Abstract

We examine the existence and stability of discrete spatial solitons in coupled nonlinear lasing cavities (waveguide resonators), addressing the case of active defocusing media, where the gain exceeds damping in the low-amplitude limit. A new family of stable localized structures is found: these are bright and gray cavity solitons representing the connections between homogeneous and inhomogeneous states. Solitons of this type can be controlled by discrete diffraction and are stable when the bistability of homogenous states is absent.

© 2012 Optical Society of America

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  1. T. Ackemann, W. J. Firth, and G.-L. Oppo, Advances in Atomic Molecular and Optical PhysicsE. Arimondo, P. R. Berman, and C. C. Lin, eds. (Elesevier, 2009), Vol. 57, pp. 323–421.
  2. N. Akhmediev and A. Ankiewicz, eds., Dissipative Solitons, Vol. 661 of Lecture Notes in Physics (Springer, 2005).
  3. F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1 (2008).
    [CrossRef]
  4. U. Peschel, O. Egorov, and F. Lederer, Opt. Lett. 29, 1909 (2004).
    [CrossRef]
  5. O. Egorov, F. Lederer, and K. Staliunas, Opt. Lett. 32, 2106 (2007).
    [CrossRef]
  6. A. V. Yulin, A. R. Champneys, and D. V. Skryabin, Phys. Rev. A 78, 011804(R) (2008).
    [CrossRef]
  7. A. V. Yulin and A. R. Champneys, SIAM J. Appl. Dyn. Syst. 9, 391 (2010).
    [CrossRef]
  8. O. Egorov, U. Peschel, and F. Lederer, Phys. Rev. E 71, 056612 (2005).
    [CrossRef]
  9. O. A. Egorov, F. Lederer, and Y. S. Kivshar, Opt. Express 15, 4149 (2007).
    [CrossRef]
  10. K. Staliunas, O. Egorov, Y. S. Kivshar, and F. Lederer, Phys. Rev. Lett. 101, 153903 (2008).
    [CrossRef]
  11. Al. S. Kiselev, An. S. Kiselev, and N. N. Rozanov, Opt. Spectrosc. 105, 547 (2008).
    [CrossRef]

2010 (1)

A. V. Yulin and A. R. Champneys, SIAM J. Appl. Dyn. Syst. 9, 391 (2010).
[CrossRef]

2008 (4)

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1 (2008).
[CrossRef]

K. Staliunas, O. Egorov, Y. S. Kivshar, and F. Lederer, Phys. Rev. Lett. 101, 153903 (2008).
[CrossRef]

Al. S. Kiselev, An. S. Kiselev, and N. N. Rozanov, Opt. Spectrosc. 105, 547 (2008).
[CrossRef]

A. V. Yulin, A. R. Champneys, and D. V. Skryabin, Phys. Rev. A 78, 011804(R) (2008).
[CrossRef]

2007 (2)

2005 (1)

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

2004 (1)

Ackemann, T.

T. Ackemann, W. J. Firth, and G.-L. Oppo, Advances in Atomic Molecular and Optical PhysicsE. Arimondo, P. R. Berman, and C. C. Lin, eds. (Elesevier, 2009), Vol. 57, pp. 323–421.

Assanto, G.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1 (2008).
[CrossRef]

Champneys, A. R.

A. V. Yulin and A. R. Champneys, SIAM J. Appl. Dyn. Syst. 9, 391 (2010).
[CrossRef]

A. V. Yulin, A. R. Champneys, and D. V. Skryabin, Phys. Rev. A 78, 011804(R) (2008).
[CrossRef]

Christodoulides, D. N.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1 (2008).
[CrossRef]

Egorov, O.

K. Staliunas, O. Egorov, Y. S. Kivshar, and F. Lederer, Phys. Rev. Lett. 101, 153903 (2008).
[CrossRef]

O. Egorov, F. Lederer, and K. Staliunas, Opt. Lett. 32, 2106 (2007).
[CrossRef]

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

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

Egorov, O. A.

Firth, W. J.

T. Ackemann, W. J. Firth, and G.-L. Oppo, Advances in Atomic Molecular and Optical PhysicsE. Arimondo, P. R. Berman, and C. C. Lin, eds. (Elesevier, 2009), Vol. 57, pp. 323–421.

Kiselev, Al. S.

Al. S. Kiselev, An. S. Kiselev, and N. N. Rozanov, Opt. Spectrosc. 105, 547 (2008).
[CrossRef]

Kiselev, An. S.

Al. S. Kiselev, An. S. Kiselev, and N. N. Rozanov, Opt. Spectrosc. 105, 547 (2008).
[CrossRef]

Kivshar, Y. S.

K. Staliunas, O. Egorov, Y. S. Kivshar, and F. Lederer, Phys. Rev. Lett. 101, 153903 (2008).
[CrossRef]

O. A. Egorov, F. Lederer, and Y. S. Kivshar, Opt. Express 15, 4149 (2007).
[CrossRef]

Lederer, F.

