Abstract

We observe experimentally optical azimuthons, a generic class of ring-shaped localised spiralling beams with azimuthal modulation, carrying phase dislocation in self-focusing nonlinear media. We observe three- and four-lobe azimuthons in 87Rb vapours and demonstrate their anomalous rotation controlled by the input phase distribution.

© 2009 Optical Society of America

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References

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  1. R. Y. Chiao, E. Garmire, and C. H. Townes, "Self-trapping of optical beams," Phys. Rev. Lett. 13, 479 (1964).
    [CrossRef]
  2. Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, 2003).
  3. A. S. Desyatnikov, Yu. S. Kivshar, and L. Torner, "Optical vortices and vortex solitons," E. Wolf, ed., Progess in Optics (Elsevier, 2005) 47, pp. 291.
    [CrossRef]
  4. V. I. Kruglov and R. A. Vlasov, "Spiral self-trapping propagation of optical beams in media with cubic nonlinearity," Phys. Lett. A 111, 401 (1985).
    [CrossRef]
  5. C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, "Solitons in nonlinear media with an infinite range of nonlocality: first observation of coherent elliptic solitons and of vortex-ring solitons," Phys. Rev. Lett. 95, 213904 (2005).
    [CrossRef] [PubMed]
  6. A. S. Desyatnikov and Yu. S. Kivshar, "Rotating optical soliton clusters," Phys. Rev. Lett. 88, 053901 (2002).
    [CrossRef] [PubMed]
  7. A. S. Desyatnikov, A. A. Sukhorukov, and Yu. S. Kivshar, "Azimuthons: spatially modulated vortex solitons," Phys. Rev. Lett. 95, 203904 (2005).
    [CrossRef] [PubMed]
  8. S. Lopez-Aguayo, A. S. Desyatnikov, Yu. S. Kivshar, S. Skupin, W. Krolikowski, and O. Bang, "Stable rotating dipole solitons in nonlocal optical media," Opt. Lett. 31, 1100 (2006).
    [CrossRef] [PubMed]
  9. S. Lopez-Aguayo, A. S. Desyatnikov, and Yu. S. Kivshar, "Azimuthons in nonlocal nonlinear media," Opt. Express 14, 7903 (2006); http://www.opticsinfobase.org/abstract.cfm?URI= oe-14-17-7903.
    [CrossRef] [PubMed]
  10. S. Skupin, M. Saffman, andW. Krolikowski, "Nonlocal stabilization of nonlinear beams in a self-focusing atomic vapor," Phys. Rev. Lett. 98, 263902 (2007).
    [CrossRef] [PubMed]
  11. M. Soljacic and M. Segev, "Integer and fractional angular momentum borne on self-trapped necklace-ring beams," Phys. Rev. Lett. 86, 420 (2001).
    [CrossRef] [PubMed]
  12. V. Tikhonenko, J. Christou, and B. Luther-Davies, "Spiraling bright spatial solitons formed by the breakup of an optical vortex in a saturable self-focusing medium," J. Opt. Soc. Am. B 12, 2046 (1995).
    [CrossRef]
  13. M. S. Bigelow, P. Zerom, and R. W. Boyd, "Breakup of ring beams carrying orbital angular momentum in sodium vapor," Phys. Rev. Lett. 92, 083902 (2004).
    [CrossRef] [PubMed]
  14. L. T. Vuong, T. D. Grow, A. Ishaaya, A. L. Gaeta, G. W. ’t Hooft, E. R. Eliel, and G. Fibich, "Collapse of optical vortices," Phys. Rev. Lett. 96, 133901 (2006).
    [CrossRef] [PubMed]
  15. G. A. Swartzlander, Jr. and C. T. Law, "Optical vortex solitons observed in Kerr nonlinear media," Phys. Rev. Lett. 69, 2503 (1992).
    [CrossRef] [PubMed]
  16. S. M. Rochester, D. S. Hsiung, D. Budker, R. Y. Chiao, D. F. Kimball, and V. V. Yashchuk, "Self-rotation of resonant elliptically polarized light in collision-free rubidium vapor," Phys. Rev. A 63, 043814 (2001).
    [CrossRef]
  17. N. N. Rozanov, "On the translational and rotational motion of nonlinear optical structures as a whole," Opt. Spectrosc. 96, 405 (2004).
    [CrossRef]

