Abstract

We demonstrate that the coherent optical waves emitted from large-Fresnel-number degenerate cavities persistently display a sort of salient intensity variations. We use the representation of the coherent states to explore the origin of the salient intensity variations and find that these coherent laser waves arise from a quadrature superposition of two degenerate coherent states. With the analytical representation of the superposed coherent states, we verify that these coherent laser waves possess a large angular momentum per photon.

© 2009 Optical Society of America

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  1. K. Staliūnas, G. Šlekys, and C. O. Weiss, "Nonlinear pattern formation in active optical systems: shocks, domains of tilted waves, and cross-roll patterns," Phys. Rev. Lett. 79, 2658-2661 (1997).
    [CrossRef]
  2. F. T. Arecchi, G. Giacomelli, P. L. Ramazza, and S. Residori, "Vortices and defect statistics in two-dimensional optical chaos," Phys. Rev. Lett. 67, 3749-3752 (1991).
    [CrossRef] [PubMed]
  3. A. M. Zhabotinshii, "Periodic liquid-phase oxidation reactions." Dokl Akad Nauk SSSR,  157, 392-395 (1964).
  4. M. Howard and A. D. Rutenberg, " Pattern Formation inside Bacteria: Fluctuations due to the Low Copy Number of Proteins," Phys. Rev. Lett. 90, 128102 (2003).
    [CrossRef] [PubMed]
  5. S. Rüdiger, D. G. Míguez, A. P. Muñuzuri, F. Sagués, and J. Casademunt, "Dynamics of Turing patterns under spatiotemporal forcing," Phys. Rev. Lett. 90, 128301 (2003).
    [CrossRef] [PubMed]
  6. L. Yang and I. R. Epstein, "Oscillatory Turing Patterns in Reaction-Diffusion Systems with Two Coupled Layers," Phys. Rev. Lett. 90, 178303 (2003).
    [CrossRef] [PubMed]
  7. V. K. Vanag and I. R. Epstein, "Translational and nontranslational motion of perturbed Turing patterns," Phys. Rev. E 67, 066219 (2003).
    [CrossRef]
  8. S. Wasserman, J. Dungan, and N. Cozzarelli, "Discovery of a predicted DNA knot substantiates a model for site-specific recombination," Science 229, 171 (1985).
    [CrossRef] [PubMed]
  9. E. Ercolini, F. Valle, J. Adamcik, G. Witz, R. Metzler, P. De Los Rios, J. Roca, and G. Dietler, "Fractal dimension and localization of DNA knots," Phys. Rev. Lett. 98, 058102 (2007).
    [CrossRef] [PubMed]
  10. M. Brambilla, F. Battipede, L. A. Lugiato, V. Penna, F. Prati, C. Tamm, and C. O. Weiss, "Transverse laser patterns. I. Phase singularity crystals," Phys. Rev. A 43, 5090-5113 (1991).
    [CrossRef] [PubMed]
  11. D. Dangoisse, D. Hennequin, C. Lepers, E. Louvergneaux, and P. Glorieux, "Two-dimensional optical lattices in a CO2 laser," Phys. Rev. A 46, 5955-5958 (1992).
    [CrossRef] [PubMed]
  12. E. Cabrera, O. G. Calderón, S. Melle, and J. M. Guerra, "Development of spatial turbulence from boundary-controlled patterns in class-B lasers," Phys. Rev. A 73, 053820 (2006).
    [CrossRef]
  13. T. H. Lu, Y. F. Chen, and K. F. Huang, "Generation of polarization-entangled optical coherent waves and manifestation of vector singularity patterns," Phys. Rev. E 75, 026614 (2007).
    [CrossRef]
  14. J. F. Nye and M. V. Berry, "Dislocations in wave trains," Proc. R. Soc. A 336, 165-190 (1974).
    [CrossRef]
  15. M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, "Topological charge and angular momentum of light beams carrying optical vortices," Phys. Rev. A 56, 4064-4075 (1997).
    [CrossRef]
  16. A. N. Alexeyev, T.A. Fadeyeva, A.V. Volyar, and M. S. Soskin, "Optical vortices and the flow of their angular momentum in a multimode fiber," Semicond. Phys. Quantum Electron. Optoelectron. 1, 82-89 (1998).
  17. M. V. Berry, M. R. Dennis and M. S. Soskin, "The plurality of optical singularities," J. Opt. A: Pure Appl. Opt. 6, S155-156 (2004).
    [CrossRef]
  18. R. A. Beth, "Mechanical detection and measurement of the angular momentum of light," Phys. Rev. 50, 115-125 (1936).
    [CrossRef]
  19. R. Zambrini and S. M. Barnett, "Quasi-intrinsic angular momentum and the measurement of its spectrum," Phys. Rev. Lett. 96, 113901 (2006).
    [CrossRef] [PubMed]
  20. A. Ya. Bershaev and M.S. Soskin, "Transverse energy flows in vectorial fields of paraxial beams with singularities," Opt. Commun. 271, 332-348 (2007).
    [CrossRef]
  21. L. Allen, M. W. Beijersbergen, 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] [PubMed]
  22. A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, "Intrinsic and Extrinsic Nature of the Orbital Angular Momentum of a Light Beam," Phys. Rev. Lett. 88, 053601 (2002).
    [CrossRef] [PubMed]
  23. P. Galajda and P. Ormosa, "Complex micromachines produced and driven by light," Appl. Phys. Lett. 78, 249 (2001).
    [CrossRef]
  24. N. B. Simpson, K. Dholokia, L. Allen and M. J. Padgett, "Mechanical equivalence of spin and orbital angular momentum of light: an optical spanner," Opt. Lett. 22, 52-54 (1997).
    [CrossRef] [PubMed]
  25. J. E. Curtis and D. G. Grier, "Structure of optical vortices," Phys. Rev. Lett. 90, 133901 (2003).
    [CrossRef] [PubMed]
  26. M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, and N. R. Heckenberg, "Optical angular-momentum transfer to trapped absorbing particles," Phys. Rev. A 54, 1593-1596 (1996).
    [CrossRef] [PubMed]
  27. Y. F. Chen, T. H. Lu, K. W. Su, and K. F. Huang, "Devil's staircase in three-dimensional coherent waves localized on Lissajous parametric surfaces," Phys. Rev. Lett. 96, 213902 (2006).
    [CrossRef] [PubMed]
  28. J. Dingjan, M. P. van Exter and J. P. Woerdman, "Geometric modes in a single-frequency Nd:YVO4 laser," Opt. Commun. 188, 345-351 (2001).
    [CrossRef]
  29. Y. F. Chen and K. F. Huang, "Vortex structure of quantum eigenstates and classical periodic orbits in two-dimensional harmonic oscillators," J. Phys. A 36, 7751-7760 (2003).
    [CrossRef]
  30. A. J. Makowski, "Comment on 'Vortex structure of quantum eigenstates and classical periodic orbits in two-dimensional harmonic oscillators'," J. Phys. A 38, 2299-2302 (2005).
    [CrossRef]
  31. Y. F. Chen, T. H. Lu, K. W. Su, and K. F. Huang, "Quantum signatures of nonlinear resonances in mesoscopic systems: Efficient extension of localized wave functions," Phys. Rev. E 72, 056210 (2005).
    [CrossRef]
  32. K. J. Górska, A. J. Makowski, and S. T. Dembiński, "Correspondence between some wave patterns and Lissajous figures," J. Phys. A 39, 13285-13294 (2006).
    [CrossRef]
  33. T. H. Lu, Y. F. Chen, and K. F. Huang, "Spatial morphology of macroscopic superposition of three-dimensional coherent laser waves in degenerate cavities," Phys. Rev. A 77, 013828 (2008).
    [CrossRef]
  34. R. Zambrini and S. M. Barnett, "Angular momentum of multimode and polarization patterns," Opt. Express 15, 15214-15227 (2007).
    [CrossRef] [PubMed]
  35. J. Leach, M. R. Dennis, J. Courtial and M. J. Padgett, "Vortex knots in light," New J. Phys. 7, 55 (2005).
    [CrossRef]
  36. A. T. Winfree, "Persistent tangles of vortex rings in excitable media," Physca D 84, 126-147 (1995).
    [CrossRef]
  37. A. Malevanets and R. Kapral, "Links, Knots, and Knotted Labyrinths in Bistable Systems," Phys. Rev. Lett. 77, 767-770 (1996).
    [CrossRef] [PubMed]

