weiss, C. O.

M. Vaupel, C. O. Weiss, “Circling optical vortices,” Phys. Rev. A 51, 4078–4085 (1995).
[CrossRef] [PubMed]

White, A. G.

Williamson, J.

J. Williamson, “On the algebraic problem concerning the normal forms of linear dynamical systems,” Am. J. Math. 58, 141–163 (1936).
[CrossRef]

Woerdman, J. P.

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]

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]

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]

Am. J. Math. (1)

J. Williamson, “On the algebraic problem concerning the normal forms of linear dynamical systems,” Am. J. Math. 58, 141–163 (1936).
[CrossRef]

J. Mod. Opt. (4)

F. Gori, M. Santarsiero, R. Borghi, S. Vicalvi, “Partially coherent sources with helicoidal modes,” J. Mod. Opt. 45, 539–554 (1998).
[CrossRef]

G. Indebetouw, “Optical vortices and their propagation,” J. Mod. Opt. 40, 73–87 (1993).
[CrossRef]

V. Yu. Bazhenov, M. S. Soskin, M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39, 985–990 (1992).
[CrossRef]

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]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (3)

J. Opt. Soc. Am. B (2)

Opt. Acta (1)

E. C. G. Sudarshan, N. Mukunda, R. Simon, “Realization of first-order optical systems using thin lenses,” Opt. Acta 32, 855–872 (1985).
[CrossRef]

Opt. Commun. (11)

L. Allen, M. Babiker, W. L. Power, “Azimuthal Doppler shift in light beams with orbital angular momentum,” Opt. Commun. 112, 141–144 (1994).
[CrossRef]

J. Courtial, K. Dholakia, L. Allen, M. J. Padgett, “Gaussian beams with very high orbital angular momentum,” Opt. Commun. 144, 210–213 (1997).
[CrossRef]

S. J. Van Enk, “Geometric phase, transformations of Gaussian light beams and angular momentum transfer,” Opt. Commun. 102, 59–64 (1993).
[CrossRef]

R. Simon, N. Mukunda, E. C. G. Sudarshan, “Partially coherent beams and a generalized abcd-law,” Opt. Commun. 65, 322–328 (1988).
[CrossRef]

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]

E. Abramochkin, N. Losevsky, V. Volostnikov, “Generation of spiral-type laser beams,” Opt. Commun. 141, 59–64 (1997).
[CrossRef]

G. Nienhuis, “Doppler effect induced by rotating lenses,” Opt. Commun. 132, 8–14 (1996).
[CrossRef]

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]

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]

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]

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]

Opt. Lett. (2)

Phys. Rev. A (7)

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]

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]

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]

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]

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]

G. S. Agarwal, R. R. Puri, R. P. Singh, “Vortex states for the quantized radiation field,” Phys. Rev. A 56, 4207–4215 (1997).
[CrossRef]

M. Vaupel, C. O. Weiss, “Circling optical vortices,” Phys. Rev. A 51, 4078–4085 (1995).
[CrossRef] [PubMed]

Phys. Rev. Lett. (5)

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]

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]

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]

I. Bialynicki-Birula, Z. Bialynicka-Birula, “Rotational frequency shift,” Phys. Rev. Lett. 78, 2539–2542 (1997).
[CrossRef]

D. Rozas, Z. S. Sacks, G. A. Swartzlander, “Experimental observation of fluidlike motion of optical vortices,” Phys. Rev. Lett. 79, 3399–3402 (1997).
[CrossRef]

Proc. R. Soc. London, Ser. A (1)

J. F. Nye, M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London, Ser. A 336, 165–190 (1974).
[CrossRef]

Other (5)

A. Siegman, “New developments in laser resonators,” in Optical Resonators, D. A. Holmes, ed., Proc. SPIE1224, 2–10 (1990).
[CrossRef]

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]

I. S. Gradshetyn, I. M. Ryzhik, Table of Integrals, Series, and Products, 5th ed. (Academic, Boston, 1994), Sec. 7.414.7, p. 850.

I. S. Gradshetyn, I. M. Ryzhik, Table of Integrals, Series, and Products, 5th ed. (Academic, Boston, 1994), Sec. 3.551.6, p. 403.

