Abstract

The existence of a type of soliton in periodic Kerr media constructed as a superposition of noninteracting gap solitons of different kinds (bright, dark, and periodic) is first demonstrated. The periodic modulation of the nonlinearity is used to suppress the cross-phase modulation between component solitons to allow the superimposed beam to propagate for long distances.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. Y. V. Kartashov, B. A. Malomed, and L. Torner, Rev. Mod. Phys. 83, 247 (2011).
    [CrossRef]
  2. M. Salerno, V. V. Konotop, and Yu. V. Bludov, Phys. Rev. Lett. 101, 030405 (2008).
    [CrossRef] [PubMed]
  3. Yu. V. Bludov, V. V. Konotop, and M. Salerno, Phys. Rev. A 80, 023623 (2009).
    [CrossRef]
  4. Yu. V. Bludov, V. V. Konotop, and M. Salerno, Europhys. Lett. 87, 20004 (2009).
    [CrossRef]
  5. H. Sakaguchi and B. A. Malomed, Phys. Rev. A 81, 013624 (2010).
    [CrossRef]

2011

Y. V. Kartashov, B. A. Malomed, and L. Torner, Rev. Mod. Phys. 83, 247 (2011).
[CrossRef]

2010

H. Sakaguchi and B. A. Malomed, Phys. Rev. A 81, 013624 (2010).
[CrossRef]

2009

Yu. V. Bludov, V. V. Konotop, and M. Salerno, Phys. Rev. A 80, 023623 (2009).
[CrossRef]

Yu. V. Bludov, V. V. Konotop, and M. Salerno, Europhys. Lett. 87, 20004 (2009).
[CrossRef]

2008

M. Salerno, V. V. Konotop, and Yu. V. Bludov, Phys. Rev. Lett. 101, 030405 (2008).
[CrossRef] [PubMed]

Bludov, Yu. V.

Yu. V. Bludov, V. V. Konotop, and M. Salerno, Phys. Rev. A 80, 023623 (2009).
[CrossRef]

Yu. V. Bludov, V. V. Konotop, and M. Salerno, Europhys. Lett. 87, 20004 (2009).
[CrossRef]

M. Salerno, V. V. Konotop, and Yu. V. Bludov, Phys. Rev. Lett. 101, 030405 (2008).
[CrossRef] [PubMed]

Kartashov, Y. V.

Y. V. Kartashov, B. A. Malomed, and L. Torner, Rev. Mod. Phys. 83, 247 (2011).
[CrossRef]

Konotop, V. V.

Yu. V. Bludov, V. V. Konotop, and M. Salerno, Europhys. Lett. 87, 20004 (2009).
[CrossRef]

Yu. V. Bludov, V. V. Konotop, and M. Salerno, Phys. Rev. A 80, 023623 (2009).
[CrossRef]

M. Salerno, V. V. Konotop, and Yu. V. Bludov, Phys. Rev. Lett. 101, 030405 (2008).
[CrossRef] [PubMed]

Malomed, B. A.

Y. V. Kartashov, B. A. Malomed, and L. Torner, Rev. Mod. Phys. 83, 247 (2011).
[CrossRef]

H. Sakaguchi and B. A. Malomed, Phys. Rev. A 81, 013624 (2010).
[CrossRef]

Sakaguchi, H.

H. Sakaguchi and B. A. Malomed, Phys. Rev. A 81, 013624 (2010).
[CrossRef]

Salerno, M.

Yu. V. Bludov, V. V. Konotop, and M. Salerno, Phys. Rev. A 80, 023623 (2009).
[CrossRef]

Yu. V. Bludov, V. V. Konotop, and M. Salerno, Europhys. Lett. 87, 20004 (2009).
[CrossRef]

M. Salerno, V. V. Konotop, and Yu. V. Bludov, Phys. Rev. Lett. 101, 030405 (2008).
[CrossRef] [PubMed]

Torner, L.

Y. V. Kartashov, B. A. Malomed, and L. Torner, Rev. Mod. Phys. 83, 247 (2011).
[CrossRef]

Europhys. Lett.

Yu. V. Bludov, V. V. Konotop, and M. Salerno, Europhys. Lett. 87, 20004 (2009).
[CrossRef]

Phys. Rev. A

H. Sakaguchi and B. A. Malomed, Phys. Rev. A 81, 013624 (2010).
[CrossRef]

Yu. V. Bludov, V. V. Konotop, and M. Salerno, Phys. Rev. A 80, 023623 (2009).
[CrossRef]

Phys. Rev. Lett.

M. Salerno, V. V. Konotop, and Yu. V. Bludov, Phys. Rev. Lett. 101, 030405 (2008).
[CrossRef] [PubMed]

Rev. Mod. Phys.

Y. V. Kartashov, B. A. Malomed, and L. Torner, Rev. Mod. Phys. 83, 247 (2011).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

(a) Families of the modes bifurcating from the lower, U 1 , and upper, U 2 , edges of the first gap, b [ 2.1659 , 0.7332 ] (the edges coincide with the panel boundaries); (b)  U 1 versus U 2 for the solitons fulfilling Eq. (4); (c)–(f) intensity distributions | q ( x , z ) | 2 and (g)–(j) spectra | Q ( b , k ) | 2 at distance z 0 = 1000 of input beams [Eq. (3)] consisting of two superimposed solitons with parameters (c), (g)  U 1 = 0.32 ( b 1 = 2.15 ), U 2 = 0.143 ( b 2 = 0.71 ); (d), (h)  U 1 = 0.645 ( b 1 = 2.1 ), U 2 = 0.33 ( b 2 = 0.6 ); (e), (i)  U 1 = 2.77 ( b 1 = 0.732 ), U 2 = 1.7 ( b 2 = 0.938 ); (f), (j)  U 1 = 2.77 ( b 1 = 0.732 ), U 2 = 5.28 ( b 2 = 1.0 ). In (c), (d), (g), and (h), solitons are near edges of the first gap while in panels (e), (f), (i), (j) are near edges of the first band. Other parameters are σ = 1 , V = 3 , (a), (b), (c), (d), (g), (h)  G = 3.05 , (e), (f), (i), (j)  G = 1.282 .

Fig. 2
Fig. 2

Propagation of two superimposed gap solitons with centers shifted at the input by (a), (c)  Δ x = 4 π or by (b), (d)  Δ x = 10 π . Soliton parameters are the same as in (a), (b) Fig. 1c or (c), (d) Fig. 1e.

Fig. 3
Fig. 3

(a) Even periodic background with the energy flux per period U 2 = 0 π w 2 2 ( x ) d x = 0.103 and b 2 = 0.76 , (b) superimposed with an odd soliton having U 1 = 0.132 and b 1 = 2.16 for the parameters σ = 1 , V = 3 , G = 6 ; (d), (e) superposition of two dark solitons bordering edges of the gap b [ 2.1659 , 0.7332 ] : (d) even dark soliton with b 2 = 0.78 and (e) odd dark soliton with b 1 = 2.18 for V = 3 , σ = 1 , G = 2.95 ; (c), (f) spectrum | Q ( b , k ) | 2 relative to superpositions of the waves in (a), (b) and in (d), (e), respectively, both taken at z 0 = 1000 .

Equations (4)

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

i q z = q x x + V ( x ) q + G ( x ) | q | 2 q .
D l χ l < 0 , D u χ u < 0 , χ = 0 ,
q ( x , z ) = w 1 ( x ) e i b 1 z + w 2 ( x ) e i b 2 z + i Θ .
w 1 w 2 d x = 0 , and G ( x ) w 1 2 w 2 2 d x = 0.

Metrics