2008 (1)

T. H. Lu, Y. F. Chen, and K. F. Huang, "Spatial morphology of macroscopic superposition of three-dimensional coherent laser waves in degenerate cavities," Phys. Rev. A 77, 013828 (2008).
[CrossRef]

2007 (4)

A. Ya. Bershaev and M.S. Soskin, "Transverse energy flows in vectorial fields of paraxial beams with singularities," Opt. Commun. 271, 332-348 (2007).
[CrossRef]

E. Ercolini, F. Valle, J. Adamcik, G. Witz, R. Metzler, P. De Los Rios, J. Roca, and G. Dietler, "Fractal dimension and localization of DNA knots," Phys. Rev. Lett. 98, 058102 (2007).
[CrossRef] [PubMed]

T. H. Lu, Y. F. Chen, and K. F. Huang, "Generation of polarization-entangled optical coherent waves and manifestation of vector singularity patterns," Phys. Rev. E 75, 026614 (2007).
[CrossRef]

R. Zambrini and S. M. Barnett, "Angular momentum of multimode and polarization patterns," Opt. Express 15, 15214-15227 (2007).
[CrossRef] [PubMed]

2006 (4)

E. Cabrera, O. G. Calderón, S. Melle, and J. M. Guerra, "Development of spatial turbulence from boundary-controlled patterns in class-B lasers," Phys. Rev. A 73, 053820 (2006).
[CrossRef]

Y. F. Chen, T. H. Lu, K. W. Su, and K. F. Huang, "Devil's staircase in three-dimensional coherent waves localized on Lissajous parametric surfaces," Phys. Rev. Lett. 96, 213902 (2006).
[CrossRef] [PubMed]

K. J. Górska, A. J. Makowski, and S. T. Dembiński, "Correspondence between some wave patterns and Lissajous figures," J. Phys. A 39, 13285-13294 (2006).
[CrossRef]

R. Zambrini and S. M. Barnett, "Quasi-intrinsic angular momentum and the measurement of its spectrum," Phys. Rev. Lett. 96, 113901 (2006).
[CrossRef] [PubMed]

2005 (3)

A. J. Makowski, "Comment on 'Vortex structure of quantum eigenstates and classical periodic orbits in two-dimensional harmonic oscillators'," J. Phys. A 38, 2299-2302 (2005).
[CrossRef]

Y. F. Chen, T. H. Lu, K. W. Su, and K. F. Huang, "Quantum signatures of nonlinear resonances in mesoscopic systems: Efficient extension of localized wave functions," Phys. Rev. E 72, 056210 (2005).
[CrossRef]

J. Leach, M. R. Dennis, J. Courtial and M. J. Padgett, "Vortex knots in light," New J. Phys. 7, 55 (2005).
[CrossRef]

2004 (1)

M. V. Berry, M. R. Dennis and M. S. Soskin, "The plurality of optical singularities," J. Opt. A: Pure Appl. Opt. 6, S155-156 (2004).
[CrossRef]

2003 (6)

M. Howard and A. D. Rutenberg, " Pattern Formation inside Bacteria: Fluctuations due to the Low Copy Number of Proteins," Phys. Rev. Lett. 90, 128102 (2003).
[CrossRef] [PubMed]

S. Rüdiger, D. G. Míguez, A. P. Muñuzuri, F. Sagués, and J. Casademunt, "Dynamics of Turing patterns under spatiotemporal forcing," Phys. Rev. Lett. 90, 128301 (2003).
[CrossRef] [PubMed]

L. Yang and I. R. Epstein, "Oscillatory Turing Patterns in Reaction-Diffusion Systems with Two Coupled Layers," Phys. Rev. Lett. 90, 178303 (2003).
[CrossRef] [PubMed]

V. K. Vanag and I. R. Epstein, "Translational and nontranslational motion of perturbed Turing patterns," Phys. Rev. E 67, 066219 (2003).
[CrossRef]

Y. F. Chen and K. F. Huang, "Vortex structure of quantum eigenstates and classical periodic orbits in two-dimensional harmonic oscillators," J. Phys. A 36, 7751-7760 (2003).
[CrossRef]

J. E. Curtis and D. G. Grier, "Structure of optical vortices," Phys. Rev. Lett. 90, 133901 (2003).
[CrossRef] [PubMed]

2002 (1)

A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, "Intrinsic and Extrinsic Nature of the Orbital Angular Momentum of a Light Beam," Phys. Rev. Lett. 88, 053601 (2002).
[CrossRef] [PubMed]

2001 (2)

P. Galajda and P. Ormosa, "Complex micromachines produced and driven by light," Appl. Phys. Lett. 78, 249 (2001).
[CrossRef]

J. Dingjan, M. P. van Exter and J. P. Woerdman, "Geometric modes in a single-frequency Nd:YVO4 laser," Opt. Commun. 188, 345-351 (2001).
[CrossRef]

1998 (1)

A. N. Alexeyev, T.A. Fadeyeva, A.V. Volyar, and M. S. Soskin, "Optical vortices and the flow of their angular momentum in a multimode fiber," Semicond. Phys. Quantum Electron. Optoelectron. 1, 82-89 (1998).

