Abstract

We develop a perturbation theory for the evolution of solitary waves in quadratic nonconservative nonlinear media. The expressions derived for the solitons’ amplitude and width permit us to estimate straightforwardly the damping–amplification rate of an arbitrary soliton of the unperturbed system. The analytical results obtained agree well with numerical experiments.

© 1999 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum Electron. 28, 1691 (1996); Yu. S. Kivshar, Opt. Quantum Electron. 30, 571 (1998).
    [CrossRef]
  2. W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
    [CrossRef] [PubMed]
  3. R. Schiek, Y. Baek, and G. I. Stegeman, Phys. Rev. E 53, 1138 (1996).
    [CrossRef]
  4. V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals (Springer-Verlag, Berlin, 1991).
    [CrossRef]
  5. R. Schiek, Y. Baek, and G. I. Stegeman, J. Opt. Soc. Am. B 15, 2255 (1998).
    [CrossRef]
  6. L. Torner, Opt. Commun. 154, 59 (1998).
    [CrossRef]
  7. M. Dinand and W. Sohler, IEEE J. Quantum Electron. 30, 1267 (1994).
    [CrossRef]
  8. C. B. Clausen, O. Bang, Yu. S. Kivshar, and P. L. Christiansen, Opt. Lett. 22, 271 (1997).
    [CrossRef] [PubMed]
  9. F. Kh. Abdullaev, S. Darmanyan, A. Kobyakov, E. Schmidt, and F. Lederer, “Spatial solitons in random quadratic media,” Opt. Commun. (to be published).
  10. S. A. Akhmanov and R. V. Khokhlov, Problems of Nonlinear Optics (Gordon & Breach, New York, 1972).
  11. K. Hayata and M. Koshiba, J. Opt. Soc. Am. B 12, 2288 (1995).
    [CrossRef]
  12. L. Torner, D. Mihalache, D. Mazilu, and N. Akhmediev, Opt. Lett. 20, 2183 (1995).
    [CrossRef]
  13. B. A. Malomed, D. Anderson, A. Bernston, M. Florjanczyk, and M. Lisak, Pure Appl. Opt. 5, 941 (1996).
    [CrossRef]

1998 (2)

1997 (1)

1996 (3)

B. A. Malomed, D. Anderson, A. Bernston, M. Florjanczyk, and M. Lisak, Pure Appl. Opt. 5, 941 (1996).
[CrossRef]

G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum Electron. 28, 1691 (1996); Yu. S. Kivshar, Opt. Quantum Electron. 30, 571 (1998).
[CrossRef]

R. Schiek, Y. Baek, and G. I. Stegeman, Phys. Rev. E 53, 1138 (1996).
[CrossRef]

1995 (3)

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

K. Hayata and M. Koshiba, J. Opt. Soc. Am. B 12, 2288 (1995).
[CrossRef]

L. Torner, D. Mihalache, D. Mazilu, and N. Akhmediev, Opt. Lett. 20, 2183 (1995).
[CrossRef]

1994 (1)

M. Dinand and W. Sohler, IEEE J. Quantum Electron. 30, 1267 (1994).
[CrossRef]

Abdullaev, F. Kh.

F. Kh. Abdullaev, S. Darmanyan, A. Kobyakov, E. Schmidt, and F. Lederer, “Spatial solitons in random quadratic media,” Opt. Commun. (to be published).

Akhmanov, S. A.

S. A. Akhmanov and R. V. Khokhlov, Problems of Nonlinear Optics (Gordon & Breach, New York, 1972).

Akhmediev, N.

Anderson, D.

B. A. Malomed, D. Anderson, A. Bernston, M. Florjanczyk, and M. Lisak, Pure Appl. Opt. 5, 941 (1996).
[CrossRef]

Baek, Y.

R. Schiek, Y. Baek, and G. I. Stegeman, J. Opt. Soc. Am. B 15, 2255 (1998).
[CrossRef]

R. Schiek, Y. Baek, and G. I. Stegeman, Phys. Rev. E 53, 1138 (1996).
[CrossRef]

Bang, O.

Bernston, A.

B. A. Malomed, D. Anderson, A. Bernston, M. Florjanczyk, and M. Lisak, Pure Appl. Opt. 5, 941 (1996).
[CrossRef]

Christiansen, P. L.

Clausen, C. B.

Darmanyan, S.

F. Kh. Abdullaev, S. Darmanyan, A. Kobyakov, E. Schmidt, and F. Lederer, “Spatial solitons in random quadratic media,” Opt. Commun. (to be published).

Dinand, M.

M. Dinand and W. Sohler, IEEE J. Quantum Electron. 30, 1267 (1994).
[CrossRef]

Dmitriev, V. G.

V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals (Springer-Verlag, Berlin, 1991).
[CrossRef]

Florjanczyk, M.

B. A. Malomed, D. Anderson, A. Bernston, M. Florjanczyk, and M. Lisak, Pure Appl. Opt. 5, 941 (1996).
[CrossRef]

Gurzadyan, G. G.

V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals (Springer-Verlag, Berlin, 1991).
[CrossRef]

Hagan, D. J.

G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum Electron. 28, 1691 (1996); Yu. S. Kivshar, Opt. Quantum Electron. 30, 571 (1998).
[CrossRef]

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

Hayata, K.

Khokhlov, R. V.

S. A. Akhmanov and R. V. Khokhlov, Problems of Nonlinear Optics (Gordon & Breach, New York, 1972).

Kivshar, Yu. S.

Kobyakov, A.

F. Kh. Abdullaev, S. Darmanyan, A. Kobyakov, E. Schmidt, and F. Lederer, “Spatial solitons in random quadratic media,” Opt. Commun. (to be published).

