Abstract

We study quasi-periodic transformations between nonlocal spatial solitons of different symmetries triggered by modulational instability and resembling a self-induced mode converter. Transformation dynamics of solitons with zero angular momentum, e.g. the quadrupole-type soliton, reveal the equidistant spectrum of spatial field oscillations typical for the breather-type solutions. In contrast, the transformations of nonlocal solitons carrying orbital angular momentum, such as 2×3 soliton matrix, are accompanied by their spiralling and corresponding spectra of field oscillations show mixing of three characteristic spatial frequencies.

© 2009 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  22. F. Ye, Y. V. Kartashov, L. Torner, "Stabilization of dipole solitons in nonlocal nonlinear media," Phys. Rev. A 77, 043821 (2008).
    [CrossRef]
  23. D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, "Boundary effects on the dynamics of higher-order optical spatial solitons in nonlocal thermal media," J. Opt. A 11, in press (2009).
    [CrossRef]
  24. E. G. Abramochkin and V. G. Volostnikov, "Generalized Gaussian beams," J. Opt. A 6, S157-S161 (2004).
    [CrossRef]
  25. D. Buccoliero, A. S. Desyatnikov,W. Krolikowski, and Yu. S. Kivshar, "Spiraling multivortex solitons in nonlocal nonlinear media," Opt. Lett. 33, 198-200 (2008).
    [CrossRef] [PubMed]
  26. S. Flach and A. Gorbach, "Discrete breathers-Advances in theory and applications," Phys. Rep. 467, 1 (2008).
    [CrossRef]
  27. A. Snyder and J. Mitchell, "Accesible Solitons," Science 276, 1538-1541 (1997).
    [CrossRef]
  28. S. Lopez-Aguayo and J. C. Guti’errez-Vega, "Elliptically modulated self-trapped singular beams in nonlocal nonlinear media: ellipticons," Opt. Express 15, 18326-18338 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-26-18326.
    [CrossRef] [PubMed]

2009

D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, "Boundary effects on the dynamics of higher-order optical spatial solitons in nonlocal thermal media," J. Opt. A 11, in press (2009).
[CrossRef]

2008

S. Flach and A. Gorbach, "Discrete breathers-Advances in theory and applications," Phys. Rep. 467, 1 (2008).
[CrossRef]

C. Rotschild, T. Schwartz, O. Cohen, and M. Segev, "Incoherent spatial solitons in effectively instantaneous nonlinear media," Nat. Photon. 2, 371-376 (2008).
[CrossRef]

F. Ye, Y. V. Kartashov, L. Torner, "Stabilization of dipole solitons in nonlocal nonlinear media," Phys. Rev. A 77, 043821 (2008).
[CrossRef]

D. Buccoliero, A. S. Desyatnikov,W. Krolikowski, and Yu. S. Kivshar, "Spiraling multivortex solitons in nonlocal nonlinear media," Opt. Lett. 33, 198-200 (2008).
[CrossRef] [PubMed]

S. Skupin, M. Grech, andW. Krolikowski, "Rotating soliton solutions in nonlocal nonlinear media," Opt. Express 16, 9118-9131 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-12-9118
[CrossRef] [PubMed]

2007

Y. V. Kartashov, V. A. Vysloukh, L. Torner, "Stability of vortex solitons in thermal nonlinear media with cylindrical symmetry," Opt. Express 15, 9378-9384 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-15-9378
[CrossRef] [PubMed]

I. Kaminer, C. Rotschild, O. Manela, and M. Segev, "Periodic solitons in nonlocal nonlinear media," Opt. Lett. 32, 3209-3211 (2007).
[CrossRef] [PubMed]

S. Lopez-Aguayo and J. C. Guti’errez-Vega, "Elliptically modulated self-trapped singular beams in nonlocal nonlinear media: ellipticons," Opt. Express 15, 18326-18338 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-26-18326.
[CrossRef] [PubMed]

A. V. Gorbach and D. V. Skryabin, "Cascaded Generation of Multiply Charged Optical Vortices and Spatiotemporal Helical Beams in a Raman Medium," Phys. Rev. Lett. 98, 243601 (2007).
[CrossRef] [PubMed]

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]

D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Yu. S. Kivshar, "Laguerre and Hermite soliton clusters in nonlocal nonlinear media," Phys. Rev. Lett. 98, 053901 (2007).
[CrossRef] [PubMed]

2006

2005

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]

D. Briedis, D. Petersen, D. Edmundson, W. Krolikowski, and O. Bang, "Ring vortex solitons in nonlocal nonlinear media," Opt. Express 13, 435-443 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-2-435
[CrossRef] [PubMed]

