Abstract

We describe what we believe to be novel types of discrete cavity solitons in nonlinear waveguide arrays that are driven by an external holding beam. We demonstrate that a holding beam with a definite inclination drives the system in a subdiffractive regime and allows the formation of stable discrete cavity solitons. We predict the existence of both bright and dark moving midband discrete cavity solitons for an identical set of system parameters for both focusing and defocusing Kerr nonlinearities.

© 2007 Optical Society of America

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References

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    [CrossRef]
  2. L. A. Lugiato and R. Lefever, Phys. Rev. Lett. 58, 2209 (1987).
    [CrossRef] [PubMed]
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    [CrossRef]
  5. D. Michaelis, U. Peschel, and F. Lederer, Phys. Rev. A 56, R3366 (1997).
    [CrossRef]
  6. M. Brambilla, L. A. Lugiato, F. Prati, L. Spinelli, and W. J. Firth, Phys. Rev. Lett. 79, 2042 (1997).
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  7. V. B. Taranenko, G. Slekys, and C. O. Weiss, Chaos 13, 777 (2003).
    [CrossRef] [PubMed]
  8. S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödl, M. Miller, and R. Jäger, Nature 419, 699 (2002).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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2007 (1)

2005 (4)

O. Egorov, U. Peschel, and F. Lederer, Phys. Rev. E 71, 056612 (2005).
[CrossRef]

O. Egorov, U. Peschel, and F. Lederer, Phys. Rev. E 72, 066603 (2005).
[CrossRef]

K. Maruno, A. Ankiewicz, and N. Akhmediev, Phys. Lett. A 347, 231 (2005).
[CrossRef]

X. Hachair, L. Furfaro, J. Javaloyes, M. Giudici, S. Balle, J. R. Tredicce, G. Tissoni, L. A. Lugiato, M. Brambilla, and T. Maggipinto, Phys. Rev. A 72, 013815 (2005).
[CrossRef]

2004 (2)

U. Peschel, O. Egorov, and F. Lederer, Opt. Lett. 29, 1909 (2004).
[CrossRef] [PubMed]

R. Iwanow, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, Phys. Rev. Lett. 93, 113902 (2004).
[CrossRef] [PubMed]

2003 (4)

N. K. Efremidis and D. N. Christodoulides, Phys. Rev. E 67, 026606 (2003).
[CrossRef]

K. Staliunas, Phys. Rev. Lett. 91, 053901 (2003).
[CrossRef] [PubMed]

U. Peschel, D. Michaelis, and C. O. Weiss, IEEE J. Quantum Electron. 39, 51 (2003).
[CrossRef]

V. B. Taranenko, G. Slekys, and C. O. Weiss, Chaos 13, 777 (2003).
[CrossRef] [PubMed]

2002 (2)

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödl, M. Miller, and R. Jäger, Nature 419, 699 (2002).
[CrossRef] [PubMed]

T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer, and F. Lederer, Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

2001 (1)

S. Fedorov, D. Michaelis, U. Peschel, C. Etrich, D. V. Skryabin, N. Rosanov, and F. Lederer, Phys. Rev. E 64, 036610 (2001).
[CrossRef]

2000 (1)

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 85, 1863 (2000).
[CrossRef] [PubMed]

1997 (2)

D. Michaelis, U. Peschel, and F. Lederer, Phys. Rev. A 56, R3366 (1997).
[CrossRef]

M. Brambilla, L. A. Lugiato, F. Prati, L. Spinelli, and W. J. Firth, Phys. Rev. Lett. 79, 2042 (1997).
[CrossRef]

1987 (2)

Chaos (1)

V. B. Taranenko, G. Slekys, and C. O. Weiss, Chaos 13, 777 (2003).
[CrossRef] [PubMed]

IEEE J. Quantum Electron. (1)

U. Peschel, D. Michaelis, and C. O. Weiss, IEEE J. Quantum Electron. 39, 51 (2003).
[CrossRef]

Nature (1)

