Dark and gray spatial optical solitons in
Kerr-type nonlocal media

doi:10.1364/OE.17.005170

Dark and gray spatial optical solitons in Kerr-type nonlocal media

Shigen Ouyang and Qi Guo »View Author Affiliations

Optics Express, Vol. 17, Issue 7, pp. 5170-5175 (2009)
http://dx.doi.org/10.1364/OE.17.005170

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Abstract
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Abstract

With the spectral renormalization method (the Fourier iteration method) we compute dark/gray soliton solutions in Kerr-type nonlocal media and find it agrees well with the analytical results. It is indicated when the characteristic nonlocal length is less than a certain critical value, the gray soliton’s maximal transverse velocity does not vary with the characteristic nonlocal length, otherwise such maximal velocity decreases with the characteristic nonlocal length.

OCIS Codes
(190.0190) Nonlinear optics : Nonlinear optics
(190.4420) Nonlinear optics : Nonlinear optics, transverse effects in
(260.5950) Physical optics : Self-focusing

ToC Category:
Nonlinear Optics

History
Original Manuscript: February 2, 2009
Revised Manuscript: March 7, 2009
Manuscript Accepted: March 13, 2009
Published: March 17, 2009

Citation
Shigen Ouyang and Qi Guo, "Dark and gray spatial optical solitons in Kerr-type nonlocal media," Opt. Express 17, 5170-5175 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-7-5170

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References

C. Conti, M. Peccianti, and G. Assanto, "Route to Nonlocality and Observation of Accessible Solitons," Phys. Rev. Lett. 91, 073901 (2003). [CrossRef] [PubMed]
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. Hu, T. Zhang, Q. Guo, L. Xuan, and S. Lan, "Nonlocality-controlled interaction of spatial solitons in nematic liquid crystals," Appl. Phys. Lett. 89, 071111 (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]
Q. Guo, B. Luo, F. Yi, S. Chi, and Y. Xie, "Large phase shift of nonlocal optical spatial solitons," Phys. Rev. E, 69, 016602 (2004). [CrossRef]
S. Ouyang, Q. Guo, and W. Hu, "Perturbative analysis of generally nonlocal spatial optical solitons," Phys. Rev. E 74, 036622 (2006). [CrossRef]
S. Ouyang and Q. Guo, "(1+2)-dimensional strongly nonlocal solitons," Phys. Rev. A 76, 053833 (2007). [CrossRef]
W. Zhong and L. Yi, "Two-dimensional Laguerre-Gaussian soliton family in strongly nonlocal nonlinear media," Phys. Rev. A 75, 061801 (2007). [CrossRef]
D. Buccoliero, A. S. Desyatnikov,W. Krolikowski, and Y. S. Kivshar, "Laguerre and Hermite Soliton Clusters in Nonlocal Nonlinear Media," Phys. Rev. Lett. 98, 053901 (2007). [CrossRef] [PubMed]
D. Deng and Q. Guo, "Ince-Gaussian solitons in strongly nonlocal nonlinear media," Opt. Lett, 32, 3206-3208 (2007). [CrossRef] [PubMed]
A. W. Snyder and D. J. Mitchell, "accessible soliton," Science 276, 1538 (1997). [CrossRef]
P. D. Rasmussen, O. Bang, W. Krolikowski, "Theory of nonlocal soliton interaction in nematic liquid crystal," Phys. Rev. E 72, 066611 (2005). [CrossRef]
S. Ouyang, W. Hu, and Q. Guo, "Light steering in a strongly nonlocal nonlinear medium," Phys. Rev. A 76, 053832 (2007). [CrossRef]
W. Hu, S. Ouyang, P. Yang, Q. Guo,and S. Lan, "Short-range interactions between strongly nonlocal spatial solitons," Phys. Rev. A 77, 033842 (2008). [CrossRef]
A. Dreischuh, D. N. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, "Observation of Attraction between Dark Solitons" Phys. Rev. Lett. 96, 043901 (2006). [CrossRef] [PubMed]
N. I. Nikolov, D. Neshev, W. Krolikowski, O Bang, J. J. Rasmussen, and P. L. Christiansen, "Attraction of nonlocal dark optical soliton," Opt. Lett. 29, 286-288 (2004). [CrossRef]
Y. V. Kartashov and L. Torner, "Gray spatial solitons in nonlocal nonlinear media," Opt. Lett. 32, 946-948 (2007) [CrossRef]
M. J. Ablowitz and Z. H. Musslimani, "Spectral renormalization method for computing self-localized solutions to nonlinear systems," Opt. Lett. 30, 2140-2142 (2005). [CrossRef]
Z. H. Musslimani, and J. Yang, "Self-trapping of light in a two-dimensional photonic lattice," J. Opt. Soc. Am. B. 21, 973-981 (2004). [CrossRef]
A. A. Zozulya, D. Z. Anderson, A. V. Mamaev and M. Saffman, "Solitary attractors and low-order filamentation in anisotropic self-focusing media," Phys. Rev. E 57, 522-534 (1998).
M. Stepic, L. Hadzievski, and M. M. Skoric, "Stability of one-dimensional array solitons," Phys. Rev. E 65, 026604 (2002) [CrossRef]
J. Hudock, P. G. Kevrekidis, B. A. Malomed, and D. N. Christodoulides, "Discrete vector solitons in two-dimensional nonlinear waveguide arrays: Solutions, stability, and dynamics," Phys. Rev. E 67, 056618 (2003). [CrossRef]
G. P. Agrawal, Nonlinear Fiber Optics, (New York: Academeic 1995).
W. Krolikowski and O. Bang, "Solitons in nonlocal nonlinear media: Exact solutions," Phys. Rev. E 63, 016610 (2000). [CrossRef]
W. Krolikowski, O. Bang, J. J. Rasmussen and J. Wyller "Modulational instability in nonlocal nonlinear Kerr media," Phys. Rev. E 64, 016612 (2001). [CrossRef]

