Multi-stable solitons in 𝒫𝒯-symmetric optical lattices

doi:10.1364/OE.20.016823

Multi-stable solitons in 𝒫𝒯-symmetric optical lattices

Chunyan Li, Haidong Liu, and Liangwei Dong »View Author Affiliations

Optics Express, Vol. 20, Issue 15, pp. 16823-16831 (2012)
http://dx.doi.org/10.1364/OE.20.016823

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Abstract

We address the existence and stability properties of optical solitons in a competing cubic-quintic medium with an imprinted complex lattice featuring a parity-time (𝒫𝒯) symmetry. Various families of solitons with even and odd geometrical symmetries are found in both the semi-infinite and the first finite gaps. Linear stability analysis corroborated by direct propagation simulations reveals that solitons with different symmetries and different number of humps can propagate stably at the same propagation constants, i.e., multi-stable solitons can exist in this scheme. Interestingly enough, in sharp contrast to the stability of solitons in a conventional (real) lattice, both even and odd solitons with the same propagation constant belonging to different branches can be stable in the first gap of 𝒫𝒯 lattice, which indicates that the imaginary part of lattice plays an important role for the stabilization of solitons.

OCIS Codes
(190.0190) Nonlinear optics : Nonlinear optics
(190.6135) Nonlinear optics : Spatial solitons

ToC Category:
Nonlinear Optics

History
Original Manuscript: June 11, 2012
Revised Manuscript: June 28, 2012
Manuscript Accepted: June 29, 2012
Published: July 10, 2012

Citation
Chunyan Li, Haidong Liu, and Liangwei Dong, "Multi-stable solitons in 𝒫𝒯-symmetric optical lattices," Opt. Express 20, 16823-16831 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-15-16823

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References

C. M. Bender and S. Boettcher, “Real spectra in non-Hermitian Hamiltonians having PT symmetry,” Phys. Rev. Lett.80, 5243–5246 (1998). [CrossRef]
C. M. Bender, D. C. Brody, and H. F. Jones, “Complex extension of quantum mechanics,” Phys. Rev. Lett. 89, 270401 (2002). [CrossRef]
C. M. Bender, G. V. Dunne, and P. N. Meisinger, “Complex periodic potentials with real band spectra,” Phys. Lett. A 252, 272–276 (1999). [CrossRef]
R. El-Ganainy, K. G. Makris, D. N. Christodoulides, and Z. H. Musslimani, “Theory of coupled optical PT-symmetric structures,” Opt. Lett. 32, 2632–2634 (2007). [CrossRef] [PubMed]
K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in 𝒫𝒯 symmetric optical lattices,” Phys. Rev. Lett. 100, 103904 (2008). [CrossRef] [PubMed]
A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of 𝒫𝒯 -symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103, 093902 (2009). [CrossRef] [PubMed]
K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “𝒫𝒯 -symmetric optical lattices,” Phys. Rev. A 81, 063807 (2010). [CrossRef]
Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodoulides, “Optical solitons in 𝒫𝒯 periodic potentials,” Phys. Rev. Lett. 100, 030402 (2008). [CrossRef] [PubMed]
K. Makris, R. El-Ganainy, D. Christodoulides, and Z. Musslimani, “PT-symmetric periodic optical potentials,” Int. J. of Theor. Phys. 50, 1019–1041 (2011). [CrossRef]
C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6, 192–195 (2010). [CrossRef]
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D. A. Zezyulin, Y. V. Kartashov, and V. V. Konotop, “Stability of solitons in PT-symmetric nonlinear potentials,” EPL-Europhys. Lett. 96, 64003 (2011). [CrossRef]
Y. He, X. Zhu, D. Mihalache, J. Liu, and Z. Chen, “Solitons in PT-symmetric optical lattices with spatially periodic modulation of nonlinearity,” Opt. Commun. 285, 3320–3324 (2012). [CrossRef]
Y. He, X. Zhu, D. Mihalache, J. Liu, and Z. Chen, “Lattice solitons in 𝒫𝒯 -symmetric mixed linear-nonlinear optical lattices,” Phys. Rev. A 85, 013831 (2012). [CrossRef]
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S. Hu, X. Ma, D. Lu, Y. Zheng, and W. Hu, “Defect solitons in parity-time-symmetric optical lattices with nonlocal nonlinearity,” Phys. Rev. A 85, 043826 (2012). [CrossRef]
Z. Shi, X. Jiang, X. Zhu, and H. Li, “Bright spatial solitons in defocusing Kerr media with 𝒫𝒯 -symmetric potentials,” Phys. Rev. A 84, 053855 (2011). [CrossRef]
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S. Nixon, L. Ge, and J. Yang, “Stability analysis for solitons in 𝒫𝒯 -symmetric optical lattices,” Phys. Rev. A8 5, 023822 (2012). [CrossRef]
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J. Wang, F. Ye, L. Dong, T. Cai, and Y.-P. Li, “Lattice solitons supported by competing cubic-quintic nonlinearity,” Phys. Lett. A 339, 74–82 (2005). [CrossRef]
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Abdullaev, F. K.
Aimez, V.
Alexander, T. J.
Bender, C. M.
Boettcher, S.
Brody, D. C.
Cai, T.
Chen, D.
Chen, L.
Chen, Z.
Christodoulides, D.
Christodoulides, D. N.
Dong, L.
Duchesne, D.
Dunne, G. V.
El-Ganainy, R.
Ge, L.
Guo, A.
Guo, Z.
He, Y.
Hu, S.
Hu, W.
Jiang, X.
Jones, H. F.
Kaplan, A. E.
Kartashov, Y. V.
Kip, D.
Kivshar, Y. S.
Konotop, V. V.
Li, H.
Li, L.
Li, R.
Li, Y.-P.
Liu, J.
Liu, S.
Lu, D.
Lu, K.
Lu, Z.
Ma, C.
Ma, X.
Makris, K.
Makris, K. G.
Meisinger, P. N.
Mihalache, D.
Morandotti, R.
Musslimani, Z.
Musslimani, Z. H.
Nixon, S.
Rüter, C. E.
Salamo, G. J.
Segev, M.
Shi, Z.
Siviloglou, G. A.
Volatier-Ravat, M.
Wang, H.
Wang, J.
Yang, J.
Yang, N.
Ye, F.
Zezyulin, D. A.
Zhang, Y.
Zhang, Z.-M.
Zheng, Y.
Zhou, K.
Zhu, X.

