Abstract

We reveal theoretically that defect superlattice solitons (DSSs) exist at the defect site in one-dimensional optical superlattices with focusing saturable nonlinearity. Solitons with some unique properties exist in superlattices with defects. For a positive defect, solitons exist at the semi-infinite gap, and solitons are stable at low power but unstable at high power. For a negative defect, most solitons exist in the first finite gap and can propagate stably. In particular, it is found that the solitons can be divided into two equal parts upon propagation in a certain regime of parameters.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |

  1. D. N. Christodoulides, F. Lederer, and Y. Silberberg, "Discretizing light behavior in linear and nonlinear waveguide lattices," Nature 424, 817-823 (2003).
    [CrossRef] [PubMed]
  2. D. K. Campbell, S. Flach, and Y. S. Kivshar, "Localizing energy through nonlinearity and discreteness," Phys. Today 57, 43-49 (2004).
    [CrossRef]
  3. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Rotary solitons in Bessel optical lattices," Phys. Rev. Lett. 93, 093904 (2004).
    [CrossRef] [PubMed]
  4. Y. J. He and H. Z. Wang, "(1+1)-dimensional dipole solitons supported by optical lattice," Opt. Express 14, 9832-9837 (2006) http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-21-9832>
    [CrossRef] [PubMed]
  5. P. J. Y. Louis, E. A. Ostrovskaya, and Y. S. Kivshar, "Dispersion control for matter waves and gap solitons in optical superlattices," Phys. Rev. A 71, 023612 (2005).
    [CrossRef]
  6. M. A. Porter, P.G. Kevrekidis, R. Carretero-González, D. J. Frantzeskakis, "Dynamics and manipulation of matter-wave solitons in optical superlattices," Phys. Lett. A 352, 210-215 (2006).
    [CrossRef]
  7. N. G. R. Broderick and C. M. de Sterke, "Theory of grating superstructures," Phys. Rev. E 55, 3634-3646 (2006).
    [CrossRef]
  8. K. Yagasaki I. M. Merhasin, B. A. Malomed, T. Wagenknecht, and A. R. Champneys, "Gap solitons in Bragg gratings with a harmonic superlattice," Europhys. Lett. 74, 1006-1012 (2006).
    [CrossRef]
  9. J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices," Nature 422, 147-150 (2003).
    [CrossRef] [PubMed]
  10. Z. Chen and K. McCarthy, "Spatial soliton pixels from partially incoherent light," Opt. Lett. 27, 2019-2021 (2002).
    [CrossRef]
  11. F. Fedele, J. Yang, and Z. Chen, "Defect modes in one-dimensional photonic lattices," Opt. Lett. 30, 1506-1508 (2005).
    [CrossRef] [PubMed]
  12. A. A. Sukhorukov and Y. S. Kivshar, "Nonlinear localized waves in a periodic medium," Phys. Rev. Lett. 87, 083901 (2001).
    [CrossRef] [PubMed]
  13. J. Yang and Z. Chen, "Defect solitons in photonic lattices," Phys. Rev. E 73, 026609 (2006).
    [CrossRef]
  14. H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, "Discrete solitons and soliton-induced dislocations in partially coherent photonic lattices," Phys. Rev. Lett. 92, 123902 (2004).
    [CrossRef] [PubMed]
  15. B. A. Malomed, T. Mayteevarunyoo, E. A. Ostrovskaya, and Y. S. Kivshar, "Coupled-mode theory for spatial gap solitons in optically induced lattices," Phys. Rev. E 71, 056616 (2005).
    [CrossRef]
  16. I. Makasyuk, Z. Chen, and J. Yang, "Observation of light confinement by defects in optically-induced photonic lattices," in Nonlinear Guided Waves and Their Applications, Technical Digest (CD) (Optical Society of America, 2005), paper TuC8.
  17. Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Surface gap solitons," Phys. Rev. Lett. 96, 073901 (2006).
    [CrossRef] [PubMed]
  18. W. H. Chen, Y. J. He, and H. Z. Wang, "Surface defect gap solitons," Opt. Express 14, 11271-11276 (2006).
    [CrossRef] [PubMed]
  19. Y. J. He, W. H. Chen, H. Z. Wang, and B. A. Malomed, "Surface superlattice gap solitons," Opt. Lett. 32, 1390-1392 (2007).
    [CrossRef] [PubMed]
  20. W. H. Chen, Y. J. He, and H. Z. Wang, "Surface defect superlattice solitons," J. Opt. Soc. Am. B 24, 2584-2588 (2007)
    [CrossRef]