2007 (1)

S. Skupin, M. Saffman, andW. Krolikowski, "Nonlocal stabilization of nonlinear beams in a self-focusing atomic vapor," Phys. Rev. Lett. 98, 263902 (2007).
[CrossRef] [PubMed]

2006 (2)

S. Lopez-Aguayo, A. S. Desyatnikov, Yu. S. Kivshar, S. Skupin, W. Krolikowski, and O. Bang, "Stable rotating dipole solitons in nonlocal optical media," Opt. Lett. 31, 1100 (2006).
[CrossRef] [PubMed]

L. T. Vuong, T. D. Grow, A. Ishaaya, A. L. Gaeta, G. W. ’t Hooft, E. R. Eliel, and G. Fibich, "Collapse of optical vortices," Phys. Rev. Lett. 96, 133901 (2006).
[CrossRef] [PubMed]

2005 (2)

A. S. Desyatnikov, A. A. Sukhorukov, and Yu. S. Kivshar, "Azimuthons: spatially modulated vortex solitons," Phys. Rev. Lett. 95, 203904 (2005).
[CrossRef] [PubMed]

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, "Solitons in nonlinear media with an infinite range of nonlocality: first observation of coherent elliptic solitons and of vortex-ring solitons," Phys. Rev. Lett. 95, 213904 (2005).
[CrossRef] [PubMed]

2004 (2)

M. S. Bigelow, P. Zerom, and R. W. Boyd, "Breakup of ring beams carrying orbital angular momentum in sodium vapor," Phys. Rev. Lett. 92, 083902 (2004).
[CrossRef] [PubMed]

N. N. Rozanov, "On the translational and rotational motion of nonlinear optical structures as a whole," Opt. Spectrosc. 96, 405 (2004).
[CrossRef]

2002 (1)

A. S. Desyatnikov and Yu. S. Kivshar, "Rotating optical soliton clusters," Phys. Rev. Lett. 88, 053901 (2002).
[CrossRef] [PubMed]

2001 (2)

M. Soljacic and M. Segev, "Integer and fractional angular momentum borne on self-trapped necklace-ring beams," Phys. Rev. Lett. 86, 420 (2001).
[CrossRef] [PubMed]

S. M. Rochester, D. S. Hsiung, D. Budker, R. Y. Chiao, D. F. Kimball, and V. V. Yashchuk, "Self-rotation of resonant elliptically polarized light in collision-free rubidium vapor," Phys. Rev. A 63, 043814 (2001).
[CrossRef]

1995 (1)

1992 (1)

G. A. Swartzlander, Jr. and C. T. Law, "Optical vortex solitons observed in Kerr nonlinear media," Phys. Rev. Lett. 69, 2503 (1992).
[CrossRef] [PubMed]

1985 (1)

V. I. Kruglov and R. A. Vlasov, "Spiral self-trapping propagation of optical beams in media with cubic nonlinearity," Phys. Lett. A 111, 401 (1985).
[CrossRef]

1964 (1)

R. Y. Chiao, E. Garmire, and C. H. Townes, "Self-trapping of optical beams," Phys. Rev. Lett. 13, 479 (1964).
[CrossRef]

’t Hooft, G. W.

L. T. Vuong, T. D. Grow, A. Ishaaya, A. L. Gaeta, G. W. ’t Hooft, E. R. Eliel, and G. Fibich, "Collapse of optical vortices," Phys. Rev. Lett. 96, 133901 (2006).
[CrossRef] [PubMed]

Bang, O.

Bigelow, M. S.

M. S. Bigelow, P. Zerom, and R. W. Boyd, "Breakup of ring beams carrying orbital angular momentum in sodium vapor," Phys. Rev. Lett. 92, 083902 (2004).
[CrossRef] [PubMed]

Boyd, R. W.

