Abstract

We investigate the emission of solitons at a nonlinear longitudinal defect. We discuss the basic physics and introduce a novel approach to achieve complete nonlinear control of the process. Theoretical results are confirmed by numerical simulations.

© 2006 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. U. Peschel and F. Lederer, J. Opt. Soc. Am. B 19, 544 (2002).
    [CrossRef]
  2. B. A. Malomed, D. F. Parker, and N. F. Smyth, Phys. Rev. E 48, 1418 (1993).
    [CrossRef]
  3. F. K. Abdullaev, E. N. Tsoy, B. A. Malomed, and R. A. Kraenke, Phys. Rev. A 68, 053606 (2003).
    [CrossRef]
  4. H. Eisenberg, Y. Silberberg, R. Morandotti, and J. Aitchison, Phys. Rev. Lett. 85, 1863 (2000).
    [CrossRef] [PubMed]
  5. J. Cuevas, B. A. Malomed, and P. G. Kevrekidis, Phys. Rev. E 71, 66614 (2005).
    [CrossRef]
  6. M. Ablowitz and Z. Musslimani, Phys. Rev. Lett. 87, 254102 (2002).
    [CrossRef]
  7. S. Burtsev, D. Kaup, and B. A. Malomed, Phys. Rev. E 52, 4474 (1995).
    [CrossRef]
  8. Y. S. Kivshar, A. M. Kosevich, and O. A. Chubykalo, Phys. Lett. A 35, 125 (1987).
    [CrossRef]
  9. V. V. Konotop, D. Cai, M. Salerno, A. R. Bishop, and N. G. Jensen, Phys. Rev. E 53, 6476 (1996).
    [CrossRef]
  10. A. Trombettoni, A. Smerzi, and A. R. Bishop, Phys. Rev. E 67, 016607 (2003).
    [CrossRef]
  11. I. Bena, A. Saxena, and J. M. Sancho, Phys. Rev. E 66, 036617 (2002).
    [CrossRef]
  12. D. I. Pushkarov and R. D. Atanasov, Phys. Lett. A 149, 287 (1990).
    [CrossRef]
  13. G. Agrawal and P. Govind, Nonlinear Fiber Optics (Academic, 1995).
  14. J. J. Satsuma and N. Yajima, Prog. Theor. Phys. Suppl. 55, 284 (1974).
    [CrossRef]
  15. J. C. Bronski, Physica D 97, 376 (1996).
    [CrossRef]
  16. J. J. Sakurai, Modern Quantum Mechanics (Wiley, 1994).
  17. T. Poston and I. Stewart, Catastrophe Theory and Its Applications (Dover, 1978).
  18. K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, Appl. Phys. Lett. 79, 314 (2001).
    [CrossRef]
  19. L. F. Mollenauer, N. D. Vieira, and L. Szeto, Opt. Lett. 7, 414 (1982).
    [CrossRef] [PubMed]
  20. R. A. Betts, T. Tjugiarto, Y. L. Xue, and P. L. Chu, IEEE J. Quantum Electron. 27, 908 (1991).
    [CrossRef]
  21. I. Jánossy and L. Szabados, Phys. Rev. E 58, 4598 (1998).
    [CrossRef]
  22. F. Simoni, L. Lucchetti, D. E. Lucchetta, and O. Francescangeli, Opt. Express 9, 85 (2001).
    [CrossRef] [PubMed]
  23. A. Pasquazi, A. Alberucci, M. Peccianti, and G. Assanto, Appl. Phys. Lett. 87, 261104 (1995).
    [CrossRef]
  24. G. Assanto, M. Peccianti, and C. Conti, Opt. Photonics News 14, 44 (2003).
    [CrossRef]
  25. C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 92, 113902 (2004).
    [CrossRef] [PubMed]

2005

J. Cuevas, B. A. Malomed, and P. G. Kevrekidis, Phys. Rev. E 71, 66614 (2005).
[CrossRef]

2004

C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 92, 113902 (2004).
[CrossRef] [PubMed]

