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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 14, Iss. 11 — Nov. 1, 1997
  • pp: 3054–3065

Propagation dynamics of optical vortices

D. Rozas, C. T. Law, and G. A. Swartzlander, Jr.  »View Author Affiliations

JOSA B, Vol. 14, Issue 11, pp. 3054-3065 (1997)

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Optical vortices in linear and nonlinear media may exhibit propagation dynamics similar to hydrodynamic vortex phenomena. Analytical and numerical methods are used to describe and investigate the interaction between vortices and the background field. We demonstrate that optical vortices that have quasi-point core functions, such as optical vortex solitons, may orbit one another at rates that are orders of magnitude larger than those with nonlocalized cores.

© 1997 Optical Society of America

D. Rozas, C. T. Law, and G. A. Swartzlander, Jr., "Propagation dynamics of optical vortices," J. Opt. Soc. Am. B 14, 3054-3065 (1997)

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  1. J. F. Nye and M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London Ser. A 336, 165–190 (1974). [CrossRef]
  2. M. V. Berry, “Singularities in waves and rays,” in Physics of Defects, R. Balian, M. Kleman, and J.-P. Poirier, eds. (North-Holland, Amsterdam, 1981), pp. 453–543.
  3. N. B. Baranova, B. Ya. Zel’dovich, A. V. Mamaev, N. F. Pilipetskii, and V. V. Shkukov, “Dislocations of the wavefront of a speckle-inhomogeneous field (theory and experiment),” Pis’ma Zh. Eksp. Teor. Fiz. 33, 206–210 (1981) [ JETP Lett. 33, 195–199 (1981)].
  4. N. B. Baranova, A. V. Mamaev, N. F. Pilipetskii, V. V. Shkukov, and B. Ya. Zel’dovich, “Wavefront dislocations: topological limitations for adaptive systems with phase conjugation,” J. Opt. Soc. Am. 73, 525–528 (1983). [CrossRef]
  5. G. Goubau and F. Schwering, “On the guided propagation of electromagnetic wave beams,” IRE Trans. Antennas Propag. 9, 248–256 (1961). [CrossRef]
  6. J. M. Vaughan and D. V. Willetts, “Temporal and interference fringe analysis of TEM01* laser modes,” J. Opt. Soc. Am. 73, 1018–1021 (1983). [CrossRef]
  7. A. G. White, C. P. Smith, N. R. Heckenberg, H. Rubinsztein-Dunlop, R. McDuff, C. O. Weiss, and Chr. Tamm, “Interferometric measurements of phase singularities in the output of a visible laser,” J. Mod. Opt. 38, 2531–2541 (1991). [CrossRef]
  8. E. Abramochkin and V. Volostnikov, “Beam transformations and nontransformed beams,” Opt. Commun. 83, 123–135 (1991). [CrossRef]
  9. L. M. Pismen and A. A. Nepomnyashchy, “On interaction of spiral waves,” Physica D 54, 183–193 (1992). [CrossRef]
  10. V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Screw dislocations in light wavefronts,” J. Mod. Opt. 39, 985–990 (1992). [CrossRef]
  11. S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, “The phase rotor filter,” J. Mod. Opt. 39, 1147–1154 (1992). [CrossRef]
  12. N. R. Heckenberg, R. McDuff, C. P. Smith, H. Rubinsztein-Dunlop, and M. J. Wegener, “Laser beams with phase singularities,” Opt. Quantum Electron. 24, S951–S962 (1992). [CrossRef]
  13. I. V. Basistiy, V. Yu. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103, 422–428 (1993). [CrossRef]
  14. G. Indebetouw, “Optical vortices and their propagation,” J. Mod. Opt. 40, 73–87 (1993). [CrossRef]