1997 (3)

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, "Topological charge and angular momentum of light beams carrying optical vortices," Phys. Rev. A 56, 4064-4075 (1997).
[CrossRef]

K. Staliūnas, G. Šlekys, and C. O. Weiss, "Nonlinear pattern formation in active optical systems: shocks, domains of tilted waves, and cross-roll patterns," Phys. Rev. Lett. 79, 2658-2661 (1997).
[CrossRef]

N. B. Simpson, K. Dholokia, L. Allen and M. J. Padgett, "Mechanical equivalence of spin and orbital angular momentum of light: an optical spanner," Opt. Lett. 22, 52-54 (1997).
[CrossRef] [PubMed]

1996 (2)

M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, and N. R. Heckenberg, "Optical angular-momentum transfer to trapped absorbing particles," Phys. Rev. A 54, 1593-1596 (1996).
[CrossRef] [PubMed]

A. Malevanets and R. Kapral, "Links, Knots, and Knotted Labyrinths in Bistable Systems," Phys. Rev. Lett. 77, 767-770 (1996).
[CrossRef] [PubMed]

1995 (1)

A. T. Winfree, "Persistent tangles of vortex rings in excitable media," Physca D 84, 126-147 (1995).
[CrossRef]

1992 (2)

L. Allen, M. W. Beijersbergen, 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] [PubMed]

D. Dangoisse, D. Hennequin, C. Lepers, E. Louvergneaux, and P. Glorieux, "Two-dimensional optical lattices in a CO2 laser," Phys. Rev. A 46, 5955-5958 (1992).
[CrossRef] [PubMed]

1991 (2)

F. T. Arecchi, G. Giacomelli, P. L. Ramazza, and S. Residori, "Vortices and defect statistics in two-dimensional optical chaos," Phys. Rev. Lett. 67, 3749-3752 (1991).
[CrossRef] [PubMed]

M. Brambilla, F. Battipede, L. A. Lugiato, V. Penna, F. Prati, C. Tamm, and C. O. Weiss, "Transverse laser patterns. I. Phase singularity crystals," Phys. Rev. A 43, 5090-5113 (1991).
[CrossRef] [PubMed]

1985 (1)

S. Wasserman, J. Dungan, and N. Cozzarelli, "Discovery of a predicted DNA knot substantiates a model for site-specific recombination," Science 229, 171 (1985).
[CrossRef] [PubMed]

1974 (1)

J. F. Nye and M. V. Berry, "Dislocations in wave trains," Proc. R. Soc. A 336, 165-190 (1974).
[CrossRef]

1964 (1)

A. M. Zhabotinshii, "Periodic liquid-phase oxidation reactions." Dokl Akad Nauk SSSR,  157, 392-395 (1964).

1936 (1)

R. A. Beth, "Mechanical detection and measurement of the angular momentum of light," Phys. Rev. 50, 115-125 (1936).
[CrossRef]

Adamcik, J.

E. Ercolini, F. Valle, J. Adamcik, G. Witz, R. Metzler, P. De Los Rios, J. Roca, and G. Dietler, "Fractal dimension and localization of DNA knots," Phys. Rev. Lett. 98, 058102 (2007).
[CrossRef] [PubMed]

Alexeyev, A. N.

A. N. Alexeyev, T.A. Fadeyeva, A.V. Volyar, and M. S. Soskin, "Optical vortices and the flow of their angular momentum in a multimode fiber," Semicond. Phys. Quantum Electron. Optoelectron. 1, 82-89 (1998).

Allen, L.

A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, "Intrinsic and Extrinsic Nature of the Orbital Angular Momentum of a Light Beam," Phys. Rev. Lett. 88, 053601 (2002).
[CrossRef] [PubMed]

N. B. Simpson, K. Dholokia, L. Allen and M. J. Padgett, "Mechanical equivalence of spin and orbital angular momentum of light: an optical spanner," Opt. Lett. 22, 52-54 (1997).
[CrossRef] [PubMed]

L. Allen, M. W. Beijersbergen, 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] [PubMed]

Arecchi, F. T.

F. T. Arecchi, G. Giacomelli, P. L. Ramazza, and S. Residori, "Vortices and defect statistics in two-dimensional optical chaos," Phys. Rev. Lett. 67, 3749-3752 (1991).
[CrossRef] [PubMed]

Barnett, S. M.

R. Zambrini and S. M. Barnett, "Angular momentum of multimode and polarization patterns," Opt. Express 15, 15214-15227 (2007).
[CrossRef] [PubMed]

R. Zambrini and S. M. Barnett, "Quasi-intrinsic angular momentum and the measurement of its spectrum," Phys. Rev. Lett. 96, 113901 (2006).
[CrossRef] [PubMed]

Battipede, F.

M. Brambilla, F. Battipede, L. A. Lugiato, V. Penna, F. Prati, C. Tamm, and C. O. Weiss, "Transverse laser patterns. I. Phase singularity crystals," Phys. Rev. A 43, 5090-5113 (1991).
[CrossRef] [PubMed]

Beijersbergen, M. W.

L. Allen, M. W. Beijersbergen, 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] [PubMed]

Berry, M. V.

M. V. Berry, M. R. Dennis and M. S. Soskin, "The plurality of optical singularities," J. Opt. A: Pure Appl. Opt. 6, S155-156 (2004).
[CrossRef]

J. F. Nye and M. V. Berry, "Dislocations in wave trains," Proc. R. Soc. A 336, 165-190 (1974).
[CrossRef]

Bershaev, A. Ya.

A. Ya. Bershaev and M.S. Soskin, "Transverse energy flows in vectorial fields of paraxial beams with singularities," Opt. Commun. 271, 332-348 (2007).
[CrossRef]

Beth, R. A.

R. A. Beth, "Mechanical detection and measurement of the angular momentum of light," Phys. Rev. 50, 115-125 (1936).
[CrossRef]

Brambilla, M.

M. Brambilla, F. Battipede, L. A. Lugiato, V. Penna, F. Prati, C. Tamm, and C. O. Weiss, "Transverse laser patterns. I. Phase singularity crystals," Phys. Rev. A 43, 5090-5113 (1991).
[CrossRef] [PubMed]

Cabrera, E.

E. Cabrera, O. G. Calderón, S. Melle, and J. M. Guerra, "Development of spatial turbulence from boundary-controlled patterns in class-B lasers," Phys. Rev. A 73, 053820 (2006).
[CrossRef]

Calderón, O. G.

E. Cabrera, O. G. Calderón, S. Melle, and J. M. Guerra, "Development of spatial turbulence from boundary-controlled patterns in class-B lasers," Phys. Rev. A 73, 053820 (2006).
[CrossRef]

Casademunt, J.

S. Rüdiger, D. G. Míguez, A. P. Muñuzuri, F. Sagués, and J. Casademunt, "Dynamics of Turing patterns under spatiotemporal forcing," Phys. Rev. Lett. 90, 128301 (2003).
[CrossRef] [PubMed]

Chen, Y. F.