M. S. Bigelow, P. Zerom, and R. W. Boyd, "Breakup of ring beams carrying orbital angular momentum in sodium vapor," Phys. Rev. Lett. 92, 083902 (2004).
[CrossRef] [PubMed]

Budker, D.

S. M. Rochester, D. S. Hsiung, D. Budker, R. Y. Chiao, D. F. Kimball, and V. V. Yashchuk, "Self-rotation of resonant elliptically polarized light in collision-free rubidium vapor," Phys. Rev. A 63, 043814 (2001).
[CrossRef]

Carmon, T.

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, "Solitons in nonlinear media with an infinite range of nonlocality: first observation of coherent elliptic solitons and of vortex-ring solitons," Phys. Rev. Lett. 95, 213904 (2005).
[CrossRef] [PubMed]

Chiao, R. Y.

S. M. Rochester, D. S. Hsiung, D. Budker, R. Y. Chiao, D. F. Kimball, and V. V. Yashchuk, "Self-rotation of resonant elliptically polarized light in collision-free rubidium vapor," Phys. Rev. A 63, 043814 (2001).
[CrossRef]

R. Y. Chiao, E. Garmire, and C. H. Townes, "Self-trapping of optical beams," Phys. Rev. Lett. 13, 479 (1964).
[CrossRef]

Christou, J.

Cohen, O.

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, "Solitons in nonlinear media with an infinite range of nonlocality: first observation of coherent elliptic solitons and of vortex-ring solitons," Phys. Rev. Lett. 95, 213904 (2005).
[CrossRef] [PubMed]

Desyatnikov, A. S.

S. Lopez-Aguayo, A. S. Desyatnikov, Yu. S. Kivshar, S. Skupin, W. Krolikowski, and O. Bang, "Stable rotating dipole solitons in nonlocal optical media," Opt. Lett. 31, 1100 (2006).
[CrossRef] [PubMed]

A. S. Desyatnikov, A. A. Sukhorukov, and Yu. S. Kivshar, "Azimuthons: spatially modulated vortex solitons," Phys. Rev. Lett. 95, 203904 (2005).
[CrossRef] [PubMed]

A. S. Desyatnikov and Yu. S. Kivshar, "Rotating optical soliton clusters," Phys. Rev. Lett. 88, 053901 (2002).
[CrossRef] [PubMed]

Eliel, E. R.

L. T. Vuong, T. D. Grow, A. Ishaaya, A. L. Gaeta, G. W. ’t Hooft, E. R. Eliel, and G. Fibich, "Collapse of optical vortices," Phys. Rev. Lett. 96, 133901 (2006).
[CrossRef] [PubMed]

Fibich, G.

L. T. Vuong, T. D. Grow, A. Ishaaya, A. L. Gaeta, G. W. ’t Hooft, E. R. Eliel, and G. Fibich, "Collapse of optical vortices," Phys. Rev. Lett. 96, 133901 (2006).
[CrossRef] [PubMed]

Gaeta, A. L.

L. T. Vuong, T. D. Grow, A. Ishaaya, A. L. Gaeta, G. W. ’t Hooft, E. R. Eliel, and G. Fibich, "Collapse of optical vortices," Phys. Rev. Lett. 96, 133901 (2006).
[CrossRef] [PubMed]

Garmire, E.

R. Y. Chiao, E. Garmire, and C. H. Townes, "Self-trapping of optical beams," Phys. Rev. Lett. 13, 479 (1964).
[CrossRef]

Grow, T. D.

L. T. Vuong, T. D. Grow, A. Ishaaya, A. L. Gaeta, G. W. ’t Hooft, E. R. Eliel, and G. Fibich, "Collapse of optical vortices," Phys. Rev. Lett. 96, 133901 (2006).
[CrossRef] [PubMed]

Hsiung, D. S.

S. M. Rochester, D. S. Hsiung, D. Budker, R. Y. Chiao, D. F. Kimball, and V. V. Yashchuk, "Self-rotation of resonant elliptically polarized light in collision-free rubidium vapor," Phys. Rev. A 63, 043814 (2001).
[CrossRef]

Ishaaya, A.