A. E. Siegman, Lasers (Oxford U. Press, Oxford, UK, 1986), Chap. 19.

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Figures (4)

Fig. 1
Fig. 1

Physically permitted values for the quality parameters Meff4, t. Inequality (2.17), which is equivalent to the optical uncertainty principle, restricts these values to the shaded region in the (Meff4, t) plane. Regions A and B, which inequalities (2.14) admit, are physically forbidden.

Fig. 2
Fig. 2

Solid curve, propagation characteristics m(z)|Φ1(r; z)| of the doughnut hole in the absence of the vortex phase, Eq. (3.21), for several values of the propagation distance z. Dashed curve, case m(z)|Ψ0±1(r, θ; z)| with the vortex phase on, Eqs. (3.19), shown for comparison. In view of the rotational invariance of these beams, only the x sections (y=0) are shown, as a function of the scaled variable x/m(z). λ=0.001 mm, w=0.1 mm.

Fig. 3
Fig. 3

Solid curve, propagation characteristics m(z)|Φ(r; z)| of a thin hole in the absence of the vortex phase, Eq. (4.8), for several values of the propagation distance z. In view of the rotational invariance, only the x sections (y=0) are shown, as a function of the scaled variable x/mw(z). λ=0.001 mm, w=0.1 mm, a=w/5. Dashed curve, fundamental Gaussian mode of the same waist size w, shown for comparison.

Fig. 4
Fig. 4

Solid curve, propagation characteristics m(z)|Ψ(r, θ; z)| of the filament vortex, relation (4.14), for several values of the propagation distance z. In view of the rotational invariance, only the x sections (y=0) are shown, as a function of the scaled variable x/mw(z). λ=0.001 mm, w=0.1 mm, a=w/10. Dashed curve, fundamental Gaussian mode of the same waist size w, shown for comparison.

Equations (78)

Equations on this page are rendered with MathJax. Learn more.