T. H. Lu, Y. F. Chen, and K. F. Huang, "Spatial morphology of macroscopic superposition of three-dimensional coherent laser waves in degenerate cavities," Phys. Rev. A 77, 013828 (2008).
[CrossRef]

T. H. Lu, Y. F. Chen, and K. F. Huang, "Generation of polarization-entangled optical coherent waves and manifestation of vector singularity patterns," Phys. Rev. E 75, 026614 (2007).
[CrossRef]

Y. F. Chen, T. H. Lu, K. W. Su, and K. F. Huang, "Devil's staircase in three-dimensional coherent waves localized on Lissajous parametric surfaces," Phys. Rev. Lett. 96, 213902 (2006).
[CrossRef] [PubMed]

Y. F. Chen, T. H. Lu, K. W. Su, and K. F. Huang, "Quantum signatures of nonlinear resonances in mesoscopic systems: Efficient extension of localized wave functions," Phys. Rev. E 72, 056210 (2005).
[CrossRef]

Y. F. Chen and K. F. Huang, "Vortex structure of quantum eigenstates and classical periodic orbits in two-dimensional harmonic oscillators," J. Phys. A 36, 7751-7760 (2003).
[CrossRef]

Courtial, J.

J. Leach, M. R. Dennis, J. Courtial and M. J. Padgett, "Vortex knots in light," New J. Phys. 7, 55 (2005).
[CrossRef]

Cozzarelli, N.

S. Wasserman, J. Dungan, and N. Cozzarelli, "Discovery of a predicted DNA knot substantiates a model for site-specific recombination," Science 229, 171 (1985).
[CrossRef] [PubMed]

Curtis, J. E.

J. E. Curtis and D. G. Grier, "Structure of optical vortices," Phys. Rev. Lett. 90, 133901 (2003).
[CrossRef] [PubMed]

Dangoisse, D.

D. Dangoisse, D. Hennequin, C. Lepers, E. Louvergneaux, and P. Glorieux, "Two-dimensional optical lattices in a CO2 laser," Phys. Rev. A 46, 5955-5958 (1992).
[CrossRef] [PubMed]

De Los Rios, P.

E. Ercolini, F. Valle, J. Adamcik, G. Witz, R. Metzler, P. De Los Rios, J. Roca, and G. Dietler, "Fractal dimension and localization of DNA knots," Phys. Rev. Lett. 98, 058102 (2007).
[CrossRef] [PubMed]

Dembinski, S. T.

K. J. Górska, A. J. Makowski, and S. T. Dembiński, "Correspondence between some wave patterns and Lissajous figures," J. Phys. A 39, 13285-13294 (2006).
[CrossRef]

Dennis, M. R.

J. Leach, M. R. Dennis, J. Courtial and M. J. Padgett, "Vortex knots in light," New J. Phys. 7, 55 (2005).
[CrossRef]

M. V. Berry, M. R. Dennis and M. S. Soskin, "The plurality of optical singularities," J. Opt. A: Pure Appl. Opt. 6, S155-156 (2004).
[CrossRef]

Dholokia, K.

Dietler, G.

E. Ercolini, F. Valle, J. Adamcik, G. Witz, R. Metzler, P. De Los Rios, J. Roca, and G. Dietler, "Fractal dimension and localization of DNA knots," Phys. Rev. Lett. 98, 058102 (2007).
[CrossRef] [PubMed]

Dingjan, J.

J. Dingjan, M. P. van Exter and J. P. Woerdman, "Geometric modes in a single-frequency Nd:YVO4 laser," Opt. Commun. 188, 345-351 (2001).
[CrossRef]

Dungan, J.

S. Wasserman, J. Dungan, and N. Cozzarelli, "Discovery of a predicted DNA knot substantiates a model for site-specific recombination," Science 229, 171 (1985).
[CrossRef] [PubMed]

Enger, J.

M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, and N. R. Heckenberg, "Optical angular-momentum transfer to trapped absorbing particles," Phys. Rev. A 54, 1593-1596 (1996).
[CrossRef] [PubMed]

Epstein, I. R.

V. K. Vanag and I. R. Epstein, "Translational and nontranslational motion of perturbed Turing patterns," Phys. Rev. E 67, 066219 (2003).
[CrossRef]

L. Yang and I. R. Epstein, "Oscillatory Turing Patterns in Reaction-Diffusion Systems with Two Coupled Layers," Phys. Rev. Lett. 90, 178303 (2003).
[CrossRef] [PubMed]

Ercolini, E.

E. Ercolini, F. Valle, J. Adamcik, G. Witz, R. Metzler, P. De Los Rios, J. Roca, and G. Dietler, "Fractal dimension and localization of DNA knots," Phys. Rev. Lett. 98, 058102 (2007).
[CrossRef] [PubMed]

Fadeyeva, T.A.

A. N. Alexeyev, T.A. Fadeyeva, A.V. Volyar, and M. S. Soskin, "Optical vortices and the flow of their angular momentum in a multimode fiber," Semicond. Phys. Quantum Electron. Optoelectron. 1, 82-89 (1998).

Friese, M. E. J.

M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, and N. R. Heckenberg, "Optical angular-momentum transfer to trapped absorbing particles," Phys. Rev. A 54, 1593-1596 (1996).
[CrossRef] [PubMed]

Galajda, P.

P. Galajda and P. Ormosa, "Complex micromachines produced and driven by light," Appl. Phys. Lett. 78, 249 (2001).
[CrossRef]

Giacomelli, G.

F. T. Arecchi, G. Giacomelli, P. L. Ramazza, and S. Residori, "Vortices and defect statistics in two-dimensional optical chaos," Phys. Rev. Lett. 67, 3749-3752 (1991).
[CrossRef] [PubMed]

Glorieux, P.

D. Dangoisse, D. Hennequin, C. Lepers, E. Louvergneaux, and P. Glorieux, "Two-dimensional optical lattices in a CO2 laser," Phys. Rev. A 46, 5955-5958 (1992).
[CrossRef] [PubMed]

Gorshkov, V. N.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, "Topological charge and angular momentum of light beams carrying optical vortices," Phys. Rev. A 56, 4064-4075 (1997).
[CrossRef]

Górska, K. J.

K. J. Górska, A. J. Makowski, and S. T. Dembiński, "Correspondence between some wave patterns and Lissajous figures," J. Phys. A 39, 13285-13294 (2006).
[CrossRef]

Grier, D. G.

J. E. Curtis and D. G. Grier, "Structure of optical vortices," Phys. Rev. Lett. 90, 133901 (2003).
[CrossRef] [PubMed]

Guerra, J. M.

E. Cabrera, O. G. Calderón, S. Melle, and J. M. Guerra, "Development of spatial turbulence from boundary-controlled patterns in class-B lasers," Phys. Rev. A 73, 053820 (2006).
[CrossRef]

Heckenberg, N. R.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, "Topological charge and angular momentum of light beams carrying optical vortices," Phys. Rev. A 56, 4064-4075 (1997).
[CrossRef]

M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, and N. R. Heckenberg, "Optical angular-momentum transfer to trapped absorbing particles," Phys. Rev. A 54, 1593-1596 (1996).
[CrossRef] [PubMed]

Hennequin, D.