  15. M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, and J. P. Woerdman, “Helical-wavefront laser beams produced with a spiral phaseplate,” Opt. Commun. 112, 321–327 (1994). [CrossRef]
  16. F. B. de Colstoun, G. Khitrova, A. V. Fedorov, T. R. Nelson, C. Lowry, T. M. Brennan, B. G. Hammons, and P. D. Maker, “Transverse modes, vortices and vertical-cavity surface-emitting lasers,” Chaos Solitons Fractals 4, 1575–1596 (1994). [CrossRef]
  17. F. S. Roux, “Dynamical behavior of optical vortices,” J. Opt. Soc. Am. B 12, 1215–1221 (1995). [CrossRef]
  18. P. Coullet, L. Gil, and F. Rocca, “Optical vortices,” Opt. Commun. 73, 403–408 (1989). [CrossRef]
  19. G. L. Lippi, T. Ackemann, L. M. Hoffer, A. Gahl, and W. Lange, “Interplay of linear and nonlinear effects in the formation of optical vortices in a nonlinear resonator,” Phys. Rev. A 48, R4043–R4046 (1993). [CrossRef]
  20. M. Brambilla, M. Cattaneo, L. A. Lugiato, R. Pirovano, F. Pratti, A. J. Kent, G.-L. Oppo, A. B. Coates, C. O Weiss, C. Green, E. J. D’Angelo, and J. R. Tredicce, “Dynamical transverse laser patterns. I. Theory,” Phys. Rev. A 49, 1427–1451 (1994). [CrossRef] [PubMed]
  21. G. Indebetouw and D. R. Korwan, “Model of vortices nucleation in a photorefractive phase-conjugate resonator,” J. Mod. Opt. 41, 941–950 (1994). [CrossRef]
  22. G. Slekys, K. Staliunas, and C. O. Weiss, “Motion of phase singularities in a class-B laser,” Opt. Commun. 119, 433–446 (1995). [CrossRef]
  23. K. Staliunas and C. O. Weiss, “Nonstationary vortex lattices in large-aperture class B lasers,” J. Opt. Soc. Am. B 12, 1142–1149 (1995). [CrossRef]
  24. N. R. Heckenberg, M. Vaupel, J. T. Malos, and C. O. Weiss, “Optical-vortex pair creation and annihilation and helical astigmatism of a nonplanar ring resonator,” Phys. Rev. A 54, 1–10 (1996).
  25. W. J. Firth and A. Lord, “Two-dimensional solitons in a Kerr cavity,” J. Mod. Opt. 43, 1071–1077 (1996). [CrossRef]
  26. V. Yu. Bazhenov, M. V. Vasnetsov, and M. S. Soskin, “Laser beams with screw dislocations in their wavefronts,” Pis’ma Zh. Eksp. Teor. Fiz. 52, 1037–1039 (1990) [ JETP Lett. 52, 429–431 (1990)].
  27. N. R. Heckenberg, R. McDuff, C. P. Smith, and A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17, 221–223 (1992). [CrossRef]
  28. G. A. Swartzlander, Jr., Z. Sacks, X. Zhang, D. Rozas, and C. T. Law, “Formation and propagation of optical vortices,” in Digest of the International Quantum Electronics Conference, 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), p. 31; D. Rozas, Z. S. Sacks, and G. A. Swartzlander, Jr., “Experimental observations of fluid-like motion of optical vortices,” Phys. Rev. Lett. (to be published).
  29. K. Staliunas, “Dynamics of optical vortices in a laser beam,” Opt. Commun. 90, 123–127 (1992). [CrossRef]
  30. K. Staliunas, “Optical vortices during three-way nonlinear coupling,” Opt. Commun. 91, 82–86 (1992). [CrossRef]
  31. I. Freund, N. Shvartsman, and V. Freilikher, “Optical dislocation networks in highly random media,” Opt. Commun. 101, 247–264 (1993). [CrossRef]
  32. I. Freund, “Optical vortices in Gaussian random wave fields: statistical probability densities,” J. Opt. Soc. Am. A 11, 1644–1652 (1994). [CrossRef]
  33. K. Staliunas, A. Berzanskis, and V. Jarutis, “Vortex statistics in optical speckle fields,” Opt. Commun. 120, 23–28 (1995). [CrossRef]