2003

G. Assanto, M. Peccianti, and C. Conti, Opt. Photonics News 14, 44 (2003).
[CrossRef]

F. K. Abdullaev, E. N. Tsoy, B. A. Malomed, and R. A. Kraenke, Phys. Rev. A 68, 053606 (2003).
[CrossRef]

A. Trombettoni, A. Smerzi, and A. R. Bishop, Phys. Rev. E 67, 016607 (2003).
[CrossRef]

2002

I. Bena, A. Saxena, and J. M. Sancho, Phys. Rev. E 66, 036617 (2002).
[CrossRef]

M. Ablowitz and Z. Musslimani, Phys. Rev. Lett. 87, 254102 (2002).
[CrossRef]

U. Peschel and F. Lederer, J. Opt. Soc. Am. B 19, 544 (2002).
[CrossRef]

2001

F. Simoni, L. Lucchetti, D. E. Lucchetta, and O. Francescangeli, Opt. Express 9, 85 (2001).
[CrossRef] [PubMed]

K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, Appl. Phys. Lett. 79, 314 (2001).
[CrossRef]

2000

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

1998

I. Jánossy and L. Szabados, Phys. Rev. E 58, 4598 (1998).
[CrossRef]

1996

V. V. Konotop, D. Cai, M. Salerno, A. R. Bishop, and N. G. Jensen, Phys. Rev. E 53, 6476 (1996).
[CrossRef]

J. C. Bronski, Physica D 97, 376 (1996).
[CrossRef]

1995

S. Burtsev, D. Kaup, and B. A. Malomed, Phys. Rev. E 52, 4474 (1995).
[CrossRef]

A. Pasquazi, A. Alberucci, M. Peccianti, and G. Assanto, Appl. Phys. Lett. 87, 261104 (1995).
[CrossRef]

1993

B. A. Malomed, D. F. Parker, and N. F. Smyth, Phys. Rev. E 48, 1418 (1993).
[CrossRef]

1991

R. A. Betts, T. Tjugiarto, Y. L. Xue, and P. L. Chu, IEEE J. Quantum Electron. 27, 908 (1991).
[CrossRef]

1990

D. I. Pushkarov and R. D. Atanasov, Phys. Lett. A 149, 287 (1990).
[CrossRef]

1987

Y. S. Kivshar, A. M. Kosevich, and O. A. Chubykalo, Phys. Lett. A 35, 125 (1987).
[CrossRef]

1982

1974

J. J. Satsuma and N. Yajima, Prog. Theor. Phys. Suppl. 55, 284 (1974).
[CrossRef]

Abdullaev, F. K.

F. K. Abdullaev, E. N. Tsoy, B. A. Malomed, and R. A. Kraenke, Phys. Rev. A 68, 053606 (2003).
[CrossRef]

Ablowitz, M.

M. Ablowitz and Z. Musslimani, Phys. Rev. Lett. 87, 254102 (2002).
[CrossRef]

Agrawal, G.

G. Agrawal and P. Govind, Nonlinear Fiber Optics (Academic, 1995).

Aitchison, J.

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

Alberucci, A.

A. Pasquazi, A. Alberucci, M. Peccianti, and G. Assanto, Appl. Phys. Lett. 87, 261104 (1995).
[CrossRef]

Assanto, G.

C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 92, 113902 (2004).
[CrossRef] [PubMed]

G. Assanto, M. Peccianti, and C. Conti, Opt. Photonics News 14, 44 (2003).
[CrossRef]

K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, Appl. Phys. Lett. 79, 314 (2001).
[CrossRef]

A. Pasquazi, A. Alberucci, M. Peccianti, and G. Assanto, Appl. Phys. Lett. 87, 261104 (1995).
[CrossRef]

Atanasov, R. D.

D. I. Pushkarov and R. D. Atanasov, Phys. Lett. A 149, 287 (1990).
[CrossRef]

Bena, I.

I. Bena, A. Saxena, and J. M. Sancho, Phys. Rev. E 66, 036617 (2002).
[CrossRef]

Betts, R. A.

R. A. Betts, T. Tjugiarto, Y. L. Xue, and P. L. Chu, IEEE J. Quantum Electron. 27, 908 (1991).
[CrossRef]

Bishop, A. R.