D. Dangoisse, D. Hennequin, C. Lepers, E. Louvergneaux, and P. Glorieux, "Two-dimensional optical lattices in a CO2 laser," Phys. Rev. A 46, 5955-5958 (1992).
[CrossRef] [PubMed]

Howard, M.

M. Howard and A. D. Rutenberg, " Pattern Formation inside Bacteria: Fluctuations due to the Low Copy Number of Proteins," Phys. Rev. Lett. 90, 128102 (2003).
[CrossRef] [PubMed]

Huang, K. F.

T. H. Lu, Y. F. Chen, and K. F. Huang, "Spatial morphology of macroscopic superposition of three-dimensional coherent laser waves in degenerate cavities," Phys. Rev. A 77, 013828 (2008).
[CrossRef]

T. H. Lu, Y. F. Chen, and K. F. Huang, "Generation of polarization-entangled optical coherent waves and manifestation of vector singularity patterns," Phys. Rev. E 75, 026614 (2007).
[CrossRef]

Y. F. Chen, T. H. Lu, K. W. Su, and K. F. Huang, "Devil's staircase in three-dimensional coherent waves localized on Lissajous parametric surfaces," Phys. Rev. Lett. 96, 213902 (2006).
[CrossRef] [PubMed]

Y. F. Chen, T. H. Lu, K. W. Su, and K. F. Huang, "Quantum signatures of nonlinear resonances in mesoscopic systems: Efficient extension of localized wave functions," Phys. Rev. E 72, 056210 (2005).
[CrossRef]

Y. F. Chen and K. F. Huang, "Vortex structure of quantum eigenstates and classical periodic orbits in two-dimensional harmonic oscillators," J. Phys. A 36, 7751-7760 (2003).
[CrossRef]

Kapral, R.

A. Malevanets and R. Kapral, "Links, Knots, and Knotted Labyrinths in Bistable Systems," Phys. Rev. Lett. 77, 767-770 (1996).
[CrossRef] [PubMed]

Leach, J.

J. Leach, M. R. Dennis, J. Courtial and M. J. Padgett, "Vortex knots in light," New J. Phys. 7, 55 (2005).
[CrossRef]

Lepers, C.

D. Dangoisse, D. Hennequin, C. Lepers, E. Louvergneaux, and P. Glorieux, "Two-dimensional optical lattices in a CO2 laser," Phys. Rev. A 46, 5955-5958 (1992).
[CrossRef] [PubMed]

Louvergneaux, E.

D. Dangoisse, D. Hennequin, C. Lepers, E. Louvergneaux, and P. Glorieux, "Two-dimensional optical lattices in a CO2 laser," Phys. Rev. A 46, 5955-5958 (1992).
[CrossRef] [PubMed]

Lu, T. H.

T. H. Lu, Y. F. Chen, and K. F. Huang, "Spatial morphology of macroscopic superposition of three-dimensional coherent laser waves in degenerate cavities," Phys. Rev. A 77, 013828 (2008).
[CrossRef]

T. H. Lu, Y. F. Chen, and K. F. Huang, "Generation of polarization-entangled optical coherent waves and manifestation of vector singularity patterns," Phys. Rev. E 75, 026614 (2007).
[CrossRef]

Y. F. Chen, T. H. Lu, K. W. Su, and K. F. Huang, "Devil's staircase in three-dimensional coherent waves localized on Lissajous parametric surfaces," Phys. Rev. Lett. 96, 213902 (2006).
[CrossRef] [PubMed]

Y. F. Chen, T. H. Lu, K. W. Su, and K. F. Huang, "Quantum signatures of nonlinear resonances in mesoscopic systems: Efficient extension of localized wave functions," Phys. Rev. E 72, 056210 (2005).
[CrossRef]

Lugiato, L. A.

M. Brambilla, F. Battipede, L. A. Lugiato, V. Penna, F. Prati, C. Tamm, and C. O. Weiss, "Transverse laser patterns. I. Phase singularity crystals," Phys. Rev. A 43, 5090-5113 (1991).
[CrossRef] [PubMed]

MacVicar, I.

A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, "Intrinsic and Extrinsic Nature of the Orbital Angular Momentum of a Light Beam," Phys. Rev. Lett. 88, 053601 (2002).
[CrossRef] [PubMed]

Makowski, A. J.

K. J. Górska, A. J. Makowski, and S. T. Dembiński, "Correspondence between some wave patterns and Lissajous figures," J. Phys. A 39, 13285-13294 (2006).
[CrossRef]

A. J. Makowski, "Comment on 'Vortex structure of quantum eigenstates and classical periodic orbits in two-dimensional harmonic oscillators'," J. Phys. A 38, 2299-2302 (2005).
[CrossRef]

Malevanets, A.

A. Malevanets and R. Kapral, "Links, Knots, and Knotted Labyrinths in Bistable Systems," Phys. Rev. Lett. 77, 767-770 (1996).
[CrossRef] [PubMed]

Malos, J. T.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, "Topological charge and angular momentum of light beams carrying optical vortices," Phys. Rev. A 56, 4064-4075 (1997).
[CrossRef]

Melle, S.

E. Cabrera, O. G. Calderón, S. Melle, and J. M. Guerra, "Development of spatial turbulence from boundary-controlled patterns in class-B lasers," Phys. Rev. A 73, 053820 (2006).
[CrossRef]

Metzler, R.

E. Ercolini, F. Valle, J. Adamcik, G. Witz, R. Metzler, P. De Los Rios, J. Roca, and G. Dietler, "Fractal dimension and localization of DNA knots," Phys. Rev. Lett. 98, 058102 (2007).
[CrossRef] [PubMed]

Míguez, D. G.

S. Rüdiger, D. G. Míguez, A. P. Muñuzuri, F. Sagués, and J. Casademunt, "Dynamics of Turing patterns under spatiotemporal forcing," Phys. Rev. Lett. 90, 128301 (2003).
[CrossRef] [PubMed]

Muñuzuri, A. P.

S. Rüdiger, D. G. Míguez, A. P. Muñuzuri, F. Sagués, and J. Casademunt, "Dynamics of Turing patterns under spatiotemporal forcing," Phys. Rev. Lett. 90, 128301 (2003).
[CrossRef] [PubMed]

Nye, J. F.

J. F. Nye and M. V. Berry, "Dislocations in wave trains," Proc. R. Soc. A 336, 165-190 (1974).
[CrossRef]

O’Neil, A. T.

A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, "Intrinsic and Extrinsic Nature of the Orbital Angular Momentum of a Light Beam," Phys. Rev. Lett. 88, 053601 (2002).
[CrossRef] [PubMed]

Ormosa, P.

P. Galajda and P. Ormosa, "Complex micromachines produced and driven by light," Appl. Phys. Lett. 78, 249 (2001).
[CrossRef]

Padgett, M. J.

