Abstract

A dissipative soliton in an amplifier with a Bragg grating is numerically investigated by direct simulation of Maxwell–Bloch equations. The result of the simulation indicates that a solitary wave can exist in such a medium. However, the pulse shape of the dissipative soliton is asymmetrical because of the gain saturation effect. This gain saturation effect results from the high power of the ultrashort dissipative soliton. The influence of amplifier gain on the solitary wave is also investigated.

© 2003 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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2003 (1)

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed. (Artech House, Norwood, Mass., 2003).

2002 (1)

2001 (1)

S. Trillo and W. Torruellas, Spatial Solitons (Springer-Verlag, Berlin, 2001).
[CrossRef]

1998 (1)

A. E. Kozhekin, G. Kurizki, and B. Malomed, Phys. Rev. Lett. 81, 3647 (1998).
[CrossRef]

1997 (1)

1996 (3)

V. S. Grigoryan, Opt. Lett. 21, 1882 (1996).
[CrossRef] [PubMed]

L. W. Liou and G. P. Agrawal, Opt. Commun. 124, 500 (1996).
[CrossRef]

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, Phys. Rev. Lett. 76, 1627 (1996).
[CrossRef] [PubMed]

1995 (2)

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, New York, 1995).

R. W. Ziolkowski, J. M. Arnold, and D. M. Gogny, Phys. Rev. A 52, 3082 (1995).
[CrossRef] [PubMed]

1994 (2)

C. M. de Sterke and J. E. Sipe, in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1994), Vol. XXXIII, pp. 203–260.
[CrossRef]

S. Chi, C. W. Chang, and S. Wen, Opt. Commun. 106, 193 (1994).
[CrossRef]

1992 (2)

T. Kitagawa, K. Hattori, K. Shuto, M. Yasu, M. Kobayashi, and M. Horiguchi, Electron. Lett. 28, 1818 (1992).
[CrossRef]

J. Shmulovich, A. Wong, Y. H. Wong, P. C. Becker, A. J. Bruce, and R. Adar, Electron. Lett. 28, 1181 (1992).
[CrossRef]

1991 (1)

1989 (2)

P. A. Bélanger, L. Gagnon, and C. Paré, Opt. Lett. 14, 943 (1989).
[CrossRef]

G. P. Agrawal and N. A. Olsson, IEEE J. Quantum Electron. 25, 2297 (1989).
[CrossRef]

Adar, R.

J. Shmulovich, A. Wong, Y. H. Wong, P. C. Becker, A. J. Bruce, and R. Adar, Electron. Lett. 28, 1181 (1992).
[CrossRef]

Agrawal, G. P.

L. W. Liou and G. P. Agrawal, Opt. Commun. 124, 500 (1996).
[CrossRef]

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, New York, 1995).

G. P. Agrawal and N. A. Olsson, IEEE J. Quantum Electron. 25, 2297 (1989).
[CrossRef]

Arnold, J. M.

R. W. Ziolkowski, J. M. Arnold, and D. M. Gogny, Phys. Rev. A 52, 3082 (1995).
[CrossRef] [PubMed]

Becker, P. C.

J. Shmulovich, A. Wong, Y. H. Wong, P. C. Becker, A. J. Bruce, and R. Adar, Electron. Lett. 28, 1181 (1992).
[CrossRef]

Bélanger, P. A.

Bruce, A. J.

J. Shmulovich, A. Wong, Y. H. Wong, P. C. Becker, A. J. Bruce, and R. Adar, Electron. Lett. 28, 1181 (1992).
[CrossRef]

Chang, C. W.

S. Chi, C. W. Chang, and S. Wen, Opt. Commun. 106, 193 (1994).
[CrossRef]

Chi, S.

S. Chi, C. W. Chang, and S. Wen, Opt. Commun. 106, 193 (1994).
[CrossRef]

de Sterke, C. M.

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, Phys. Rev. Lett. 76, 1627 (1996).
[CrossRef] [PubMed]

C. M. de Sterke and J. E. Sipe, in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1994), Vol. XXXIII, pp. 203–260.
[CrossRef]

Eggleton, B. J.

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, Phys. Rev. Lett. 76, 1627 (1996).
[CrossRef] [PubMed]

Gagnon, L.

Gogny, D. M.

R. W. Ziolkowski, J. M. Arnold, and D. M. Gogny, Phys. Rev. A 52, 3082 (1995).
[CrossRef] [PubMed]

Golles, M.

Grigoryan, V. S.

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed. (Artech House, Norwood, Mass., 2003).

Hattori, K.

T. Kitagawa, K. Hattori, K. Shuto, M. Yasu, M. Kobayashi, and M. Horiguchi, Electron. Lett. 28, 1818 (1992).
[CrossRef]

Horiguchi, M.

T. Kitagawa, K. Hattori, K. Shuto, M. Yasu, M. Kobayashi, and M. Horiguchi, Electron. Lett. 28, 1818 (1992).
[CrossRef]

Kitagawa, T.

T. Kitagawa, K. Hattori, K. Shuto, M. Yasu, M. Kobayashi, and M. Horiguchi, Electron. Lett. 28, 1818 (1992).
[CrossRef]

Kivshar, Y. S.

Kobayashi, M.

T. Kitagawa, K. Hattori, K. Shuto, M. Yasu, M. Kobayashi, and M. Horiguchi, Electron. Lett. 28, 1818 (1992).
[CrossRef]

Kozhekin, A. E.

A. E. Kozhekin, G. Kurizki, and B. Malomed, Phys. Rev. Lett. 81, 3647 (1998).
[CrossRef]

Krug, P. A.