A. Trombettoni, A. Smerzi, and A. R. Bishop, Phys. Rev. E 67, 016607 (2003).
[CrossRef]

V. V. Konotop, D. Cai, M. Salerno, A. R. Bishop, and N. G. Jensen, Phys. Rev. E 53, 6476 (1996).
[CrossRef]

Bronski, J. C.

J. C. Bronski, Physica D 97, 376 (1996).
[CrossRef]

Burtsev, S.

S. Burtsev, D. Kaup, and B. A. Malomed, Phys. Rev. E 52, 4474 (1995).
[CrossRef]

Cai, D.

V. V. Konotop, D. Cai, M. Salerno, A. R. Bishop, and N. G. Jensen, Phys. Rev. E 53, 6476 (1996).
[CrossRef]

Chu, P. L.

R. A. Betts, T. Tjugiarto, Y. L. Xue, and P. L. Chu, IEEE J. Quantum Electron. 27, 908 (1991).
[CrossRef]

Chubykalo, O. A.

Y. S. Kivshar, A. M. Kosevich, and O. A. Chubykalo, Phys. Lett. A 35, 125 (1987).
[CrossRef]

Conti, C.

C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 92, 113902 (2004).
[CrossRef] [PubMed]

G. Assanto, M. Peccianti, and C. Conti, Opt. Photonics News 14, 44 (2003).
[CrossRef]

Cuevas, J.

J. Cuevas, B. A. Malomed, and P. G. Kevrekidis, Phys. Rev. E 71, 66614 (2005).
[CrossRef]

Eisenberg, H.

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

Fejer, M. M.

K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, Appl. Phys. Lett. 79, 314 (2001).
[CrossRef]

Francescangeli, O.

Gallo, K.

K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, Appl. Phys. Lett. 79, 314 (2001).
[CrossRef]

Govind, P.

G. Agrawal and P. Govind, Nonlinear Fiber Optics (Academic, 1995).

Jánossy, I.

I. Jánossy and L. Szabados, Phys. Rev. E 58, 4598 (1998).
[CrossRef]

Jensen, N. G.

V. V. Konotop, D. Cai, M. Salerno, A. R. Bishop, and N. G. Jensen, Phys. Rev. E 53, 6476 (1996).
[CrossRef]

Kaup, D.

S. Burtsev, D. Kaup, and B. A. Malomed, Phys. Rev. E 52, 4474 (1995).
[CrossRef]

Kevrekidis, P. G.

J. Cuevas, B. A. Malomed, and P. G. Kevrekidis, Phys. Rev. E 71, 66614 (2005).
[CrossRef]

Kivshar, Y. S.

Y. S. Kivshar, A. M. Kosevich, and O. A. Chubykalo, Phys. Lett. A 35, 125 (1987).
[CrossRef]

Konotop, V. V.

V. V. Konotop, D. Cai, M. Salerno, A. R. Bishop, and N. G. Jensen, Phys. Rev. E 53, 6476 (1996).
[CrossRef]

Kosevich, A. M.

Y. S. Kivshar, A. M. Kosevich, and O. A. Chubykalo, Phys. Lett. A 35, 125 (1987).
[CrossRef]

Kraenke, R. A.

F. K. Abdullaev, E. N. Tsoy, B. A. Malomed, and R. A. Kraenke, Phys. Rev. A 68, 053606 (2003).
[CrossRef]

Lederer, F.

Lucchetta, D. E.

Lucchetti, L.

Malomed, B. A.

J. Cuevas, B. A. Malomed, and P. G. Kevrekidis, Phys. Rev. E 71, 66614 (2005).
[CrossRef]

F. K. Abdullaev, E. N. Tsoy, B. A. Malomed, and R. A. Kraenke, Phys. Rev. A 68, 053606 (2003).
[CrossRef]

S. Burtsev, D. Kaup, and B. A. Malomed, Phys. Rev. E 52, 4474 (1995).
[CrossRef]

B. A. Malomed, D. F. Parker, and N. F. Smyth, Phys. Rev. E 48, 1418 (1993).
[CrossRef]

Mollenauer, L. F.

Morandotti, R.

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

Musslimani, Z.