J. Leach, M. R. Dennis, J. Courtial and M. J. Padgett, "Vortex knots in light," New J. Phys. 7, 55 (2005).
[CrossRef]

A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, "Intrinsic and Extrinsic Nature of the Orbital Angular Momentum of a Light Beam," Phys. Rev. Lett. 88, 053601 (2002).
[CrossRef] [PubMed]

N. B. Simpson, K. Dholokia, L. Allen and M. J. Padgett, "Mechanical equivalence of spin and orbital angular momentum of light: an optical spanner," Opt. Lett. 22, 52-54 (1997).
[CrossRef] [PubMed]

Penna, V.

M. Brambilla, F. Battipede, L. A. Lugiato, V. Penna, F. Prati, C. Tamm, and C. O. Weiss, "Transverse laser patterns. I. Phase singularity crystals," Phys. Rev. A 43, 5090-5113 (1991).
[CrossRef] [PubMed]

Prati, F.

M. Brambilla, F. Battipede, L. A. Lugiato, V. Penna, F. Prati, C. Tamm, and C. O. Weiss, "Transverse laser patterns. I. Phase singularity crystals," Phys. Rev. A 43, 5090-5113 (1991).
[CrossRef] [PubMed]

Ramazza, P. L.

F. T. Arecchi, G. Giacomelli, P. L. Ramazza, and S. Residori, "Vortices and defect statistics in two-dimensional optical chaos," Phys. Rev. Lett. 67, 3749-3752 (1991).
[CrossRef] [PubMed]

Residori, S.

F. T. Arecchi, G. Giacomelli, P. L. Ramazza, and S. Residori, "Vortices and defect statistics in two-dimensional optical chaos," Phys. Rev. Lett. 67, 3749-3752 (1991).
[CrossRef] [PubMed]

Roca, J.

E. Ercolini, F. Valle, J. Adamcik, G. Witz, R. Metzler, P. De Los Rios, J. Roca, and G. Dietler, "Fractal dimension and localization of DNA knots," Phys. Rev. Lett. 98, 058102 (2007).
[CrossRef] [PubMed]

Rubinsztein-Dunlop, H.

M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, and N. R. Heckenberg, "Optical angular-momentum transfer to trapped absorbing particles," Phys. Rev. A 54, 1593-1596 (1996).
[CrossRef] [PubMed]

Rüdiger, S.

S. Rüdiger, D. G. Míguez, A. P. Muñuzuri, F. Sagués, and J. Casademunt, "Dynamics of Turing patterns under spatiotemporal forcing," Phys. Rev. Lett. 90, 128301 (2003).
[CrossRef] [PubMed]

Rutenberg, A. D.

M. Howard and A. D. Rutenberg, " Pattern Formation inside Bacteria: Fluctuations due to the Low Copy Number of Proteins," Phys. Rev. Lett. 90, 128102 (2003).
[CrossRef] [PubMed]

Sagués, F.

S. Rüdiger, D. G. Míguez, A. P. Muñuzuri, F. Sagués, and J. Casademunt, "Dynamics of Turing patterns under spatiotemporal forcing," Phys. Rev. Lett. 90, 128301 (2003).
[CrossRef] [PubMed]

Simpson, N. B.

Šlekys, G.

K. Staliūnas, G. Šlekys, and C. O. Weiss, "Nonlinear pattern formation in active optical systems: shocks, domains of tilted waves, and cross-roll patterns," Phys. Rev. Lett. 79, 2658-2661 (1997).
[CrossRef]

Soskin, M. S.

M. V. Berry, M. R. Dennis and M. S. Soskin, "The plurality of optical singularities," J. Opt. A: Pure Appl. Opt. 6, S155-156 (2004).
[CrossRef]

A. N. Alexeyev, T.A. Fadeyeva, A.V. Volyar, and M. S. Soskin, "Optical vortices and the flow of their angular momentum in a multimode fiber," Semicond. Phys. Quantum Electron. Optoelectron. 1, 82-89 (1998).

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, "Topological charge and angular momentum of light beams carrying optical vortices," Phys. Rev. A 56, 4064-4075 (1997).
[CrossRef]

Soskin, M.S.

A. Ya. Bershaev and M.S. Soskin, "Transverse energy flows in vectorial fields of paraxial beams with singularities," Opt. Commun. 271, 332-348 (2007).
[CrossRef]

Spreeuw, R. J. C.

L. Allen, M. W. Beijersbergen, 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] [PubMed]

Staliunas, K.

K. Staliūnas, G. Šlekys, and C. O. Weiss, "Nonlinear pattern formation in active optical systems: shocks, domains of tilted waves, and cross-roll patterns," Phys. Rev. Lett. 79, 2658-2661 (1997).
[CrossRef]

Su, K. W.

Y. F. Chen, T. H. Lu, K. W. Su, and K. F. Huang, "Devil's staircase in three-dimensional coherent waves localized on Lissajous parametric surfaces," Phys. Rev. Lett. 96, 213902 (2006).
[CrossRef] [PubMed]

Y. F. Chen, T. H. Lu, K. W. Su, and K. F. Huang, "Quantum signatures of nonlinear resonances in mesoscopic systems: Efficient extension of localized wave functions," Phys. Rev. E 72, 056210 (2005).
[CrossRef]

Tamm, C.

M. Brambilla, F. Battipede, L. A. Lugiato, V. Penna, F. Prati, C. Tamm, and C. O. Weiss, "Transverse laser patterns. I. Phase singularity crystals," Phys. Rev. A 43, 5090-5113 (1991).
[CrossRef] [PubMed]

Valle, F.

E. Ercolini, F. Valle, J. Adamcik, G. Witz, R. Metzler, P. De Los Rios, J. Roca, and G. Dietler, "Fractal dimension and localization of DNA knots," Phys. Rev. Lett. 98, 058102 (2007).
[CrossRef] [PubMed]

van Exter, M. P.

J. Dingjan, M. P. van Exter and J. P. Woerdman, "Geometric modes in a single-frequency Nd:YVO4 laser," Opt. Commun. 188, 345-351 (2001).
[CrossRef]

Vanag, V. K.

V. K. Vanag and I. R. Epstein, "Translational and nontranslational motion of perturbed Turing patterns," Phys. Rev. E 67, 066219 (2003).
[CrossRef]

Vasnetsov, M. V.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, "Topological charge and angular momentum of light beams carrying optical vortices," Phys. Rev. A 56, 4064-4075 (1997).
[CrossRef]

Volyar, A.V.

A. N. Alexeyev, T.A. Fadeyeva, A.V. Volyar, and M. S. Soskin, "Optical vortices and the flow of their angular momentum in a multimode fiber," Semicond. Phys. Quantum Electron. Optoelectron. 1, 82-89 (1998).

Wasserman, S.

S. Wasserman, J. Dungan, and N. Cozzarelli, "Discovery of a predicted DNA knot substantiates a model for site-specific recombination," Science 229, 171 (1985).
[CrossRef] [PubMed]

Weiss, C. O.

