Abstract

The evolution of a strip (one-dimensional) fundamental beam with propagation distance owing to spatial modulational instabilities was analyzed in a quadratic medium near type  I phase matching. We obtained the gain coefficient for the modulational instability and showed that the wave evolves into a clean periodic sequence of solitary waves and does not reproduce the incident beam.

© 1998 Optical Society of America

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References

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  1. V. E. Zakharov and A. M. Rubenchik, Sov. Phys. JETP 38, 494 (1973).
  2. A. J. Campillo, S. L. Shapiro, and B. R. Suydam, Appl. Phys. Lett. 23, 628 (1973).
    [CrossRef]
  3. A. V. Mamaev, M. Saffman, and A. A. Zozulya, Europhys. Lett. 35, 25 (1996).
    [CrossRef]
  4. R. Fuerst, D.-M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, Phys. Rev. Lett. 78, 2756 (1997).
    [CrossRef]
  5. N. N. Akhmediev, D. R. Heatley, G. I. Stegeman, and E. M. Wright, Phys. Rev. Lett. 65, 1423 (1990).
    [CrossRef] [PubMed]
  6. S. Trillo and P. Ferro, Opt. Lett. 20, 438 (1995); A. V. Buryak and Yu. S. Kivshar, Opt. Lett. 19, 1612 (1994).
    [CrossRef] [PubMed]
  7. N. N. Akhmediev, V. I. Korneev, and R. F. Nabiev, Opt. Lett. 17, 393 (1992).
    [CrossRef] [PubMed]
  8. A. A. Kanashov and A. M. Rubenchik, Phys. D 4, 122 (1981).
    [CrossRef]
  9. C. R. Menyuk, R. Schiek, and L. Torner, J. Opt. Soc. Am. B 11, 2434 (1994).
    [CrossRef]
  10. V. V. Steblina, Y. S. Kivshar, M. Lisak, and B. A. Malomed, Opt. Commun. 118, 345 (1995).
    [CrossRef]
  11. L. Torner, Opt. Commun. 114, 136 (1995).
    [CrossRef]
  12. F. Wijnands, H. J. W. M. Hoekstra, G. J. M. Krijnen, and R. M. de Ridder, J. Lightwave Technol. 12, 2066 (1994).
    [CrossRef]
  13. A. De Rossi, S. Trillo, A. V. Buryak, and Y. S. Kivshar, Opt. Lett. 22, 868 (1997).
    [CrossRef] [PubMed]
  14. C. Etrich, U. Peschel, F. Lederer, B. A. Malomed, and Y. S. Kivshar, Phys. Rev. E 54, 4321 (1996).
    [CrossRef]

1997 (2)

R. Fuerst, D.-M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, Phys. Rev. Lett. 78, 2756 (1997).
[CrossRef]

A. De Rossi, S. Trillo, A. V. Buryak, and Y. S. Kivshar, Opt. Lett. 22, 868 (1997).
[CrossRef] [PubMed]

1996 (2)

C. Etrich, U. Peschel, F. Lederer, B. A. Malomed, and Y. S. Kivshar, Phys. Rev. E 54, 4321 (1996).
[CrossRef]

A. V. Mamaev, M. Saffman, and A. A. Zozulya, Europhys. Lett. 35, 25 (1996).
[CrossRef]

1995 (3)

S. Trillo and P. Ferro, Opt. Lett. 20, 438 (1995); A. V. Buryak and Yu. S. Kivshar, Opt. Lett. 19, 1612 (1994).
[CrossRef] [PubMed]

V. V. Steblina, Y. S. Kivshar, M. Lisak, and B. A. Malomed, Opt. Commun. 118, 345 (1995).
[CrossRef]

L. Torner, Opt. Commun. 114, 136 (1995).
[CrossRef]

1994 (2)

F. Wijnands, H. J. W. M. Hoekstra, G. J. M. Krijnen, and R. M. de Ridder, J. Lightwave Technol. 12, 2066 (1994).
[CrossRef]

C. R. Menyuk, R. Schiek, and L. Torner, J. Opt. Soc. Am. B 11, 2434 (1994).
[CrossRef]

1992 (1)

1990 (1)

N. N. Akhmediev, D. R. Heatley, G. I. Stegeman, and E. M. Wright, Phys. Rev. Lett. 65, 1423 (1990).
[CrossRef] [PubMed]

1981 (1)

A. A. Kanashov and A. M. Rubenchik, Phys. D 4, 122 (1981).
[CrossRef]

1973 (2)

V. E. Zakharov and A. M. Rubenchik, Sov. Phys. JETP 38, 494 (1973).

A. J. Campillo, S. L. Shapiro, and B. R. Suydam, Appl. Phys. Lett. 23, 628 (1973).
[CrossRef]

Akhmediev, N. N.