L. T. Vuong, T. D. Grow, A. Ishaaya, A. L. Gaeta, G. W. ’t Hooft, E. R. Eliel, and G. Fibich, "Collapse of optical vortices," Phys. Rev. Lett. 96, 133901 (2006).
[CrossRef] [PubMed]

Kimball, D. F.

S. M. Rochester, D. S. Hsiung, D. Budker, R. Y. Chiao, D. F. Kimball, and V. V. Yashchuk, "Self-rotation of resonant elliptically polarized light in collision-free rubidium vapor," Phys. Rev. A 63, 043814 (2001).
[CrossRef]

Kivshar, Yu. S.

S. Lopez-Aguayo, A. S. Desyatnikov, Yu. S. Kivshar, S. Skupin, W. Krolikowski, and O. Bang, "Stable rotating dipole solitons in nonlocal optical media," Opt. Lett. 31, 1100 (2006).
[CrossRef] [PubMed]

A. S. Desyatnikov, A. A. Sukhorukov, and Yu. S. Kivshar, "Azimuthons: spatially modulated vortex solitons," Phys. Rev. Lett. 95, 203904 (2005).
[CrossRef] [PubMed]

A. S. Desyatnikov and Yu. S. Kivshar, "Rotating optical soliton clusters," Phys. Rev. Lett. 88, 053901 (2002).
[CrossRef] [PubMed]

Krolikowski, W.

Kruglov, V. I.

V. I. Kruglov and R. A. Vlasov, "Spiral self-trapping propagation of optical beams in media with cubic nonlinearity," Phys. Lett. A 111, 401 (1985).
[CrossRef]

Law, C. T.

G. A. Swartzlander, Jr. and C. T. Law, "Optical vortex solitons observed in Kerr nonlinear media," Phys. Rev. Lett. 69, 2503 (1992).
[CrossRef] [PubMed]

Lopez-Aguayo, S.

Luther-Davies, B.

Manela, O.

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, "Solitons in nonlinear media with an infinite range of nonlocality: first observation of coherent elliptic solitons and of vortex-ring solitons," Phys. Rev. Lett. 95, 213904 (2005).
[CrossRef] [PubMed]

Rochester, S. M.

S. M. Rochester, D. S. Hsiung, D. Budker, R. Y. Chiao, D. F. Kimball, and V. V. Yashchuk, "Self-rotation of resonant elliptically polarized light in collision-free rubidium vapor," Phys. Rev. A 63, 043814 (2001).
[CrossRef]

Rotschild, C.

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, "Solitons in nonlinear media with an infinite range of nonlocality: first observation of coherent elliptic solitons and of vortex-ring solitons," Phys. Rev. Lett. 95, 213904 (2005).
[CrossRef] [PubMed]

Rozanov, N. N.

N. N. Rozanov, "On the translational and rotational motion of nonlinear optical structures as a whole," Opt. Spectrosc. 96, 405 (2004).
[CrossRef]

Saffman, M.

S. Skupin, M. Saffman, andW. Krolikowski, "Nonlocal stabilization of nonlinear beams in a self-focusing atomic vapor," Phys. Rev. Lett. 98, 263902 (2007).
[CrossRef] [PubMed]

Segev, M.

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, "Solitons in nonlinear media with an infinite range of nonlocality: first observation of coherent elliptic solitons and of vortex-ring solitons," Phys. Rev. Lett. 95, 213904 (2005).
[CrossRef] [PubMed]

M. Soljacic and M. Segev, "Integer and fractional angular momentum borne on self-trapped necklace-ring beams," Phys. Rev. Lett. 86, 420 (2001).
[CrossRef] [PubMed]

Skupin, S.

S. Skupin, M. Saffman, andW. Krolikowski, "Nonlocal stabilization of nonlinear beams in a self-focusing atomic vapor," Phys. Rev. Lett. 98, 263902 (2007).
[CrossRef] [PubMed]

S. Lopez-Aguayo, A. S. Desyatnikov, Yu. S. Kivshar, S. Skupin, W. Krolikowski, and O. Bang, "Stable rotating dipole solitons in nonlocal optical media," Opt. Lett. 31, 1100 (2006).
[CrossRef] [PubMed]

Soljacic, M.