  34. C. O. Weiss, H. R. Telle, and K. Staliunas, “Restless optical vortex,” Phys. Rev. A 47, R1616–R1619 (1993). [CrossRef] [PubMed]
  35. D. Y. Tang, N. R. Heckenberg, and C. O. Weiss, “Phase-dependent helical pattern formation in a laser,” Opt. Commun. 114, 95–100 (1995). [CrossRef]
  36. G. A. Swartzlander, Jr., and C. T. Law, “Optical vortex solitons observed in Kerr nonlinear media,” Phys. Rev. Lett. 69, 2503–2506 (1992). [CrossRef] [PubMed]
  37. G. A. Swartzlander, Jr., and C. T. Law, “The optical vortex soliton,” Opt. Photonics News 4 (12), 10 (1993). [CrossRef]
  38. A. V. Mamaev, M. Saffman, D. Z. Anderson, and A. A. Zozulya, “Propagation of light beams in anisotropic nonlinear media: from symmetry breaking to spatial turbulence,” Phys. Rev. A 54, 870–879 (1996). [CrossRef] [PubMed]
  39. A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Break-up of two-dimensional bright spatial solitons due to transverse modulation instability,” Europhys. Lett. 35, 25–30 (1996). [CrossRef]
  40. A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Propagation of dark stripe beams in nonlinear media: snake instability and creation of optical vortices,” Phys. Rev. Lett. 76, 2262–2265 (1996). [CrossRef] [PubMed]
  41. V. Tikhonenko, J. Christou, B. Luther-Davies, and Yu. S. Kivshar, “Observation of vortex solitons created by the instability of dark soliton stripes,” Opt. Lett. 21, 1129–1131 (1996). [CrossRef] [PubMed]
  42. G. S. McDonald, K. S. Syed, and W. J. Firth, “Optical vortices in beam propagation through a self-defocusing medium,” Opt. Commun. 94, 469–476 (1992). [CrossRef]
  43. A. W. Snyder, L. Poladian, and D. J. Mitchell, “Stable black self-guided beams of circular symmetry in a bulk Kerr medium,” Opt. Lett. 17, 789–791 (1992). [CrossRef] [PubMed]
  44. R. Y. Chiao, I. H. Deutsch, J. C. Garrison, and E. M. Wright, in Serge Akhmanov: A Memorial Volume, H. Walther, ed. (Hilger, Bristol, UK, 1992), pp. 151–182.
  45. C. T. Law and G. A. Swartzlander, Jr., “Optical vortex solitons and the stability of dark soliton stripes,” Opt. Lett. 18, 586–588 (1993). [CrossRef]
  46. G. S. McDonald, K. S. Syed, and W. J. Firth, “Dark spatial soliton break-up in the transverse plane,” Opt. Commun. 95, 281–288 (1993). [CrossRef]
  47. K. Staliunas, “Vortices and dark solitons in the two-dimensional nonlinear Schrödinger equation,” Chaos Solitons Fractals 4, 1783–1796 (1994). [CrossRef]
  48. C. T. Law and G. A. Swartzlander, Jr., “Polarized optical vortex solitons: instabilities and dynamics in Kerr nonlinear media,” Chaos Solitons Fractals 4, 1759–1766 (1994). [CrossRef]
  49. I. Velchev, A. Dreischuh, D. Neshev, and S. Dinev, “Interactions of optical vortex solitons superimposed on different background beams,” Opt. Commun. 130, 385–392 (1996). [CrossRef]
  50. Y. Chen and J. Atai, “Dynamics of optical-vortex solitons in a perturbed nonlinear medium,” J. Opt. Soc. Am. B 11, 2000–2003 (1994). [CrossRef]
  51. J. Christou, V. Tikhonenko, Yu. S. Kivshar, and B. Luther-Davies, “Vortex soliton motion and steering,” Opt. Lett. 21, 1649–1651 (1996). [CrossRef] [PubMed]
  52. See, for example, M. S. El Naschie, ed., “Special issue on nonlinear optical structures, patterns, chaos,” Chaos Solitons Fractals 4(8/9) (1994).
  53. E. M. Wright, R. Y. Chiao, and J. C. Garrison, “Optical anyons: atoms trapped on electromagnetic vortices,” Chaos Solitons Fractals 4, 1797–1803 (1994). [CrossRef]