EPL-Europhys. Lett.

D. A. Zezyulin, Y. V. Kartashov, and V. V. Konotop, “Stability of solitons in PT-symmetric nonlinear potentials,” EPL-Europhys. Lett. 96, 64003 (2011). [CrossRef]

Int. J. of Theor. Phys.

K. Makris, R. El-Ganainy, D. Christodoulides, and Z. Musslimani, “PT-symmetric periodic optical potentials,” Int. J. of Theor. Phys. 50, 1019–1041 (2011). [CrossRef]

Nat. Phys.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity-time symmetry in optics,” Nat. Phys. 6, 192–195 (2010). [CrossRef]

Opt. Commun.

Y. He, X. Zhu, D. Mihalache, J. Liu, and Z. Chen, “Solitons in PT-symmetric optical lattices with spatially periodic modulation of nonlinearity,” Opt. Commun. 285, 3320–3324 (2012). [CrossRef]
S. Liu, C. Ma, Y. Zhang, and K. Lu, “Bragg gap solitons in symmetric lattices with competing nonlinearity,” Opt. Commun. 285, 1934–1939 (2012). [CrossRef]

Opt. Express

Opt. Lett.

Phys. Lett. A

C. M. Bender, G. V. Dunne, and P. N. Meisinger, “Complex periodic potentials with real band spectra,” Phys. Lett. A 252, 272–276 (1999). [CrossRef]
J. Wang, F. Ye, L. Dong, T. Cai, and Y.-P. Li, “Lattice solitons supported by competing cubic-quintic nonlinearity,” Phys. Lett. A 339, 74–82 (2005). [CrossRef]

Phys. Rev. A

J. Wang, J. Yang, T. J. Alexander, and Y. S. Kivshar, “Truncated-Bloch-wave solitons in optical lattices,” Phys. Rev. A 79, 043610 (2009). [CrossRef]
S. Nixon, L. Ge, and J. Yang, “Stability analysis for solitons in 𝒫𝒯 -symmetric optical lattices,” Phys. Rev. A8 5, 023822 (2012). [CrossRef]
Y. He, X. Zhu, D. Mihalache, J. Liu, and Z. Chen, “Lattice solitons in 𝒫𝒯 -symmetric mixed linear-nonlinear optical lattices,” Phys. Rev. A 85, 013831 (2012). [CrossRef]
S. Hu, X. Ma, D. Lu, Y. Zheng, and W. Hu, “Defect solitons in parity-time-symmetric optical lattices with nonlocal nonlinearity,” Phys. Rev. A 85, 043826 (2012). [CrossRef]
Z. Shi, X. Jiang, X. Zhu, and H. Li, “Bright spatial solitons in defocusing Kerr media with 𝒫𝒯 -symmetric potentials,” Phys. Rev. A 84, 053855 (2011). [CrossRef]
F. K. Abdullaev, Y. V. Kartashov, V. V. Konotop, and D. A. Zezyulin, “Solitons in 𝒫𝒯 -symmetric nonlinear lattices,” Phys. Rev. A 83, 041805 (2011). [CrossRef]
K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “𝒫𝒯 -symmetric optical lattices,” Phys. Rev. A 81, 063807 (2010). [CrossRef]

Phys. Rev. Lett.

Z. H. Musslimani, K. G. Makris, R. El-Ganainy, and D. N. Christodoulides, “Optical solitons in 𝒫𝒯 periodic potentials,” Phys. Rev. Lett. 100, 030402 (2008). [CrossRef] [PubMed]
K. G. Makris, R. El-Ganainy, D. N. Christodoulides, and Z. H. Musslimani, “Beam dynamics in 𝒫𝒯 symmetric optical lattices,” Phys. Rev. Lett. 100, 103904 (2008). [CrossRef] [PubMed]
A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, and D. N. Christodoulides, “Observation of 𝒫𝒯 -symmetry breaking in complex optical potentials,” Phys. Rev. Lett. 103, 093902 (2009). [CrossRef] [PubMed]
C. M. Bender and S. Boettcher, “Real spectra in non-Hermitian Hamiltonians having PT symmetry,” Phys. Rev. Lett.80, 5243–5246 (1998). [CrossRef]
C. M. Bender, D. C. Brody, and H. F. Jones, “Complex extension of quantum mechanics,” Phys. Rev. Lett. 89, 270401 (2002). [CrossRef]
A. E. Kaplan, “Bistable solitons,” Phys. Rev. Lett. 55, 1291–1294 (1985). [CrossRef] [PubMed]

Proc. Romanian Acad. A

L. Chen, R. Li, N. Yang, D. Chen, and L. Li, “Optical modes in PT-symmetric double-channel waveguides,” Proc. Romanian Acad. A 13, 46–54 (2012).

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