Ablowitz, M. J.
Anderson, D. Z.
Assanto, G.
Bang, O
Bang, O.
Buccoliero, D.
Carmon, T.
Chi, S.
Christiansen, P. L.
Christodoulides, D. N.
Cohen, O.
Conti, C.
Deng, D.
Desyatnikov, A. S.
Dreischuh, A.
Guo, Q.
Hadzievski, L.
Hu, W.
Hudock, J.
Kartashov, Y. V.
Kevrekidis, P. G.
Kivshar, Y. S.
Krolikowski, W.
Lan, S.
Luo, B.
Malomed, B. A.
Mamaev, A. V.
Manela, O.
Mitchell, D. J.
Musslimani, Z. H.
Neshev, D.
Neshev, D. N.
Nikolov, N. I.
Ouyang, S.
Peccianti, M.
Petersen, D. E.
Rasmussen, J. J.
Rasmussen, P. D.
Rotschild, C.
Saffman, M.
Segev, M.
Skoric, M. M.
Snyder, A. W.
Stepic, M.
Torner, L.
Wyller, J.
Xie, Y.
Xuan, L.
Yang, J.
Yang, P.
Yi, F.
Yi, L.
Zhang, T.
Zhong, W.
Zozulya, A. A.

Appl. Phys. Lett.

W. Hu, T. Zhang, Q. Guo, L. Xuan, and S. Lan, "Nonlocality-controlled interaction of spatial solitons in nematic liquid crystals," Appl. Phys. Lett. 89, 071111 (2006). [CrossRef]

J. Opt. Soc. Am. B.

Z. H. Musslimani, and J. Yang, "Self-trapping of light in a two-dimensional photonic lattice," J. Opt. Soc. Am. B. 21, 973-981 (2004). [CrossRef]

Opt. Lett

D. Deng and Q. Guo, "Ince-Gaussian solitons in strongly nonlocal nonlinear media," Opt. Lett, 32, 3206-3208 (2007). [CrossRef] [PubMed]
N. I. Nikolov, D. Neshev, W. Krolikowski, O Bang, J. J. Rasmussen, and P. L. Christiansen, "Attraction of nonlocal dark optical soliton," Opt. Lett. 29, 286-288 (2004). [CrossRef]
Y. V. Kartashov and L. Torner, "Gray spatial solitons in nonlocal nonlinear media," Opt. Lett. 32, 946-948 (2007) [CrossRef]
M. J. Ablowitz and Z. H. Musslimani, "Spectral renormalization method for computing self-localized solutions to nonlinear systems," Opt. Lett. 30, 2140-2142 (2005). [CrossRef]