  54. G. Duree, M. Morin, G. Salamo, M. Segev, B. Crosignani, P. DiPorto, E. Sharp, and A. Yariv, “Dark photorefractive spatial solitons and photorefractive vortex solitons,” Phys. Rev. Lett. 74, 1978–1981 (1995). [CrossRef] [PubMed]
  55. M. Morin, G. Duree, and M. Segev, “Waveguides formed by quasi-steady-state photorefractive spatial solitons,” Opt. Lett. 20, 2066–2068 (1995). [CrossRef] [PubMed]
  56. J. Feinberg, “Asymmetric self-defocusing of an optical beam from the photorefractive effect,” J. Opt. Soc. Am. 72, 46–51 (1982). [CrossRef]
  57. B. Luther-Davies, R. Powles, and V. Tikhonenko, “Nonlinear rotation of three-dimensional dark spatial solitons in a Gaussian laser beam,” Opt. Lett. 19, 1816–1818 (1994). [CrossRef]
  58. T. Ackemann, E. Kriege, and W. Lange, “Phase singularities via nonlinear beam propagation in sodium vapor,” Opt. Commun. 115, 339–346 (1995). [CrossRef]
  59. V. L. Ginzburg and L. P. Pitaevskii, “On the theory of superfluidity,” Zh. Eksp. Teor. Fiz. 34, 1240–1245 (1958) [ Sov. Phys. JETP 7, 858–861 (1958)].
  60. L. P. Pitaevskii, “Vortex lines in an imperfect Bose gas,” Zh. Eksp. Teor. Fiz. 40, 646–651 (1961) [ Sov. Phys. JETP 13, 451–454 (1961)].
  61. P. G. de Gennes, Superconductivity of Metals and Alloys (Addison-Wesley, Reading, Mass., 1989); R. J. Donnelly, Quantized Vortices in Helium II (Cambridge U. Press, New York, 1991).
  62. A. L. Fetter, “Vortices in an imperfect Bose gas,” Phys. Rev. 138, A429–A431 (1965). [CrossRef]
  63. G. A. Askar’yan, “Effects of the gradient of a strong electromagnetic beam on electrons and atoms,” Sov. Phys. JETP 15, 1088–1090 (1962).
  64. A. Ashkin, “Forces of a single-beam gradient laser trap on a dielectric sphere in array optic regime,” Biophys. J. 61, 569–582 (1992). [CrossRef] [PubMed]
  65. M. W. Beijersbergen, L. Allen, H. E. L. O. van der Veen, and J. P. Woerdman, “Astigmatic laser mode converters and transfer of orbital angular momentum,” Opt. Commun. 96, 123–132 (1993). [CrossRef]
  66. H. He, M. E. J. Friese, N. R. Heckenberg, and 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]
  67. H. He, N. R. Heckenberg, and H. Rubinsztein-Dunlop, “Optical particle trapping with higher-order doughnut beams produced using high-efficiency computer generated holograms,” J. Mod. Opt. 42, 217–223 (1995). [CrossRef]
  68. K. T. Gahagan and G. A. Swartzlander, Jr., “Optical vortex trapping of particles,” Opt. Lett. 21, 827–829 (1996). [CrossRef] [PubMed]
  69. A. E. Siegman, Lasers (University Science Books, Mill Valley, Calif., 1986).
  70. L. G. Gouy, “Sur la propagation anomale des ondes,” Ann. Chim. Phys. Ser. 6 24, 145–213 (1891).
  71. J. H. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  72. W. G. Wagner, H. A. Haus, and J. H. Marburger, “Large-scale self-trapping of optical beams in the paraxial ray approximation,” Phys. Rev. 175, 256–266 (1968). [CrossRef]
  73. C. Nore, M. E. Brachet, and S. Fauve, “Numerical study of hydrodynamics using the nonlinear Schrödinger (NLS) equation,” Physica D 65, 154–162 (1993). [CrossRef]
  74. L. M. Milne-Thomson, Theoretical Hydrodynamics (Macmillan, New York, 1968).
  75. M. D. Feit and J. A. Fleck, Jr., “Light propagation in graded-index optical fibers,” Appl. Opt. 17, 3990–3998 (1978). [CrossRef] [PubMed]

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