2004

C. Conti, M. Peccianti, and G. Assanto, "Observation of Optical Spatial Solitons in a Highly Nonlocal Medium," Phys. Rev. Lett. 92, 113902 (2004).
[CrossRef] [PubMed]

W. Krolikowski, O. Bang, N.I. Nikolov, D. Neshev, J. Wyller, J.J. Rasmussen, and D. Edmundson, "Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media," J. Opt. B 6, S288-S294 (2004).
[CrossRef]

E. G. Abramochkin and V. G. Volostnikov, "Generalized Gaussian beams," J. Opt. A 6, S157-S161 (2004).
[CrossRef]

1997

A. Snyder and J. Mitchell, "Accesible Solitons," Science 276, 1538-1541 (1997).
[CrossRef]

Abramochkin, E. G.

E. G. Abramochkin and V. G. Volostnikov, "Generalized Gaussian beams," J. Opt. A 6, S157-S161 (2004).
[CrossRef]

Alfassi, B.

C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, "Long-range interactions between optical solitons," Nat. Phys. 2, 769-774 (2006).
[CrossRef]

Assanto, G.

C. Conti, M. Peccianti, and G. Assanto, "Observation of Optical Spatial Solitons in a Highly Nonlocal Medium," Phys. Rev. Lett. 92, 113902 (2004).
[CrossRef] [PubMed]

Bang, O.

Briedis, D.

Buccoliero, D.

D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, "Boundary effects on the dynamics of higher-order optical spatial solitons in nonlocal thermal media," J. Opt. A 11, in press (2009).
[CrossRef]

D. Buccoliero, A. S. Desyatnikov,W. Krolikowski, and Yu. S. Kivshar, "Spiraling multivortex solitons in nonlocal nonlinear media," Opt. Lett. 33, 198-200 (2008).
[CrossRef] [PubMed]

D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Yu. S. Kivshar, "Laguerre and Hermite soliton clusters in nonlocal nonlinear media," Phys. Rev. Lett. 98, 053901 (2007).
[CrossRef] [PubMed]

Buljan, H.

O. Cohen, H. Buljan, T. Schwartz, J. W. Fleischer, and M. Segev, "Incoherent solitons in instantaneous nonlocal nonlinear media," Phys. Rev. E 73, 015601(R) (2006).
[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]

Cohen, O.

C. Rotschild, T. Schwartz, O. Cohen, and M. Segev, "Incoherent spatial solitons in effectively instantaneous nonlinear media," Nat. Photon. 2, 371-376 (2008).
[CrossRef]

C. Rotschild, M. Segev, Z. Xu, Y. V. Kartashov, L. Torner, and O. Cohen, "Two-dimensional multipole solitons in nonlocal nonlinear media," Opt. Lett. 31, 3312-3314 (2006).
[CrossRef] [PubMed]

C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, "Long-range interactions between optical solitons," Nat. Phys. 2, 769-774 (2006).
[CrossRef]

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]

O. Cohen, H. Buljan, T. Schwartz, J. W. Fleischer, and M. Segev, "Incoherent solitons in instantaneous nonlocal nonlinear media," Phys. Rev. E 73, 015601(R) (2006).
[CrossRef]

Conti, C.

C. Conti, M. Peccianti, and G. Assanto, "Observation of Optical Spatial Solitons in a Highly Nonlocal Medium," Phys. Rev. Lett. 92, 113902 (2004).
[CrossRef] [PubMed]

Desyatnikov, A. S.

Edmundson, D.

D. Briedis, D. Petersen, D. Edmundson, W. Krolikowski, and O. Bang, "Ring vortex solitons in nonlocal nonlinear media," Opt. Express 13, 435-443 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-2-435
[CrossRef] [PubMed]

W. Krolikowski, O. Bang, N.I. Nikolov, D. Neshev, J. Wyller, J.J. Rasmussen, and D. Edmundson, "Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media," J. Opt. B 6, S288-S294 (2004).
[CrossRef]

Flach, S.

S. Flach and A. Gorbach, "Discrete breathers-Advances in theory and applications," Phys. Rep. 467, 1 (2008).
[CrossRef]

Fleischer, J. W.

O. Cohen, H. Buljan, T. Schwartz, J. W. Fleischer, and M. Segev, "Incoherent solitons in instantaneous nonlocal nonlinear media," Phys. Rev. E 73, 015601(R) (2006).
[CrossRef]

Gorbach, A.

S. Flach and A. Gorbach, "Discrete breathers-Advances in theory and applications," Phys. Rep. 467, 1 (2008).
[CrossRef]

Gorbach, A. V.