K. Staliūnas, G. Šlekys, and C. O. Weiss, "Nonlinear pattern formation in active optical systems: shocks, domains of tilted waves, and cross-roll patterns," Phys. Rev. Lett. 79, 2658-2661 (1997).
[CrossRef]

M. Brambilla, F. Battipede, L. A. Lugiato, V. Penna, F. Prati, C. Tamm, and C. O. Weiss, "Transverse laser patterns. I. Phase singularity crystals," Phys. Rev. A 43, 5090-5113 (1991).
[CrossRef] [PubMed]

Winfree, A. T.

A. T. Winfree, "Persistent tangles of vortex rings in excitable media," Physca D 84, 126-147 (1995).
[CrossRef]

Witz, G.

E. Ercolini, F. Valle, J. Adamcik, G. Witz, R. Metzler, P. De Los Rios, J. Roca, and G. Dietler, "Fractal dimension and localization of DNA knots," Phys. Rev. Lett. 98, 058102 (2007).
[CrossRef] [PubMed]

Woerdman, J. P.

J. Dingjan, M. P. van Exter and J. P. Woerdman, "Geometric modes in a single-frequency Nd:YVO4 laser," Opt. Commun. 188, 345-351 (2001).
[CrossRef]

L. Allen, M. W. Beijersbergen, 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] [PubMed]

Yang, L.

L. Yang and I. R. Epstein, "Oscillatory Turing Patterns in Reaction-Diffusion Systems with Two Coupled Layers," Phys. Rev. Lett. 90, 178303 (2003).
[CrossRef] [PubMed]

Zambrini, R.

R. Zambrini and S. M. Barnett, "Angular momentum of multimode and polarization patterns," Opt. Express 15, 15214-15227 (2007).
[CrossRef] [PubMed]

R. Zambrini and S. M. Barnett, "Quasi-intrinsic angular momentum and the measurement of its spectrum," Phys. Rev. Lett. 96, 113901 (2006).
[CrossRef] [PubMed]

Zhabotinshii, A. M.

A. M. Zhabotinshii, "Periodic liquid-phase oxidation reactions." Dokl Akad Nauk SSSR,  157, 392-395 (1964).

Appl. Phys. Lett. (1)

P. Galajda and P. Ormosa, "Complex micromachines produced and driven by light," Appl. Phys. Lett. 78, 249 (2001).
[CrossRef]

Dokl Akad Nauk SSSR (1)

A. M. Zhabotinshii, "Periodic liquid-phase oxidation reactions." Dokl Akad Nauk SSSR,  157, 392-395 (1964).

J. Opt. A: Pure Appl. Opt. (1)

M. V. Berry, M. R. Dennis and M. S. Soskin, "The plurality of optical singularities," J. Opt. A: Pure Appl. Opt. 6, S155-156 (2004).
[CrossRef]

J. Phys. A (3)

Y. F. Chen and K. F. Huang, "Vortex structure of quantum eigenstates and classical periodic orbits in two-dimensional harmonic oscillators," J. Phys. A 36, 7751-7760 (2003).
[CrossRef]

A. J. Makowski, "Comment on 'Vortex structure of quantum eigenstates and classical periodic orbits in two-dimensional harmonic oscillators'," J. Phys. A 38, 2299-2302 (2005).
[CrossRef]

K. J. Górska, A. J. Makowski, and S. T. Dembiński, "Correspondence between some wave patterns and Lissajous figures," J. Phys. A 39, 13285-13294 (2006).
[CrossRef]

New J. Phys. (1)

J. Leach, M. R. Dennis, J. Courtial and M. J. Padgett, "Vortex knots in light," New J. Phys. 7, 55 (2005).
[CrossRef]

Opt. Commun. (2)

A. Ya. Bershaev and M.S. Soskin, "Transverse energy flows in vectorial fields of paraxial beams with singularities," Opt. Commun. 271, 332-348 (2007).
[CrossRef]

J. Dingjan, M. P. van Exter and J. P. Woerdman, "Geometric modes in a single-frequency Nd:YVO4 laser," Opt. Commun. 188, 345-351 (2001).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. (1)

R. A. Beth, "Mechanical detection and measurement of the angular momentum of light," Phys. Rev. 50, 115-125 (1936).
[CrossRef]

Phys. Rev. A (7)

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, "Topological charge and angular momentum of light beams carrying optical vortices," Phys. Rev. A 56, 4064-4075 (1997).
[CrossRef]

M. Brambilla, F. Battipede, L. A. Lugiato, V. Penna, F. Prati, C. Tamm, and C. O. Weiss, "Transverse laser patterns. I. Phase singularity crystals," Phys. Rev. A 43, 5090-5113 (1991).
[CrossRef] [PubMed]

D. Dangoisse, D. Hennequin, C. Lepers, E. Louvergneaux, and P. Glorieux, "Two-dimensional optical lattices in a CO2 laser," Phys. Rev. A 46, 5955-5958 (1992).
[CrossRef] [PubMed]

E. Cabrera, O. G. Calderón, S. Melle, and J. M. Guerra, "Development of spatial turbulence from boundary-controlled patterns in class-B lasers," Phys. Rev. A 73, 053820 (2006).
[CrossRef]

T. H. Lu, Y. F. Chen, and K. F. Huang, "Spatial morphology of macroscopic superposition of three-dimensional coherent laser waves in degenerate cavities," Phys. Rev. A 77, 013828 (2008).
[CrossRef]

M. E. J. Friese, J. Enger, H. Rubinsztein-Dunlop, and N. R. Heckenberg, "Optical angular-momentum transfer to trapped absorbing particles," Phys. Rev. A 54, 1593-1596 (1996).
[CrossRef] [PubMed]

L. Allen, M. W. Beijersbergen, 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] [PubMed]

Phys. Rev. E (3)

Y. F. Chen, T. H. Lu, K. W. Su, and K. F. Huang, "Quantum signatures of nonlinear resonances in mesoscopic systems: Efficient extension of localized wave functions," Phys. Rev. E 72, 056210 (2005).
[CrossRef]

T. H. Lu, Y. F. Chen, and K. F. Huang, "Generation of polarization-entangled optical coherent waves and manifestation of vector singularity patterns," Phys. Rev. E 75, 026614 (2007).
[CrossRef]

V. K. Vanag and I. R. Epstein, "Translational and nontranslational motion of perturbed Turing patterns," Phys. Rev. E 67, 066219 (2003).
[CrossRef]

Phys. Rev. Lett. (11)

K. Staliūnas, G. Šlekys, and C. O. Weiss, "Nonlinear pattern formation in active optical systems: shocks, domains of tilted waves, and cross-roll patterns," Phys. Rev. Lett. 79, 2658-2661 (1997).
[CrossRef]

F. T. Arecchi, G. Giacomelli, P. L. Ramazza, and S. Residori, "Vortices and defect statistics in two-dimensional optical chaos," Phys. Rev. Lett. 67, 3749-3752 (1991).
[CrossRef] [PubMed]