2007

2006

M. A. Porter, P.G. Kevrekidis, R. Carretero-González, D. J. Frantzeskakis, "Dynamics and manipulation of matter-wave solitons in optical superlattices," Phys. Lett. A 352, 210-215 (2006).
[CrossRef]

N. G. R. Broderick and C. M. de Sterke, "Theory of grating superstructures," Phys. Rev. E 55, 3634-3646 (2006).
[CrossRef]

K. Yagasaki I. M. Merhasin, B. A. Malomed, T. Wagenknecht, and A. R. Champneys, "Gap solitons in Bragg gratings with a harmonic superlattice," Europhys. Lett. 74, 1006-1012 (2006).
[CrossRef]

J. Yang and Z. Chen, "Defect solitons in photonic lattices," Phys. Rev. E 73, 026609 (2006).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Surface gap solitons," Phys. Rev. Lett. 96, 073901 (2006).
[CrossRef] [PubMed]

Y. J. He and H. Z. Wang, "(1+1)-dimensional dipole solitons supported by optical lattice," Opt. Express 14, 9832-9837 (2006) http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-21-9832>
[CrossRef] [PubMed]

W. H. Chen, Y. J. He, and H. Z. Wang, "Surface defect gap solitons," Opt. Express 14, 11271-11276 (2006).
[CrossRef] [PubMed]

2005

B. A. Malomed, T. Mayteevarunyoo, E. A. Ostrovskaya, and Y. S. Kivshar, "Coupled-mode theory for spatial gap solitons in optically induced lattices," Phys. Rev. E 71, 056616 (2005).
[CrossRef]

F. Fedele, J. Yang, and Z. Chen, "Defect modes in one-dimensional photonic lattices," Opt. Lett. 30, 1506-1508 (2005).
[CrossRef] [PubMed]

P. J. Y. Louis, E. A. Ostrovskaya, and Y. S. Kivshar, "Dispersion control for matter waves and gap solitons in optical superlattices," Phys. Rev. A 71, 023612 (2005).
[CrossRef]

2004

D. K. Campbell, S. Flach, and Y. S. Kivshar, "Localizing energy through nonlinearity and discreteness," Phys. Today 57, 43-49 (2004).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Rotary solitons in Bessel optical lattices," Phys. Rev. Lett. 93, 093904 (2004).
[CrossRef] [PubMed]

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, "Discrete solitons and soliton-induced dislocations in partially coherent photonic lattices," Phys. Rev. Lett. 92, 123902 (2004).
[CrossRef] [PubMed]

2003

D. N. Christodoulides, F. Lederer, and Y. Silberberg, "Discretizing light behavior in linear and nonlinear waveguide lattices," Nature 424, 817-823 (2003).
[CrossRef] [PubMed]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices," Nature 422, 147-150 (2003).
[CrossRef] [PubMed]

2002

2001

A. A. Sukhorukov and Y. S. Kivshar, "Nonlinear localized waves in a periodic medium," Phys. Rev. Lett. 87, 083901 (2001).
[CrossRef] [PubMed]

Europhys. Lett.

K. Yagasaki I. M. Merhasin, B. A. Malomed, T. Wagenknecht, and A. R. Champneys, "Gap solitons in Bragg gratings with a harmonic superlattice," Europhys. Lett. 74, 1006-1012 (2006).
[CrossRef]

J. Opt. Soc. Am. B

Nature

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices," Nature 422, 147-150 (2003).
[CrossRef] [PubMed]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, "Discretizing light behavior in linear and nonlinear waveguide lattices," Nature 424, 817-823 (2003).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

Phys. Lett. A

M. A. Porter, P.G. Kevrekidis, R. Carretero-González, D. J. Frantzeskakis, "Dynamics and manipulation of matter-wave solitons in optical superlattices," Phys. Lett. A 352, 210-215 (2006).
[CrossRef]

Phys. Rev. A

P. J. Y. Louis, E. A. Ostrovskaya, and Y. S. Kivshar, "Dispersion control for matter waves and gap solitons in optical superlattices," Phys. Rev. A 71, 023612 (2005).
[CrossRef]

Phys. Rev. E

N. G. R. Broderick and C. M. de Sterke, "Theory of grating superstructures," Phys. Rev. E 55, 3634-3646 (2006).
[CrossRef]

J. Yang and Z. Chen, "Defect solitons in photonic lattices," Phys. Rev. E 73, 026609 (2006).
[CrossRef]

B. A. Malomed, T. Mayteevarunyoo, E. A. Ostrovskaya, and Y. S. Kivshar, "Coupled-mode theory for spatial gap solitons in optically induced lattices," Phys. Rev. E 71, 056616 (2005).
[CrossRef]

Phys. Rev. Lett.