M. Soljacic and M. Segev, "Integer and fractional angular momentum borne on self-trapped necklace-ring beams," Phys. Rev. Lett. 86, 420 (2001).
[CrossRef] [PubMed]

Sukhorukov, A. A.

A. S. Desyatnikov, A. A. Sukhorukov, and Yu. S. Kivshar, "Azimuthons: spatially modulated vortex solitons," Phys. Rev. Lett. 95, 203904 (2005).
[CrossRef] [PubMed]

Swartzlander, G. A.

G. A. Swartzlander, Jr. and C. T. Law, "Optical vortex solitons observed in Kerr nonlinear media," Phys. Rev. Lett. 69, 2503 (1992).
[CrossRef] [PubMed]

Tikhonenko, V.

Townes, C. H.

R. Y. Chiao, E. Garmire, and C. H. Townes, "Self-trapping of optical beams," Phys. Rev. Lett. 13, 479 (1964).
[CrossRef]

Vlasov, R. A.

V. I. Kruglov and R. A. Vlasov, "Spiral self-trapping propagation of optical beams in media with cubic nonlinearity," Phys. Lett. A 111, 401 (1985).
[CrossRef]

Vuong, L. T.

L. T. Vuong, T. D. Grow, A. Ishaaya, A. L. Gaeta, G. W. ’t Hooft, E. R. Eliel, and G. Fibich, "Collapse of optical vortices," Phys. Rev. Lett. 96, 133901 (2006).
[CrossRef] [PubMed]

Yashchuk, V. V.

S. M. Rochester, D. S. Hsiung, D. Budker, R. Y. Chiao, D. F. Kimball, and V. V. Yashchuk, "Self-rotation of resonant elliptically polarized light in collision-free rubidium vapor," Phys. Rev. A 63, 043814 (2001).
[CrossRef]

Zerom, P.

M. S. Bigelow, P. Zerom, and R. W. Boyd, "Breakup of ring beams carrying orbital angular momentum in sodium vapor," Phys. Rev. Lett. 92, 083902 (2004).
[CrossRef] [PubMed]

J. Opt. Soc. Am. B (1)

Opt. Lett. (1)

Opt. Spectrosc. (1)

N. N. Rozanov, "On the translational and rotational motion of nonlinear optical structures as a whole," Opt. Spectrosc. 96, 405 (2004).
[CrossRef]

Phys. Lett. A (1)

V. I. Kruglov and R. A. Vlasov, "Spiral self-trapping propagation of optical beams in media with cubic nonlinearity," Phys. Lett. A 111, 401 (1985).
[CrossRef]

Phys. Rev. A (1)

S. M. Rochester, D. S. Hsiung, D. Budker, R. Y. Chiao, D. F. Kimball, and V. V. Yashchuk, "Self-rotation of resonant elliptically polarized light in collision-free rubidium vapor," Phys. Rev. A 63, 043814 (2001).
[CrossRef]

Phys. Rev. Lett. (9)

S. Skupin, M. Saffman, andW. Krolikowski, "Nonlocal stabilization of nonlinear beams in a self-focusing atomic vapor," Phys. Rev. Lett. 98, 263902 (2007).
[CrossRef] [PubMed]

M. Soljacic and M. Segev, "Integer and fractional angular momentum borne on self-trapped necklace-ring beams," Phys. Rev. Lett. 86, 420 (2001).
[CrossRef] [PubMed]

M. S. Bigelow, P. Zerom, and R. W. Boyd, "Breakup of ring beams carrying orbital angular momentum in sodium vapor," Phys. Rev. Lett. 92, 083902 (2004).
[CrossRef] [PubMed]

L. T. Vuong, T. D. Grow, A. Ishaaya, A. L. Gaeta, G. W. ’t Hooft, E. R. Eliel, and G. Fibich, "Collapse of optical vortices," Phys. Rev. Lett. 96, 133901 (2006).
[CrossRef] [PubMed]