M. Howard and A. D. Rutenberg, " Pattern Formation inside Bacteria: Fluctuations due to the Low Copy Number of Proteins," Phys. Rev. Lett. 90, 128102 (2003).
[CrossRef] [PubMed]

S. Rüdiger, D. G. Míguez, A. P. Muñuzuri, F. Sagués, and J. Casademunt, "Dynamics of Turing patterns under spatiotemporal forcing," Phys. Rev. Lett. 90, 128301 (2003).
[CrossRef] [PubMed]

L. Yang and I. R. Epstein, "Oscillatory Turing Patterns in Reaction-Diffusion Systems with Two Coupled Layers," Phys. Rev. Lett. 90, 178303 (2003).
[CrossRef] [PubMed]

R. Zambrini and S. M. Barnett, "Quasi-intrinsic angular momentum and the measurement of its spectrum," Phys. Rev. Lett. 96, 113901 (2006).
[CrossRef] [PubMed]

A. Malevanets and R. Kapral, "Links, Knots, and Knotted Labyrinths in Bistable Systems," Phys. Rev. Lett. 77, 767-770 (1996).
[CrossRef] [PubMed]

A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, "Intrinsic and Extrinsic Nature of the Orbital Angular Momentum of a Light Beam," Phys. Rev. Lett. 88, 053601 (2002).
[CrossRef] [PubMed]

J. E. Curtis and D. G. Grier, "Structure of optical vortices," Phys. Rev. Lett. 90, 133901 (2003).
[CrossRef] [PubMed]

Y. F. Chen, T. H. Lu, K. W. Su, and K. F. Huang, "Devil's staircase in three-dimensional coherent waves localized on Lissajous parametric surfaces," Phys. Rev. Lett. 96, 213902 (2006).
[CrossRef] [PubMed]

E. Ercolini, F. Valle, J. Adamcik, G. Witz, R. Metzler, P. De Los Rios, J. Roca, and G. Dietler, "Fractal dimension and localization of DNA knots," Phys. Rev. Lett. 98, 058102 (2007).
[CrossRef] [PubMed]

Physca D (1)

A. T. Winfree, "Persistent tangles of vortex rings in excitable media," Physca D 84, 126-147 (1995).
[CrossRef]

Proc. R. Soc. A (1)

J. F. Nye and M. V. Berry, "Dislocations in wave trains," Proc. R. Soc. A 336, 165-190 (1974).
[CrossRef]

Science (1)

S. Wasserman, J. Dungan, and N. Cozzarelli, "Discovery of a predicted DNA knot substantiates a model for site-specific recombination," Science 229, 171 (1985).
[CrossRef] [PubMed]

Semicond. Phys. Quantum Electron. Optoelectron. (1)

A. N. Alexeyev, T.A. Fadeyeva, A.V. Volyar, and M. S. Soskin, "Optical vortices and the flow of their angular momentum in a multimode fiber," Semicond. Phys. Quantum Electron. Optoelectron. 1, 82-89 (1998).

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Figures (8)

Fig. 1.
Fig. 1.

Experimental setup for the generation of superposed 3D coherent waves with off-axis pumping scheme.

Fig. 2.
Fig. 2.

(a). numerical tomographic transverse patterns for ψmo,no p,q (x, y, z) in Eq. (1) with the parameters of (mo , no ) = (110,110) , (p,q)= (2,2) , P/Q = 1/4 , φo = 0 and M = 10 for the range from z = 0.4 L to z =100L; (b): the Lissajous parametric surface corresponding to the numerical transverse patterns; (c): the experimental transverse patterns for comparing with (a).

Fig. 3.
Fig. 3.

Numerical tomographic transverse patterns calculated with Ψmo,no p,q (x,y,Z;r,ϕ) in Eq. (3) with r = 1 and the parameters are the same in Fig. 2(a) for reconstructing the experimental results shown in Fig. 2(c).

Fig. 4.
Fig. 4.

(a) and (b). Experimental far-field transverse patterns for (p,q) = (5,2) and (p,q) = (5,-2) , respectively. (a’) and (b’): numerical transverse patterns calculated with Eq. (3) for Ψ130,30 5,2 (x, y, z), ϕ 0 = 0 , M = 5 and Ψ130,30 5,-2 (x, y,z), ϕ 0 = 0, M = 5, respectively.

Fig. 5.
Fig. 5.

(a1) - (a4). the superposed coherent state Ψ130,30 p,q (x,y,z;r, π/2) with r = 1~4 for (p,q) = (5,2) , respectively. (b1)-5(b4): the superposed coherent state Ψ130,30 p,q (x,y,z;r,π/2) with r = 1 ~ 4 for (p, q) = (5, - 2), respectively.

Fig. 6.
Fig. 6.

(a1)-(a4): the superposed coherent state Ψ130,30 p,q (x,y,z; 1, φ) with φ=0, π/5, π/4 , and π/3 for (p,q) = (5,2) , respectively. (b1)-5(b4): the superposed coherent state Ψ130,30 p,q (x, y, z; 1, φ) with φ=0, π/5, π/4, and π/3 for (p, q) = (5,-2), respectively.

Fig. 7.
Fig. 7.

(a). experimental far-field transverse pattern of dotted structure for (p, q) = (5,-2). (b): numerical results for the superposed state Ψ120,25;138,31 5,-2 (x, y, z) in Eq. (4) with M = 5.

Fig. 8.
Fig. 8.

Numerical result for the angular momentum density of the superposed state Ψ mo,no p,q (x,y,z;1, π/2) with the parameters of (mo ,no ) = (110,110), (p,q) = (2,2) , and M =10 corresponding to the intensity distribution shown in Fig. 3.

Equations (5)

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Ψ m o , n o , l o p , q , s ( x , y , z ) = 1 2 M + 1 k = M M e ik ϕ o Φ m o + pk + n o + qk + l o + sk ( HG ) ( x , y , z )
Φ m , n , l ( HG ) ( x , y , z ) = 1 2 m + n 1 π m ! n ! 1 W ( z ) H m ( 2 x w ( z ) ) H n ( 2 y w ( z ) ) e [ x 2 + y 2 w ( z ) 2 ]
× e i ( m + n + 1 ) tan 1 ( z zR ) e i ( π z L ) [ l + ( m + n + 1 ) P Q ] [ x 2 + y 2 2 ( z 2 + z R 2 ) + 1 ]
Ψ m o , n o p , q ( x , y , z ; r , φ ) = [ ψ m o , n o p , q ( x , y , z ) + e ψ m o + r , n o r p , q ( x , y , z ) ] / 2
Ψ m 1 , n 1 ; m 2 , n 2 p , q ( x , y , z ) = [ Ψ m 1 , n 1 p , q ( x , y , z ; 1 , π / 2 ) + Ψ m 2 , n 2 p , q ( x , y , z ; 1 , π / 2 ) ] / 2

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