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, "Discrete solitons and soliton-induced dislocations in partially coherent photonic lattices," Phys. Rev. Lett. 92, 123902 (2004).
[CrossRef] [PubMed]

A. A. Sukhorukov and Y. S. Kivshar, "Nonlinear localized waves in a periodic medium," Phys. Rev. Lett. 87, 083901 (2001).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Rotary solitons in Bessel optical lattices," Phys. Rev. Lett. 93, 093904 (2004).
[CrossRef] [PubMed]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Surface gap solitons," Phys. Rev. Lett. 96, 073901 (2006).
[CrossRef] [PubMed]

Phys. Today

D. K. Campbell, S. Flach, and Y. S. Kivshar, "Localizing energy through nonlinearity and discreteness," Phys. Today 57, 43-49 (2004).
[CrossRef]

Other

I. Makasyuk, Z. Chen, and J. Yang, "Observation of light confinement by defects in optically-induced photonic lattices," in Nonlinear Guided Waves and Their Applications, Technical Digest (CD) (Optical Society of America, 2005), paper TuC8.

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 (6)

Fig. 1.
Fig. 1.

Lattice intensity profile with I0=3 and ε 2=0.3: (a) ε 2=0.45, (b) ε 2= -0.45, and (c) ε 2=0; (d) applied dc field parameter E0 versus the propagation constant μ. Gray regions are Bloch bands.

Fig. 2.
Fig. 2.

(a) Power versus propagation constant (blue regions are Bloch bands) in the semi-infinite gap for ε 2=0.45; the solid curve is stable and the dashed curve is unstable. (b) Perturbation growth rate Re(δ). Stable DSSs at (c) A: μ=-2.35, (d) B: μ=-1.8, and unstable DSSs at (e) C: μ=-1.5. (f)-(h) DSSs propagate corresponding to (c)-(e), respectively.

Fig. 3.
Fig. 3.

(a) Power versus propagation constant (blue regions are Bloch bands) in the semi-infinite gap for ε 2=0; solid curve is stable except for near point A; near point A and the dashed curve are unstable. (b) Perturbation growth rate Re(δ) Stable DSSs at (c) B: μ= -2.4, (d) C: μ= -1.9, and unstable DSSs at (e) A: μ= -2.55. (d)-(f) DSSs propagate corresponding to (f)-(h), respectively.

Fig. 4.
Fig. 4.

Power versus propagation constant (blue regions are Bloch bands) in the first finite gap for ε 2=-0.45. Stable DSSs at (b) B: μ= -3.31, (c) A: μ= -3.85.

Fig. 5.
Fig. 5.

Stable (gray) and unstable (white) domains of DSSs in the semi-infinite gap (a) and the first finite gap (b), respectively.

Fig. 6.
Fig. 6.

For ε 1=0.1 and ε 2=-0.2, DSSs with different propagation constants (a) μ=-2.67 and (b) μ=-2.7. (c) and (d) DSSs propagate corresponding to (a) and (b), respectively.

Tables (1)

Tables Icon

Table 1. Regions of DSSs dividing into two parts along propagation direction.

Equations (6)

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

i q z + 2 q x 2 E 0 q [ 1 + I L ( x ) + q 2 ] = 0 .
I L = { I 0 { ε 1 sin 2 ( x + π 2 ) + ( 1 ε 1 ) sin 2 [ 2 ( x + π 2 ) ] } , x π 2 and x π 2 , I 0 ( c + ε 2 ) sin 2 ( x + π 2 ) , π 2 x π 2 .
μf = d 2 f dx 2 + 2 ikdf dx k 2 f E 0 f [ 1 + I L ( x ) ] .
d 2 f dx 2 E 0 f [ 1 + I L ( x ) + f 2 ] μf = 0 .
δh = 2 e x 2 + μe + E 0 e ( 1 + I L + f 2 )
δe = 2 h x 2 μh E 0 h [ 1 ( 1 + I L + f 2 ) 2 f 2 ( 1 + I L + f 2 ) 2 ] .

Metrics