G. A. Swartzlander, Jr. and C. T. Law, "Optical vortex solitons observed in Kerr nonlinear media," Phys. Rev. Lett. 69, 2503 (1992).
[CrossRef] [PubMed]

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, "Solitons in nonlinear media with an infinite range of nonlocality: first observation of coherent elliptic solitons and of vortex-ring solitons," Phys. Rev. Lett. 95, 213904 (2005).
[CrossRef] [PubMed]

A. S. Desyatnikov and Yu. S. Kivshar, "Rotating optical soliton clusters," Phys. Rev. Lett. 88, 053901 (2002).
[CrossRef] [PubMed]

A. S. Desyatnikov, A. A. Sukhorukov, and Yu. S. Kivshar, "Azimuthons: spatially modulated vortex solitons," Phys. Rev. Lett. 95, 203904 (2005).
[CrossRef] [PubMed]

R. Y. Chiao, E. Garmire, and C. H. Townes, "Self-trapping of optical beams," Phys. Rev. Lett. 13, 479 (1964).
[CrossRef]

Other (3)

Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, 2003).

A. S. Desyatnikov, Yu. S. Kivshar, and L. Torner, "Optical vortices and vortex solitons," E. Wolf, ed., Progess in Optics (Elsevier, 2005) 47, pp. 291.
[CrossRef]

S. Lopez-Aguayo, A. S. Desyatnikov, and Yu. S. Kivshar, "Azimuthons in nonlocal nonlinear media," Opt. Express 14, 7903 (2006); http://www.opticsinfobase.org/abstract.cfm?URI= oe-14-17-7903.
[CrossRef] [PubMed]

Supplementary Material (4)

» Media 1: MOV (2370 KB)     
» Media 2: MOV (4270 KB)     
» Media 3: MOV (3050 KB)     
» Media 4: MOV (820 KB)     

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Figures (5)

Fig. 1.
Fig. 1.

Numerical results on phase imprinting: (a, Media 1) four-lobe unstable soliton cluster; (b, Media 2) four-lobe localised azimuthon formation; and (c, Media 3) unstable vortex soliton. Left: input phase profiles with superimposed intensity contours of the Gaussian beam. Right: intensity profiles after propagation distance indicated in the images.

Fig. 2.
Fig. 2.

(a) Phase distribution for generation of azimuthons. (b) Experimental setup: VA - variable attenuator, SLM - spatial light modulator, Rb - Rubidium cell, λ/4 - quarter wave-plate, CCD - cameras. (c, d) Experimental results: Input (top) and output (bottom) intensities for (c) an azimuthon with α=0° and (d) vortex with α=45°. Input power 830µW.

Fig. 3.
Fig. 3.

Calculated dynamics of three beams in saturable media (Media 4). (a) 3D and (b) transverse views of the interacting beams showing their twist due to interaction. The twist is characterized by the angle βA (c) and by the angular velocity Ω (d).

Fig. 4.
Fig. 4.

Three lobe azimuthon experiments. (a–d) Measured output profiles for input tilts α=1°,15°,29°, 43° and power 690µW. (e) Output positions of the three lobes compared with the position of a single noninteracting lobe, marked “A, alone”. The azimuthon radius R and the average width of each beam w are shown in (f) and their ratio in (g).

Fig. 5.
Fig. 5.

Anomalous spiralling: (a) markers show the output angles measured for each beam such as βA in Fig. 4(e), the error bars indicate standard deviation from the mean value β (solid line). Numerically calculated OAM (b) and angular velocity (c) for the three-lobe azimuthon Eq. (3) in saturable media; shaded is the domain 1≤R/w≤2.

Equations (3)

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

θ ( φ ) = m φ m φ n + m ( r / R ) sin ( φ φ n ) + . . . ,
θ ( φ ) = m φ n + m ( φ φ n ) tan α , for φ φ n < π / N .
G n = A exp ( r r n 2 / 2 w 2 + im φ n + ik v n ( r r n ) ) ,

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