A. V. Gorbach and D. V. Skryabin, "Cascaded Generation of Multiply Charged Optical Vortices and Spatiotemporal Helical Beams in a Raman Medium," Phys. Rev. Lett. 98, 243601 (2007).
[CrossRef] [PubMed]

Grech, M.

Guti’errez-Vega, J. C.

Kaminer, I.

Kartashov, Y. V.

Kivshar, Y. S.

D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, "Boundary effects on the dynamics of higher-order optical spatial solitons in nonlocal thermal media," J. Opt. A 11, in press (2009).
[CrossRef]

Kivshar, Yu. S.

Krolikowski, W.

D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Y. S. Kivshar, "Boundary effects on the dynamics of higher-order optical spatial solitons in nonlocal thermal media," J. Opt. A 11, in press (2009).
[CrossRef]

D. Buccoliero, A. S. Desyatnikov,W. Krolikowski, and Yu. S. Kivshar, "Spiraling multivortex solitons in nonlocal nonlinear media," Opt. Lett. 33, 198-200 (2008).
[CrossRef] [PubMed]

D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Yu. S. Kivshar, "Laguerre and Hermite soliton clusters in nonlocal nonlinear media," Phys. Rev. Lett. 98, 053901 (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, 1100-1102 (2006).
[CrossRef] [PubMed]

D. Briedis, D. Petersen, D. Edmundson, W. Krolikowski, and O. Bang, "Ring vortex solitons in nonlocal nonlinear media," Opt. Express 13, 435-443 (2005), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-2-435
[CrossRef] [PubMed]

W. Krolikowski, O. Bang, N.I. Nikolov, D. Neshev, J. Wyller, J.J. Rasmussen, and D. Edmundson, "Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media," J. Opt. B 6, S288-S294 (2004).
[CrossRef]

Lashkin, V. M.

A. I. Yakimenko, V. M. Lashkin, and O. O. Prikhodko, "Dynamics of two-dimensional coherent structures in nonlocal nonlinear media," Phys. Rev. E 73, 066605 (2006).
[CrossRef]

Lopez-Aguayo, S.

Manela, O.

I. Kaminer, C. Rotschild, O. Manela, and M. Segev, "Periodic solitons in nonlocal nonlinear media," Opt. Lett. 32, 3209-3211 (2007).
[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]

Mihalache, D.

Mitchell, J.

A. Snyder and J. Mitchell, "Accesible Solitons," Science 276, 1538-1541 (1997).
[CrossRef]

Neshev, D.

W. Krolikowski, O. Bang, N.I. Nikolov, D. Neshev, J. Wyller, J.J. Rasmussen, and D. Edmundson, "Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media," J. Opt. B 6, S288-S294 (2004).
[CrossRef]

Nikolov, N.I.

W. Krolikowski, O. Bang, N.I. Nikolov, D. Neshev, J. Wyller, J.J. Rasmussen, and D. Edmundson, "Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media," J. Opt. B 6, S288-S294 (2004).
[CrossRef]

Peccianti, M.

C. Conti, M. Peccianti, and G. Assanto, "Observation of Optical Spatial Solitons in a Highly Nonlocal Medium," Phys. Rev. Lett. 92, 113902 (2004).
[CrossRef] [PubMed]

Petersen, D.

Prikhodko, O. O.

A. I. Yakimenko, V. M. Lashkin, and O. O. Prikhodko, "Dynamics of two-dimensional coherent structures in nonlocal nonlinear media," Phys. Rev. E 73, 066605 (2006).
[CrossRef]

Rasmussen, J.J.

W. Krolikowski, O. Bang, N.I. Nikolov, D. Neshev, J. Wyller, J.J. Rasmussen, and D. Edmundson, "Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media," J. Opt. B 6, S288-S294 (2004).
[CrossRef]

Rotschild, C.

C. Rotschild, T. Schwartz, O. Cohen, and M. Segev, "Incoherent spatial solitons in effectively instantaneous nonlinear media," Nat. Photon. 2, 371-376 (2008).
[CrossRef]

I. Kaminer, C. Rotschild, O. Manela, and M. Segev, "Periodic solitons in nonlocal nonlinear media," Opt. Lett. 32, 3209-3211 (2007).
[CrossRef] [PubMed]

C. Rotschild, M. Segev, Z. Xu, Y. V. Kartashov, L. Torner, and O. Cohen, "Two-dimensional multipole solitons in nonlocal nonlinear media," Opt. Lett. 31, 3312-3314 (2006).
[CrossRef] [PubMed]

C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, "Long-range interactions between optical solitons," Nat. Phys. 2, 769-774 (2006).
[CrossRef]

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]

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]

Schwartz, T.