M. Ablowitz and Z. Musslimani, Phys. Rev. Lett. 87, 254102 (2002).
[CrossRef]

Parameswaran, K. R.

K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, Appl. Phys. Lett. 79, 314 (2001).
[CrossRef]

Parker, D. F.

B. A. Malomed, D. F. Parker, and N. F. Smyth, Phys. Rev. E 48, 1418 (1993).
[CrossRef]

Pasquazi, A.

A. Pasquazi, A. Alberucci, M. Peccianti, and G. Assanto, Appl. Phys. Lett. 87, 261104 (1995).
[CrossRef]

Peccianti, M.

C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 92, 113902 (2004).
[CrossRef] [PubMed]

G. Assanto, M. Peccianti, and C. Conti, Opt. Photonics News 14, 44 (2003).
[CrossRef]

A. Pasquazi, A. Alberucci, M. Peccianti, and G. Assanto, Appl. Phys. Lett. 87, 261104 (1995).
[CrossRef]

Peschel, U.

Poston, T.

T. Poston and I. Stewart, Catastrophe Theory and Its Applications (Dover, 1978).

Pushkarov, D. I.

D. I. Pushkarov and R. D. Atanasov, Phys. Lett. A 149, 287 (1990).
[CrossRef]

Sakurai, J. J.

J. J. Sakurai, Modern Quantum Mechanics (Wiley, 1994).

Salerno, M.

V. V. Konotop, D. Cai, M. Salerno, A. R. Bishop, and N. G. Jensen, Phys. Rev. E 53, 6476 (1996).
[CrossRef]

Sancho, J. M.

I. Bena, A. Saxena, and J. M. Sancho, Phys. Rev. E 66, 036617 (2002).
[CrossRef]

Satsuma, J. J.

J. J. Satsuma and N. Yajima, Prog. Theor. Phys. Suppl. 55, 284 (1974).
[CrossRef]

Saxena, A.

I. Bena, A. Saxena, and J. M. Sancho, Phys. Rev. E 66, 036617 (2002).
[CrossRef]

Silberberg, Y.

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

Simoni, F.

Smerzi, A.

A. Trombettoni, A. Smerzi, and A. R. Bishop, Phys. Rev. E 67, 016607 (2003).
[CrossRef]

Smyth, N. F.

B. A. Malomed, D. F. Parker, and N. F. Smyth, Phys. Rev. E 48, 1418 (1993).
[CrossRef]

Stewart, I.

T. Poston and I. Stewart, Catastrophe Theory and Its Applications (Dover, 1978).

Szabados, L.

I. Jánossy and L. Szabados, Phys. Rev. E 58, 4598 (1998).
[CrossRef]

Szeto, L.

Tjugiarto, T.

R. A. Betts, T. Tjugiarto, Y. L. Xue, and P. L. Chu, IEEE J. Quantum Electron. 27, 908 (1991).
[CrossRef]

Trombettoni, A.

A. Trombettoni, A. Smerzi, and A. R. Bishop, Phys. Rev. E 67, 016607 (2003).
[CrossRef]

Tsoy, E. N.

F. K. Abdullaev, E. N. Tsoy, B. A. Malomed, and R. A. Kraenke, Phys. Rev. A 68, 053606 (2003).
[CrossRef]

Vieira, N. D.

Xue, Y. L.

R. A. Betts, T. Tjugiarto, Y. L. Xue, and P. L. Chu, IEEE J. Quantum Electron. 27, 908 (1991).
[CrossRef]

Yajima, N.

J. J. Satsuma and N. Yajima, Prog. Theor. Phys. Suppl. 55, 284 (1974).
[CrossRef]

Appl. Phys. Lett.

K. Gallo, G. Assanto, K. R. Parameswaran, and M. M. Fejer, Appl. Phys. Lett. 79, 314 (2001).
[CrossRef]

A. Pasquazi, A. Alberucci, M. Peccianti, and G. Assanto, Appl. Phys. Lett. 87, 261104 (1995).
[CrossRef]

IEEE J. Quantum Electron.

R. A. Betts, T. Tjugiarto, Y. L. Xue, and P. L. Chu, IEEE J. Quantum Electron. 27, 908 (1991).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Express

Opt. Lett.