Phys. Rev. A

S. Ouyang, W. Hu, and Q. Guo, "Light steering in a strongly nonlocal nonlinear medium," Phys. Rev. A 76, 053832 (2007). [CrossRef]
W. Hu, S. Ouyang, P. Yang, Q. Guo,and S. Lan, "Short-range interactions between strongly nonlocal spatial solitons," Phys. Rev. A 77, 033842 (2008). [CrossRef]
S. Ouyang and Q. Guo, "(1+2)-dimensional strongly nonlocal solitons," Phys. Rev. A 76, 053833 (2007). [CrossRef]
W. Zhong and L. Yi, "Two-dimensional Laguerre-Gaussian soliton family in strongly nonlocal nonlinear media," Phys. Rev. A 75, 061801 (2007). [CrossRef]

Phys. Rev. E

Q. Guo, B. Luo, F. Yi, S. Chi, and Y. Xie, "Large phase shift of nonlocal optical spatial solitons," Phys. Rev. E, 69, 016602 (2004). [CrossRef]
S. Ouyang, Q. Guo, and W. Hu, "Perturbative analysis of generally nonlocal spatial optical solitons," Phys. Rev. E 74, 036622 (2006). [CrossRef]
A. A. Zozulya, D. Z. Anderson, A. V. Mamaev and M. Saffman, "Solitary attractors and low-order filamentation in anisotropic self-focusing media," Phys. Rev. E 57, 522-534 (1998).
M. Stepic, L. Hadzievski, and M. M. Skoric, "Stability of one-dimensional array solitons," Phys. Rev. E 65, 026604 (2002) [CrossRef]
J. Hudock, P. G. Kevrekidis, B. A. Malomed, and D. N. Christodoulides, "Discrete vector solitons in two-dimensional nonlinear waveguide arrays: Solutions, stability, and dynamics," Phys. Rev. E 67, 056618 (2003). [CrossRef]
W. Krolikowski and O. Bang, "Solitons in nonlocal nonlinear media: Exact solutions," Phys. Rev. E 63, 016610 (2000). [CrossRef]
W. Krolikowski, O. Bang, J. J. Rasmussen and J. Wyller "Modulational instability in nonlocal nonlinear Kerr media," Phys. Rev. E 64, 016612 (2001). [CrossRef]
P. D. Rasmussen, O. Bang, W. Krolikowski, "Theory of nonlocal soliton interaction in nematic liquid crystal," Phys. Rev. E 72, 066611 (2005). [CrossRef]

Phys. Rev. Lett.

A. Dreischuh, D. N. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, "Observation of Attraction between Dark Solitons" Phys. Rev. Lett. 96, 043901 (2006). [CrossRef] [PubMed]
D. Buccoliero, A. S. Desyatnikov,W. Krolikowski, and Y. S. Kivshar, "Laguerre and Hermite Soliton Clusters in Nonlocal Nonlinear Media," Phys. Rev. Lett. 98, 053901 (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]
C. Conti, M. Peccianti, and G. Assanto, "Route to Nonlocality and Observation of Accessible Solitons," Phys. Rev. Lett. 91, 073901 (2003). [CrossRef] [PubMed]
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]

Science

A. W. Snyder and D. J. Mitchell, "accessible soliton," Science 276, 1538 (1997). [CrossRef]

Other

G. P. Agrawal, Nonlinear Fiber Optics, (New York: Academeic 1995).

2008, Hu, Phys. Rev. A
2007, Kartashov, Opt. Lett
2007, Ouyang, Phys. Rev. A
2007, Zhong, Phys. Rev. A
2007, Buccoliero, Phys. Rev. Lett.
2007, Deng, Opt. Lett
2007, Ouyang, Phys. Rev. A
2006, Hu, Appl. Phys. Lett.
2006, Dreischuh, Phys. Rev. Lett.
2006, Ouyang, Phys. Rev. E
2005, Rasmussen, Phys. Rev. E
2005, Ablowitz, Opt. Lett
2005, Rotschild, Phys. Rev. Lett.
2004, Guo, Phys. Rev. E
2004, Conti, Phys. Rev. Lett.
2004, Musslimani, J. Opt. Soc. Am. B.
2004, Nikolov, Opt. Lett
2003, Conti, Phys. Rev. Lett.
2003, Hudock, Phys. Rev. E
2002, Stepic, Phys. Rev. E
2001, Krolikowski, Phys. Rev. E
2000, Krolikowski, Phys. Rev. E
1998, Zozulya, Phys. Rev. E
1997, Snyder, Science

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[1] C. Conti, M. Peccianti, and G. Assanto, "Route to Nonlocality and Observation of Accessible Solitons," Phys. Rev. Lett. 91, 073901 (2003). [CrossRef] [PubMed]

[2] 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]