C. Rotschild, T. Schwartz, O. Cohen, and M. Segev, "Incoherent spatial solitons in effectively instantaneous nonlinear media," Nat. Photon. 2, 371-376 (2008).
[CrossRef]

O. Cohen, H. Buljan, T. Schwartz, J. W. Fleischer, and M. Segev, "Incoherent solitons in instantaneous nonlocal nonlinear media," Phys. Rev. E 73, 015601(R) (2006).
[CrossRef]

Segev, M.

C. Rotschild, T. Schwartz, O. Cohen, and M. Segev, "Incoherent spatial solitons in effectively instantaneous nonlinear media," Nat. Photon. 2, 371-376 (2008).
[CrossRef]

I. Kaminer, C. Rotschild, O. Manela, and M. Segev, "Periodic solitons in nonlocal nonlinear media," Opt. Lett. 32, 3209-3211 (2007).
[CrossRef] [PubMed]

C. Rotschild, M. Segev, Z. Xu, Y. V. Kartashov, L. Torner, and O. Cohen, "Two-dimensional multipole solitons in nonlocal nonlinear media," Opt. Lett. 31, 3312-3314 (2006).
[CrossRef] [PubMed]

C. Rotschild, B. Alfassi, O. Cohen, and M. Segev, "Long-range interactions between optical solitons," Nat. Phys. 2, 769-774 (2006).
[CrossRef]

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]

O. Cohen, H. Buljan, T. Schwartz, J. W. Fleischer, and M. Segev, "Incoherent solitons in instantaneous nonlocal nonlinear media," Phys. Rev. E 73, 015601(R) (2006).
[CrossRef]

Skryabin, D. V.

A. V. Gorbach and D. V. Skryabin, "Cascaded Generation of Multiply Charged Optical Vortices and Spatiotemporal Helical Beams in a Raman Medium," Phys. Rev. Lett. 98, 243601 (2007).
[CrossRef] [PubMed]

Skupin, S.

Snyder, A.

A. Snyder and J. Mitchell, "Accesible Solitons," Science 276, 1538-1541 (1997).
[CrossRef]

Torner, L.

Volostnikov, V. G.

E. G. Abramochkin and V. G. Volostnikov, "Generalized Gaussian beams," J. Opt. A 6, S157-S161 (2004).
[CrossRef]

Vysloukh, V. A.

Wyller, J.

W. Krolikowski, O. Bang, N.I. Nikolov, D. Neshev, J. Wyller, J.J. Rasmussen, and D. Edmundson, "Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media," J. Opt. B 6, S288-S294 (2004).
[CrossRef]

Xu, Z.

Yakimenko, A. I.

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Supplementary Material (3)

» Media 1: MOV (456 KB)     
» Media 2: MOV (544 KB)     
» Media 3: MOV (1217 KB)     

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Figures (4)

Fig. 1.
Fig. 1.

Top row: intensities of generalized quadrupole GN11 for several values of α. (a) Power vs. propagation constant and (b) Hamiltonian vs. power for three different families GN mn with indices (m,n) indicated next to the curves; for each family five curves are shown with α=π (0,1,2,3,4)/16. (c) Stability domain of the generalized quadrupole.

Fig. 2.
Fig. 2.

Quasi-periodic breather-like dynamics of the GN11 soliton with P=200 and α=π/8 is shown at small (a, Media 1) and large (b, Media 2) propagation distances. At one spatial location in the transverse plane we show (c) the intensity and (d) the spectrum of oscillations of the field. (e) Transformation frequency νt vs. power P for α=π (1,2,3)/16.

Fig. 3.
Fig. 3.

Family of the 2×3 soliton matrix GN21; top row: intensities for P=200. (a) Normalized OAM, (b) stability diagram, and (c) the spiralling velocity vs. k.

Fig. 4.
Fig. 4.

Quasi-periodic transformations and spiralling of the GN21(x, y;π/8) soliton with power P=300 (Media 3). Bottom: the averaged spectrum of oscillations with vertical lines showing composite spatial frequencies νij .

Equations (7)

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iEz+2Ex2+2Ey2+ER(rr)E(r)2dr=0 ,
𝓗=U2dr12R(rr)U(r)2U(r)2d r d r .
GNmn(x,y;α)=A exp (x2+y22a2) j=0n+mCmnj(α) Hn+mj (xb) Hj (yb),
GN11(x,y;α)=A exp (x2+y22a2) [(x2+y2b2)sin2α2ixycos2α] b2 ,
GN21(x,y;α)=A exp (x2y22a2){y(x2y2+b2)cosα+y (3x2+y23b2)cos(3α)+
2 i x sinα [x2+y22b2+(x2+3y23b2)cos(2α)]} b3 .
vij=k 2π+i vt +j vr ,

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