px=λ¯ix,py=λ¯iy;
[x, px]=[y, py]=iλ¯.
Vx2xy(xpx)sxpyyxy2ypx(ypy)s(pxx)spxypx2pxpypyx(pyy)spypxpy2.
SΩST=Ω,Ω=01-10.
S:VinVout=SVinST.
S:VinΩVoutΩ=SVinΩS-1.
Tl(-1)l tr(VΩ)2l=tr(VΩVΩT)l,
SV;τ:VSV;τV(SV;τ)T=diag(κ1τ, κ2τ, κ1/τ, κ2/τ);
SV;τ:VΩSV;τVΩ(SV;τ)-1=00κ1τ0000κ2τ-κ1/τ0000-κ2/τ00.
Tl(-1)l tr(VΩ)2l=2(κ12l+κ22l),
det V=κ12κ22=18T12-14T2,
T3=34T2T1-18T13.
x2px2(λ¯/2)2,y2py2(λ¯/2)2.
κ1λ¯/2,κ2λ¯/2.
2κ1/λ¯2κ2/λ¯1.
T=κ12+κ22=12T1,Meff4=2κ1λ¯2κ2λ¯,
t=122κ1λ¯2+2κ2λ¯2,α=122κ1λ¯-2κ2λ¯.
Meff41,t1.
2t+2Meff4-2t-2Meff42.
t-1t2-(Meff4)2,
tMeff42t-11.
Φl(r;0)=1π2wl+1rll!exp-r2w2,
x2=y2=12r2,px2=py2=12-λ¯22,
22x2+2y2.
V=diag(l+1)2w22,(l+1)2w22,λ¯2w2,λ¯2w2.
Meff42λ¯2(det V)1/2=(l+1),
α122κ1λ¯-2κ2λ¯=0.
Ψ0±l(r, θ)exp(±ilθ)Φl(r; 0)=1π2wl+1rll!exp-r2w2exp(±ilθ).
xpy=-ypx=-iλ¯2θ.
V=(l+1)2w2200lλ¯20(l+1)2w22±lλ¯200±lλ¯2(l+1)λ¯2w20lλ¯200(l+1)λ¯2w2.
Sτ=12100τ01τ00±τ-110±τ-1001,
Sτ:VSτVSτT=diag(κ1τ, κ2τ,κ1/τ, κ2/τ),
κ1=(2l+1)λ¯/2,κ2=λ¯/2.
Meff4=2κ1λ¯2κ2λ¯=2l+1,
α=(κ1-κ2)λ¯=l.
zR=x2px21/2=y2py21/2.
zR=w22λ¯=2λ¯x2=2λ¯y2.
zR=l+12w2λ¯=1l+12λ¯x2.
zR=w22λ¯=1l+12λ¯x2.
Δθ=(px2)1/2=λ¯21(x2)1/2,
Δθ=(px2)1/2=l+1λ¯21(x2)1/2,
Δθ=(px2)1/2=(l+1)λ¯21(x2)1/2.
Ψp±l(r, θ; 0)=1π2wl+1p!(p+l)!1/2×rlLpl2r2w2exp-r2w2exp(±ilθ).
Ψp±l(r, θ; z)=1m(z)Ψp±lrm(z), θ; 0×expir22λ¯R(z)exp[iφp,l(z)];
m(z)=1+z2zw21/2,R(z)=z+zw2R,
φp,l(z)=-(2p+l+1)arctanzzw,zw=w22λ¯.
Φl(r; 0)=pcpΨp0(r; 0),
cp=2πw211!(-1)pp![Γ(1+l2)]2Γ(1-p+l2).
Φl(r; z)=pcpΨp0(r;z)=pcpΨp0rm(z); 0exp[iφp,0(z)]1m(z)×expir22λ¯R(z).
h(r)=1-exp(-r2/a2),
Φ(r; 0)Ψ(r)h(r)=2π1/21wexp-r2w21-exp-r2a2,
w=w2-4w2a2w2+2a2+w2a2w2+a21/2.
Ψ(r, θ; 0)=2π1/21wexp-r2w2×1-exp-r2a2exp(ilθ),
Φ(r; 0)=2π1/21wexp-r2w2-exp-r2b2,
b=1a2+1w2-1/2a.
Φ(r; z)=2π1/21mw(z)wexp-r2mw2(z)w2×expir22λ¯Rw(z)exp[iφw(z)]-bw2π1/21mb(z)bexp-r2mb2(z)b2×expir22λ¯Rb(z)exp[iφb(z)],
mb(z)=1+z2zb21/2,Rb(z)=z+zb2z,
φb(z)=-arctanzzb, zb=b22λ¯,
Φ(r; z)=2π1/2w2λ¯zexp-iπ2expir22λ¯z×exp-wr2λ¯z2-b2w2exp-br2λ¯z2.
r02z2=4λ¯2w2-b2lnw2b2.
Ψ(r, θ; 0)=cpΨp±l(r, θ; 0).
cp=p!(p+l)!1/20dt[exp(-t)-exp(-st)]tl/2Lpl(t),
s=1+w22a2.
0dt exp(-st)tβLpα(t)=Γ(β+1)Γ(α+p+1)p!Γ(α+1)F-p, β+1; α+1; -1s.
cp=(p+l)!p!1/2Γl2+1Γ(l+1)F-p,l2+1; l+1;1-s-(l/2+1)F-p,l2+1; l+1; s-1.
Ψ(r,θ; 0)Ψ(r, θ; z)=cpΨp±l(r, θ; z),
V=diagw24,w24,2λ¯2w2,2λ¯2w2,
Meff4=2λ¯2(det V)1/2=2,α=0.
zR=x2px21/2=12πw2λ¯.
0exp(-βx)xsinh(γx)dx=12lnβ+γβ-γ,
V=w2400λ¯l20w24-λ¯l200-λ¯l22λ¯2w2(1+η2l)0λ¯l2002λ¯2w2(1+η2l),
η=12lnw24a2.
τ=12w22λ¯11+ηl2,
VSτVSτT=diag(κ1τ, κ2τ, κ1/τ, κ2/τ);
κ1=2λ¯2(1+ηl2)1/2+lλ¯2,
κ2=2λ¯2(1+ηl2)1/2-lλ¯2.
Meff4=2κ1λ¯2κ2λ¯=2+l2lnw24a2-1,
α=122κ1λ¯-2κ2λ¯=l.

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