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, Phys. Rev. Lett. 76, 1627 (1996).
[CrossRef] [PubMed]

Kurizki, G.

A. E. Kozhekin, G. Kurizki, and B. Malomed, Phys. Rev. Lett. 81, 3647 (1998).
[CrossRef]

Lederer, F.

Liou, L. W.

L. W. Liou and G. P. Agrawal, Opt. Commun. 124, 500 (1996).
[CrossRef]

Malomed, B.

A. E. Kozhekin, G. Kurizki, and B. Malomed, Phys. Rev. Lett. 81, 3647 (1998).
[CrossRef]

Muradyan, T. S.

Olsson, N. A.

G. P. Agrawal and N. A. Olsson, IEEE J. Quantum Electron. 25, 2297 (1989).
[CrossRef]

Paré, C.

Shmulovich, J.

J. Shmulovich, A. Wong, Y. H. Wong, P. C. Becker, A. J. Bruce, and R. Adar, Electron. Lett. 28, 1181 (1992).
[CrossRef]

Shuto, K.

T. Kitagawa, K. Hattori, K. Shuto, M. Yasu, M. Kobayashi, and M. Horiguchi, Electron. Lett. 28, 1818 (1992).
[CrossRef]

Sipe, J. E.

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, Phys. Rev. Lett. 76, 1627 (1996).
[CrossRef] [PubMed]

C. M. de Sterke and J. E. Sipe, in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1994), Vol. XXXIII, pp. 203–260.
[CrossRef]

Slusher, R. E.

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, Phys. Rev. Lett. 76, 1627 (1996).
[CrossRef] [PubMed]

Sukhorukov, A. A.

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed. (Artech House, Norwood, Mass., 2003).

Torruellas, W.

S. Trillo and W. Torruellas, Spatial Solitons (Springer-Verlag, Berlin, 2001).
[CrossRef]

Trillo, S.

S. Trillo and W. Torruellas, Spatial Solitons (Springer-Verlag, Berlin, 2001).
[CrossRef]

Uzunov, I. M.

Wen, S.

S. Chi, C. W. Chang, and S. Wen, Opt. Commun. 106, 193 (1994).
[CrossRef]

Wong, A.

J. Shmulovich, A. Wong, Y. H. Wong, P. C. Becker, A. J. Bruce, and R. Adar, Electron. Lett. 28, 1181 (1992).
[CrossRef]

Wong, Y. H.

J. Shmulovich, A. Wong, Y. H. Wong, P. C. Becker, A. J. Bruce, and R. Adar, Electron. Lett. 28, 1181 (1992).
[CrossRef]

Yasu, M.

T. Kitagawa, K. Hattori, K. Shuto, M. Yasu, M. Kobayashi, and M. Horiguchi, Electron. Lett. 28, 1818 (1992).
[CrossRef]

Ziolkowski, R. W.

R. W. Ziolkowski, J. M. Arnold, and D. M. Gogny, Phys. Rev. A 52, 3082 (1995).
[CrossRef] [PubMed]

Electron. Lett. (2)

T. Kitagawa, K. Hattori, K. Shuto, M. Yasu, M. Kobayashi, and M. Horiguchi, Electron. Lett. 28, 1818 (1992).
[CrossRef]

J. Shmulovich, A. Wong, Y. H. Wong, P. C. Becker, A. J. Bruce, and R. Adar, Electron. Lett. 28, 1181 (1992).
[CrossRef]

IEEE J. Quantum Electron. (1)

G. P. Agrawal and N. A. Olsson, IEEE J. Quantum Electron. 25, 2297 (1989).
[CrossRef]

J. Opt. Soc. Am. B (2)

Opt. Commun. (2)

L. W. Liou and G. P. Agrawal, Opt. Commun. 124, 500 (1996).
[CrossRef]

S. Chi, C. W. Chang, and S. Wen, Opt. Commun. 106, 193 (1994).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. A (1)

R. W. Ziolkowski, J. M. Arnold, and D. M. Gogny, Phys. Rev. A 52, 3082 (1995).
[CrossRef] [PubMed]

Phys. Rev. Lett. (2)

A. E. Kozhekin, G. Kurizki, and B. Malomed, Phys. Rev. Lett. 81, 3647 (1998).
[CrossRef]

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, Phys. Rev. Lett. 76, 1627 (1996).
[CrossRef] [PubMed]

Other (4)

C. M. de Sterke and J. E. Sipe, in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1994), Vol. XXXIII, pp. 203–260.
[CrossRef]

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed. (Artech House, Norwood, Mass., 2003).

G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, New York, 1995).

S. Trillo and W. Torruellas, Spatial Solitons (Springer-Verlag, Berlin, 2001).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Propagation over 15 ps of a dissipative soliton in an amplifier with a Bragg grating.

Fig. 2
Fig. 2

(a) Stable pulse shape of a dissipative soliton and (b) difference in population of the active medium. Inset, enlarged plot of the cloudy black zone.

Fig. 3
Fig. 3

Evolution of the peak power of the dissipative soliton.

Fig. 4
Fig. 4

(a) Peak power and (b) pulse width of a dissipative soliton versus the small-signal gain coefficient.

Equations (3)

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

Hyz,tt=1μ0Exz,tz-σ0rzHyz,t,  Dxz,tt=Hyz,tz-σEzz,t,  Dxz,t=0rzExz,t+PxNLz,t+PxRz,t,
tu=-1T2u+ωrv,  tv=-ωru-1T2v+2 µwEx,  tw=-2 µExv-1T1w-w0,
Gpz,t=ηNDμwz,t,

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