[3] W. Hu, T. Zhang, Q. Guo, L. Xuan, and S. Lan, "Nonlocality-controlled interaction of spatial solitons in nematic liquid crystals," Appl. Phys. Lett. 89, 071111 (2006). [CrossRef]

[4] 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]

[5] Q. Guo, B. Luo, F. Yi, S. Chi, and Y. Xie, "Large phase shift of nonlocal optical spatial solitons," Phys. Rev. E, 69, 016602 (2004). [CrossRef]

[6] S. Ouyang, Q. Guo, and W. Hu, "Perturbative analysis of generally nonlocal spatial optical solitons," Phys. Rev. E 74, 036622 (2006). [CrossRef]

[7] S. Ouyang and Q. Guo, "(1+2)-dimensional strongly nonlocal solitons," Phys. Rev. A 76, 053833 (2007). [CrossRef]

[8] W. Zhong and L. Yi, "Two-dimensional Laguerre-Gaussian soliton family in strongly nonlocal nonlinear media," Phys. Rev. A 75, 061801 (2007). [CrossRef]

[9] D. Buccoliero, A. S. Desyatnikov,W. Krolikowski, and Y. S. Kivshar, "Laguerre and Hermite Soliton Clusters in Nonlocal Nonlinear Media," Phys. Rev. Lett. 98, 053901 (2007). [CrossRef] [PubMed]

[10] D. Deng and Q. Guo, "Ince-Gaussian solitons in strongly nonlocal nonlinear media," Opt. Lett, 32, 3206-3208 (2007). [CrossRef] [PubMed]

[11] A. W. Snyder and D. J. Mitchell, "accessible soliton," Science 276, 1538 (1997). [CrossRef]

[12] P. D. Rasmussen, O. Bang, W. Krolikowski, "Theory of nonlocal soliton interaction in nematic liquid crystal," Phys. Rev. E 72, 066611 (2005). [CrossRef]

[13] S. Ouyang, W. Hu, and Q. Guo, "Light steering in a strongly nonlocal nonlinear medium," Phys. Rev. A 76, 053832 (2007). [CrossRef]

[14] W. Hu, S. Ouyang, P. Yang, Q. Guo,and S. Lan, "Short-range interactions between strongly nonlocal spatial solitons," Phys. Rev. A 77, 033842 (2008). [CrossRef]

[15] A. Dreischuh, D. N. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, "Observation of Attraction between Dark Solitons" Phys. Rev. Lett. 96, 043901 (2006). [CrossRef] [PubMed]

[16] N. I. Nikolov, D. Neshev, W. Krolikowski, O Bang, J. J. Rasmussen, and P. L. Christiansen, "Attraction of nonlocal dark optical soliton," Opt. Lett. 29, 286-288 (2004). [CrossRef]

[17] Y. V. Kartashov and L. Torner, "Gray spatial solitons in nonlocal nonlinear media," Opt. Lett. 32, 946-948 (2007) [CrossRef]

[18] M. J. Ablowitz and Z. H. Musslimani, "Spectral renormalization method for computing self-localized solutions to nonlinear systems," Opt. Lett. 30, 2140-2142 (2005). [CrossRef]

[19] Z. H. Musslimani, and J. Yang, "Self-trapping of light in a two-dimensional photonic lattice," J. Opt. Soc. Am. B. 21, 973-981 (2004). [CrossRef]

[20] A. A. Zozulya, D. Z. Anderson, A. V. Mamaev and M. Saffman, "Solitary attractors and low-order filamentation in anisotropic self-focusing media," Phys. Rev. E 57, 522-534 (1998).

[21] M. Stepic, L. Hadzievski, and M. M. Skoric, "Stability of one-dimensional array solitons," Phys. Rev. E 65, 026604 (2002) [CrossRef]

[22] J. Hudock, P. G. Kevrekidis, B. A. Malomed, and D. N. Christodoulides, "Discrete vector solitons in two-dimensional nonlinear waveguide arrays: Solutions, stability, and dynamics," Phys. Rev. E 67, 056618 (2003). [CrossRef]

[23] G. P. Agrawal, Nonlinear Fiber Optics, (New York: Academeic 1995).

[24] W. Krolikowski and O. Bang, "Solitons in nonlocal nonlinear media: Exact solutions," Phys. Rev. E 63, 016610 (2000). [CrossRef]

[25] W. Krolikowski, O. Bang, J. J. Rasmussen and J. Wyller "Modulational instability in nonlocal nonlinear Kerr media," Phys. Rev. E 64, 016612 (2001). [CrossRef]

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