S. Barland, J. R. Tredicce, M. Brambilla, L. A. Lugiato, S. Balle, M. Giudici, T. Maggipinto, L. Spinelli, G. Tissoni, T. Knödl, M. Miller, and R. Jäger, Nature 419, 699 (2002).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (2)

Phys. Lett. A (1)

K. Maruno, A. Ankiewicz, and N. Akhmediev, Phys. Lett. A 347, 231 (2005).
[CrossRef]

Phys. Rev. A (2)

X. Hachair, L. Furfaro, J. Javaloyes, M. Giudici, S. Balle, J. R. Tredicce, G. Tissoni, L. A. Lugiato, M. Brambilla, and T. Maggipinto, Phys. Rev. A 72, 013815 (2005).
[CrossRef]

D. Michaelis, U. Peschel, and F. Lederer, Phys. Rev. A 56, R3366 (1997).
[CrossRef]

Phys. Rev. E (4)

S. Fedorov, D. Michaelis, U. Peschel, C. Etrich, D. V. Skryabin, N. Rosanov, and F. Lederer, Phys. Rev. E 64, 036610 (2001).
[CrossRef]

O. Egorov, U. Peschel, and F. Lederer, Phys. Rev. E 72, 066603 (2005).
[CrossRef]

N. K. Efremidis and D. N. Christodoulides, Phys. Rev. E 67, 026606 (2003).
[CrossRef]

O. Egorov, U. Peschel, and F. Lederer, Phys. Rev. E 71, 056612 (2005).
[CrossRef]

Phys. Rev. Lett. (6)

R. Iwanow, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, Phys. Rev. Lett. 93, 113902 (2004).
[CrossRef] [PubMed]

K. Staliunas, Phys. Rev. Lett. 91, 053901 (2003).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 85, 1863 (2000).
[CrossRef] [PubMed]

T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer, and F. Lederer, Phys. Rev. Lett. 88, 093901 (2002).
[CrossRef] [PubMed]

M. Brambilla, L. A. Lugiato, F. Prati, L. Spinelli, and W. J. Firth, Phys. Rev. Lett. 79, 2042 (1997).
[CrossRef]

L. A. Lugiato and R. Lefever, Phys. Rev. Lett. 58, 2209 (1987).
[CrossRef] [PubMed]

Other (2)

N. N. Rosanov, Spatial Hysteresis and Optical Patterns (Springer, 2002).

N.Akhmediev and A.Ankiewicz, eds., Lecture Notes in Physics (Springer, 2005).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Profiles of (a) bright fundamental and (b) higher order, as well as (c) dark fundamental and (d) higher order DMCSs calculated both in the quasi-continuous (full curves) and discrete model (dark diamonds). Parameters: E 0 = 1.95 , Δ = 3 , and C = 1 .

Fig. 2
Fig. 2

(a) Branches of the bright and dark DMCSs depending on the holding beam amplitude ( Δ = 3 ) (solid curves represent stable solutions, dashed curves represent unstable solutions); (b) instability domain of PW (dashed area), bright and dark DMCSs existence domains (filled areas) in Δ b parameter space ( C = 1 ) .

Fig. 3
Fig. 3

(a) Width (expressed in waveguides) of the central peak of fundamental bright DMCS versus the coupling constant C. (b) Velocity (waveguides per photon lifetime) of DMCS versus the coupling constant C. Solid and dashed curves apply to the discrete (1) and the quasi-continuous (2) models, respectively.

Equations (2)

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i u n T + C ( u n 1 + u n + 1 2 u n ) + ( i + Δ ) u n + γ u n 2 u n = E 0 exp ( i q n ) .
i u T + i D ( 1 ) u x + D ( 2 ) 2 u x 2 + i D ( 3 ) 3 u x 3 + D ( 4 ) 4 u x 4 + ( i + Δ ) u + γ u 2 u = E 0 ,

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