K. Staliunas, O. Egorov, Y. S. Kivshar, and F. Lederer, Phys. Rev. Lett. 101, 153903 (2008).
[CrossRef]

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1 (2008).
[CrossRef]

O. A. Egorov, F. Lederer, and Y. S. Kivshar, Opt. Express 15, 4149 (2007).
[CrossRef]

O. Egorov, F. Lederer, and K. Staliunas, Opt. Lett. 32, 2106 (2007).
[CrossRef]

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

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

Oppo, G.-L.

T. Ackemann, W. J. Firth, and G.-L. Oppo, Advances in Atomic Molecular and Optical PhysicsE. Arimondo, P. R. Berman, and C. C. Lin, eds. (Elesevier, 2009), Vol. 57, pp. 323–421.

Peschel, U.

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

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

Rozanov, N. N.

Al. S. Kiselev, An. S. Kiselev, and N. N. Rozanov, Opt. Spectrosc. 105, 547 (2008).
[CrossRef]

Segev, M.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1 (2008).
[CrossRef]

Silberberg, Y.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1 (2008).
[CrossRef]

Skryabin, D. V.

A. V. Yulin, A. R. Champneys, and D. V. Skryabin, Phys. Rev. A 78, 011804(R) (2008).
[CrossRef]

Staliunas, K.

K. Staliunas, O. Egorov, Y. S. Kivshar, and F. Lederer, Phys. Rev. Lett. 101, 153903 (2008).
[CrossRef]

O. Egorov, F. Lederer, and K. Staliunas, Opt. Lett. 32, 2106 (2007).
[CrossRef]

Stegeman, G. I.

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1 (2008).
[CrossRef]

Yulin, A. V.

A. V. Yulin and A. R. Champneys, SIAM J. Appl. Dyn. Syst. 9, 391 (2010).
[CrossRef]

A. V. Yulin, A. R. Champneys, and D. V. Skryabin, Phys. Rev. A 78, 011804(R) (2008).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Opt. Spectrosc. (1)

Al. S. Kiselev, An. S. Kiselev, and N. N. Rozanov, Opt. Spectrosc. 105, 547 (2008).
[CrossRef]

Phys. Rep. (1)

F. Lederer, G. I. Stegeman, D. N. Christodoulides, G. Assanto, M. Segev, and Y. Silberberg, Phys. Rep. 463, 1 (2008).
[CrossRef]

Phys. Rev. A (1)

A. V. Yulin, A. R. Champneys, and D. V. Skryabin, Phys. Rev. A 78, 011804(R) (2008).
[CrossRef]

Phys. Rev. E (1)

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

Phys. Rev. Lett. (1)

K. Staliunas, O. Egorov, Y. S. Kivshar, and F. Lederer, Phys. Rev. Lett. 101, 153903 (2008).
[CrossRef]

SIAM J. Appl. Dyn. Syst. (1)

A. V. Yulin and A. R. Champneys, SIAM J. Appl. Dyn. Syst. 9, 391 (2010).
[CrossRef]

Other (2)

T. Ackemann, W. J. Firth, and G.-L. Oppo, Advances in Atomic Molecular and Optical PhysicsE. Arimondo, P. R. Berman, and C. C. Lin, eds. (Elesevier, 2009), Vol. 57, pp. 323–421.

N. Akhmediev and A. Ankiewicz, eds., Dissipative Solitons, Vol. 661 of Lecture Notes in Physics (Springer, 2005).

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Figures (3)

Fig. 1.
Fig. 1.

Response curves for (a) homogeneous (H) and (b) two-site periodic (I) solutions, with stable regions highlighted by thick solid lines. (a)  P ( | A | ) for H-solutions, with stable lower (H1) and higher (H2) states, (b)  P ( | A max | ) and P ( | A min | ) for the I-solution; the direction of “evolution” from the curve coalescence points (marked by ||) is identified with arrows. Regions of H-H and H-I bistability are marked on the P axes; the active region ( F ( | A | ) > 0 ) is highlighted on the | A | axes.

Fig. 2.
Fig. 2.

Left pane: snaking diagram for bright DCS corresponding to H1-I-H1 connection (stable regions are highlighted). The inset shows a magnified part of the snake. Right panes show particular field distributions for DCS: the top pane shows a stable DCS corresponding to the H1-H2-H1 connection ( P = 4.3 ), and the two lower panes show the distributions for the stable DCS corresponding to H1-I-H1. The latter correspond to the points marked 1 and 2 on the snake.

Fig. 3.
Fig. 3.

Snaking diagram P ( | A min | ) for the grey DCS corresponding to the H2-I-H2 connection. The inset shows the particular distribution of stable DCS referring to the point marked as 3.

Equations (1)

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( i d d t + Δ + α | A n | 2 ) A n + + C ( A n + 1 + A n 1 2 A n ) i F ( A n ) = P ,

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