Koshiba, M.

Lederer, F.

F. Kh. Abdullaev, S. Darmanyan, A. Kobyakov, E. Schmidt, and F. Lederer, “Spatial solitons in random quadratic media,” Opt. Commun. (to be published).

Lisak, M.

B. A. Malomed, D. Anderson, A. Bernston, M. Florjanczyk, and M. Lisak, Pure Appl. Opt. 5, 941 (1996).
[CrossRef]

Malomed, B. A.

B. A. Malomed, D. Anderson, A. Bernston, M. Florjanczyk, and M. Lisak, Pure Appl. Opt. 5, 941 (1996).
[CrossRef]

Mazilu, D.

Menyuk, C. R.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

Mihalache, D.

Nikogosyan, D. N.

V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals (Springer-Verlag, Berlin, 1991).
[CrossRef]

Schiek, R.

R. Schiek, Y. Baek, and G. I. Stegeman, J. Opt. Soc. Am. B 15, 2255 (1998).
[CrossRef]

R. Schiek, Y. Baek, and G. I. Stegeman, Phys. Rev. E 53, 1138 (1996).
[CrossRef]

Schmidt, E.

F. Kh. Abdullaev, S. Darmanyan, A. Kobyakov, E. Schmidt, and F. Lederer, “Spatial solitons in random quadratic media,” Opt. Commun. (to be published).

Sohler, W.

M. Dinand and W. Sohler, IEEE J. Quantum Electron. 30, 1267 (1994).
[CrossRef]

Stegeman, G. I.

R. Schiek, Y. Baek, and G. I. Stegeman, J. Opt. Soc. Am. B 15, 2255 (1998).
[CrossRef]

R. Schiek, Y. Baek, and G. I. Stegeman, Phys. Rev. E 53, 1138 (1996).
[CrossRef]

G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum Electron. 28, 1691 (1996); Yu. S. Kivshar, Opt. Quantum Electron. 30, 571 (1998).
[CrossRef]

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

Torner, L.

L. Torner, Opt. Commun. 154, 59 (1998).
[CrossRef]

G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum Electron. 28, 1691 (1996); Yu. S. Kivshar, Opt. Quantum Electron. 30, 571 (1998).
[CrossRef]

L. Torner, D. Mihalache, D. Mazilu, and N. Akhmediev, Opt. Lett. 20, 2183 (1995).
[CrossRef]

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

Torruellas, W. E.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

Van Stryland, E. W.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

Wang, Z.

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

IEEE J. Quantum Electron. (1)

M. Dinand and W. Sohler, IEEE J. Quantum Electron. 30, 1267 (1994).
[CrossRef]

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

Opt. Commun. (1)

L. Torner, Opt. Commun. 154, 59 (1998).
[CrossRef]

Opt. Lett. (2)

Opt. Quantum Electron. (1)

G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum Electron. 28, 1691 (1996); Yu. S. Kivshar, Opt. Quantum Electron. 30, 571 (1998).
[CrossRef]

Phys. Rev. E (1)

R. Schiek, Y. Baek, and G. I. Stegeman, Phys. Rev. E 53, 1138 (1996).
[CrossRef]

Phys. Rev. Lett. (1)

W. E. Torruellas, Z. Wang, D. J. Hagan, E. W. Van Stryland, G. I. Stegeman, L. Torner, and C. R. Menyuk, Phys. Rev. Lett. 74, 5036 (1995).
[CrossRef] [PubMed]

Pure Appl. Opt. (1)

B. A. Malomed, D. Anderson, A. Bernston, M. Florjanczyk, and M. Lisak, Pure Appl. Opt. 5, 941 (1996).
[CrossRef]

Other (3)

V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals (Springer-Verlag, Berlin, 1991).
[CrossRef]

F. Kh. Abdullaev, S. Darmanyan, A. Kobyakov, E. Schmidt, and F. Lederer, “Spatial solitons in random quadratic media,” Opt. Commun. (to be published).

S. A. Akhmanov and R. V. Khokhlov, Problems of Nonlinear Optics (Gordon & Breach, New York, 1972).

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 (3)

Fig. 1
Fig. 1

Squared peak amplitudes and widths of the QS [Eqs. (2)] with q=-3 versus propagation length: solid curves, numerical integration of Eqs. (1); long-dashed curves, numerical integration of Eqs. (4) and (5); short-dashed curves, analytical formulas (5)–(7). (a) γ1=0.01, γ2=0, (b) γ1=0, γ2=0.01.

Fig. 2
Fig. 2

Same as Fig. 1 for the amplification of the FW and damping of the SH. γ1=-0.1, γ2=0.01.

Fig. 3
Fig. 3

Same as Fig. 1 for a numerically found QS with q=3. γ1=0.02, γ2=0.

Equations (8)

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

iAz+Axx/2+A*B+iγ1A=0,iBz+sBxx/2+A2/2+iγ2-qB=0.
Asz,x=A0 expikzcosh2 µx, Bsz,x=B0 expi2kzcosh2 µx,
Az,x=azAsz,η1zx,Bz,x=bzBsz,η2zx,
a0z-a0ηz/2η+4/5qa0b0 sin θ+γ1a0=0,b0z-b0ηz/2η-2/5q a02 sin θ+γ2b0=0,θz-q1+η2/5+2/5q4b0-a02/b0cos θ=0,
η2z=3a02zb0zcos θz/2a02z+b02z.
θzθ0exp2γz-cos βz,
a0zexp-34γz/45-14θ0/5βsin βz,b0zexp-16γz/45+4θ0/5βsin βz.
a0zexp-γ1+γ2/3z,b0zη2zexp-5γ1/4+γ2/12z.

Metrics