N. N. Akhmediev, V. I. Korneev, and R. F. Nabiev, Opt. Lett. 17, 393 (1992).
[CrossRef] [PubMed]

N. N. Akhmediev, D. R. Heatley, G. I. Stegeman, and E. M. Wright, Phys. Rev. Lett. 65, 1423 (1990).
[CrossRef] [PubMed]

Baboiu, D.-M.

R. Fuerst, D.-M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, Phys. Rev. Lett. 78, 2756 (1997).
[CrossRef]

Buryak, A. V.

Campillo, A. J.

A. J. Campillo, S. L. Shapiro, and B. R. Suydam, Appl. Phys. Lett. 23, 628 (1973).
[CrossRef]

de Ridder, R. M.

F. Wijnands, H. J. W. M. Hoekstra, G. J. M. Krijnen, and R. M. de Ridder, J. Lightwave Technol. 12, 2066 (1994).
[CrossRef]

De Rossi, A.

Etrich, C.

C. Etrich, U. Peschel, F. Lederer, B. A. Malomed, and Y. S. Kivshar, Phys. Rev. E 54, 4321 (1996).
[CrossRef]

Ferro, P.

Fuerst, R.

R. Fuerst, D.-M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, Phys. Rev. Lett. 78, 2756 (1997).
[CrossRef]

Heatley, D. R.

N. N. Akhmediev, D. R. Heatley, G. I. Stegeman, and E. M. Wright, Phys. Rev. Lett. 65, 1423 (1990).
[CrossRef] [PubMed]

Hoekstra, H. J. W. M.

F. Wijnands, H. J. W. M. Hoekstra, G. J. M. Krijnen, and R. M. de Ridder, J. Lightwave Technol. 12, 2066 (1994).
[CrossRef]

Kanashov, A. A.

A. A. Kanashov and A. M. Rubenchik, Phys. D 4, 122 (1981).
[CrossRef]

Kivshar, Y. S.

A. De Rossi, S. Trillo, A. V. Buryak, and Y. S. Kivshar, Opt. Lett. 22, 868 (1997).
[CrossRef] [PubMed]

C. Etrich, U. Peschel, F. Lederer, B. A. Malomed, and Y. S. Kivshar, Phys. Rev. E 54, 4321 (1996).
[CrossRef]

V. V. Steblina, Y. S. Kivshar, M. Lisak, and B. A. Malomed, Opt. Commun. 118, 345 (1995).
[CrossRef]

Korneev, V. I.

Krijnen, G. J. M.

F. Wijnands, H. J. W. M. Hoekstra, G. J. M. Krijnen, and R. M. de Ridder, J. Lightwave Technol. 12, 2066 (1994).
[CrossRef]

Lawrence, B.

R. Fuerst, D.-M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, Phys. Rev. Lett. 78, 2756 (1997).
[CrossRef]

Lederer, F.

C. Etrich, U. Peschel, F. Lederer, B. A. Malomed, and Y. S. Kivshar, Phys. Rev. E 54, 4321 (1996).
[CrossRef]

Lisak, M.

V. V. Steblina, Y. S. Kivshar, M. Lisak, and B. A. Malomed, Opt. Commun. 118, 345 (1995).
[CrossRef]

Malomed, B. A.

C. Etrich, U. Peschel, F. Lederer, B. A. Malomed, and Y. S. Kivshar, Phys. Rev. E 54, 4321 (1996).
[CrossRef]

V. V. Steblina, Y. S. Kivshar, M. Lisak, and B. A. Malomed, Opt. Commun. 118, 345 (1995).
[CrossRef]

Mamaev, A. V.

A. V. Mamaev, M. Saffman, and A. A. Zozulya, Europhys. Lett. 35, 25 (1996).
[CrossRef]

Menyuk, C. R.

Nabiev, R. F.

Peschel, U.

C. Etrich, U. Peschel, F. Lederer, B. A. Malomed, and Y. S. Kivshar, Phys. Rev. E 54, 4321 (1996).
[CrossRef]

Rubenchik, A. M.

A. A. Kanashov and A. M. Rubenchik, Phys. D 4, 122 (1981).
[CrossRef]

V. E. Zakharov and A. M. Rubenchik, Sov. Phys. JETP 38, 494 (1973).

Saffman, M.

A. V. Mamaev, M. Saffman, and A. A. Zozulya, Europhys. Lett. 35, 25 (1996).
[CrossRef]

Schiek, R.