Opt. Photonics News

G. Assanto, M. Peccianti, and C. Conti, Opt. Photonics News 14, 44 (2003).
[CrossRef]

Phys. Lett. A

D. I. Pushkarov and R. D. Atanasov, Phys. Lett. A 149, 287 (1990).
[CrossRef]

Y. S. Kivshar, A. M. Kosevich, and O. A. Chubykalo, Phys. Lett. A 35, 125 (1987).
[CrossRef]

Phys. Rev. A

F. K. Abdullaev, E. N. Tsoy, B. A. Malomed, and R. A. Kraenke, Phys. Rev. A 68, 053606 (2003).
[CrossRef]

Phys. Rev. E

J. Cuevas, B. A. Malomed, and P. G. Kevrekidis, Phys. Rev. E 71, 66614 (2005).
[CrossRef]

V. V. Konotop, D. Cai, M. Salerno, A. R. Bishop, and N. G. Jensen, Phys. Rev. E 53, 6476 (1996).
[CrossRef]

A. Trombettoni, A. Smerzi, and A. R. Bishop, Phys. Rev. E 67, 016607 (2003).
[CrossRef]

I. Bena, A. Saxena, and J. M. Sancho, Phys. Rev. E 66, 036617 (2002).
[CrossRef]

B. A. Malomed, D. F. Parker, and N. F. Smyth, Phys. Rev. E 48, 1418 (1993).
[CrossRef]

S. Burtsev, D. Kaup, and B. A. Malomed, Phys. Rev. E 52, 4474 (1995).
[CrossRef]

I. Jánossy and L. Szabados, Phys. Rev. E 58, 4598 (1998).
[CrossRef]

Phys. Rev. Lett.

M. Ablowitz and Z. Musslimani, Phys. Rev. Lett. 87, 254102 (2002).
[CrossRef]

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

C. Conti, M. Peccianti, and G. Assanto, Phys. Rev. Lett. 92, 113902 (2004).
[CrossRef] [PubMed]

Physica D

J. C. Bronski, Physica D 97, 376 (1996).
[CrossRef]

Prog. Theor. Phys. Suppl.

J. J. Satsuma and N. Yajima, Prog. Theor. Phys. Suppl. 55, 284 (1974).
[CrossRef]

Other

J. J. Sakurai, Modern Quantum Mechanics (Wiley, 1994).

T. Poston and I. Stewart, Catastrophe Theory and Its Applications (Dover, 1978).

G. Agrawal and P. Govind, Nonlinear Fiber Optics (Academic, 1995).

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 (2)

Fig. 1
Fig. 1

Effective potential distribution V eff for (a) δ = 0.25 and (b) δ = 0.65 ; corresponding light evolution ( Z 0 = 0 , n = 2 , A = 1 ) for (c) δ = 0.25 and (d) δ = 0.65 .

Fig. 2
Fig. 2

(a) Calculated real part of the ground-state eigenvalue ζ (pseudocolor plot) and predicted bifurcation (dotted curve) versus defect position Z 0 and strength δ; (b) transverse intensity distributions after a distance Z = L = 9 Z T + Z 0 versus input power P ( Z 0 = 0.6 , δ = 0.18 , d = 0.08 ) (pseudocolor plot). Corresponding to the vertical dotted line an oscillation peak crosses Z 0 .

Equations (4)

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

i ψ Z + 2 ψ X 2 + 2 ( 1 + R ) ψ 2 ψ = 0 ,
i v X + Uv ζ σ 3 v = 0 , U = [ 0 q q * 0 ] ,
4 ϵ 4 [ 2 s 1 Y 2 2 s 2 Y 2 ] = [ α β η η α + β ] [ s 1 ( Y ) s 2 ( Y ) ] ,
w ± : { Y 1 = ± γ ϵ 2 2 T i 2 ( 2 P 2 + Q 1 λ 1 ϵ 2 ) γ σ = 2 P 0 γ 2 [ γ λ 1 + ( 2 P 2 ϵ 2 + Q 1 λ 1 ) 2 ] γ γ ϵ 2 } .

Metrics