Shapiro, S. L.

A. J. Campillo, S. L. Shapiro, and B. R. Suydam, Appl. Phys. Lett. 23, 628 (1973).
[CrossRef]

Steblina, V. V.

V. V. Steblina, Y. S. Kivshar, M. Lisak, and B. A. Malomed, Opt. Commun. 118, 345 (1995).
[CrossRef]

Stegeman, G. I.

R. Fuerst, D.-M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, Phys. Rev. Lett. 78, 2756 (1997).
[CrossRef]

N. N. Akhmediev, D. R. Heatley, G. I. Stegeman, and E. M. Wright, Phys. Rev. Lett. 65, 1423 (1990).
[CrossRef] [PubMed]

Suydam, B. R.

A. J. Campillo, S. L. Shapiro, and B. R. Suydam, Appl. Phys. Lett. 23, 628 (1973).
[CrossRef]

Torner, L.

Torruellas, W. E.

R. Fuerst, D.-M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, Phys. Rev. Lett. 78, 2756 (1997).
[CrossRef]

Trillo, S.

Wabnitz, S.

R. Fuerst, D.-M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, Phys. Rev. Lett. 78, 2756 (1997).
[CrossRef]

Wijnands, F.

F. Wijnands, H. J. W. M. Hoekstra, G. J. M. Krijnen, and R. M. de Ridder, J. Lightwave Technol. 12, 2066 (1994).
[CrossRef]

Wright, E. M.

N. N. Akhmediev, D. R. Heatley, G. I. Stegeman, and E. M. Wright, Phys. Rev. Lett. 65, 1423 (1990).
[CrossRef] [PubMed]

Zakharov, V. E.

V. E. Zakharov and A. M. Rubenchik, Sov. Phys. JETP 38, 494 (1973).

Zozulya, A. A.

A. V. Mamaev, M. Saffman, and A. A. Zozulya, Europhys. Lett. 35, 25 (1996).
[CrossRef]

Appl. Phys. Lett. (1)

A. J. Campillo, S. L. Shapiro, and B. R. Suydam, Appl. Phys. Lett. 23, 628 (1973).
[CrossRef]

Europhys. Lett. (1)

A. V. Mamaev, M. Saffman, and A. A. Zozulya, Europhys. Lett. 35, 25 (1996).
[CrossRef]

J. Lightwave Technol. (1)

F. Wijnands, H. J. W. M. Hoekstra, G. J. M. Krijnen, and R. M. de Ridder, J. Lightwave Technol. 12, 2066 (1994).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Commun. (2)

V. V. Steblina, Y. S. Kivshar, M. Lisak, and B. A. Malomed, Opt. Commun. 118, 345 (1995).
[CrossRef]

L. Torner, Opt. Commun. 114, 136 (1995).
[CrossRef]

Opt. Lett. (3)

Phys. D (1)

A. A. Kanashov and A. M. Rubenchik, Phys. D 4, 122 (1981).
[CrossRef]

Phys. Rev. E (1)

C. Etrich, U. Peschel, F. Lederer, B. A. Malomed, and Y. S. Kivshar, Phys. Rev. E 54, 4321 (1996).
[CrossRef]

Phys. Rev. Lett. (2)

R. Fuerst, D.-M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, Phys. Rev. Lett. 78, 2756 (1997).
[CrossRef]

N. N. Akhmediev, D. R. Heatley, G. I. Stegeman, and E. M. Wright, Phys. Rev. Lett. 65, 1423 (1990).
[CrossRef] [PubMed]

Sov. Phys. JETP (1)

V. E. Zakharov and A. M. Rubenchik, Sov. Phys. JETP 38, 494 (1973).

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Figures (4)

Fig. 1
Fig. 1

Squared instability growth rate γ2 versus squared modulational frequency κ2 for three different phase mismatches β. The straight solid line at the origin is the analytically calculated asymptote for β=-3.

Fig. 2
Fig. 2

Perturbation FW and SH profiles for β=-3 and κ=1.517.

Fig. 3
Fig. 3

Evolution of a 2D strip wave (the section along the homogeneous coordinate y) input with a small periodic amplitude modulation close to the point of maximum gain κ=1. Only the fundamental wave is shown.

Fig. 4
Fig. 4

Output profile and contour plots of the intensity distribution of the fundamental wave in the xy plane after six diffraction lengths.

Equations (3)

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ia1Z-r22a1X2+2a1Y2+a1*a2 exp-iβz=0, ia2Z-α22a2X2+2a2Y2+a12 expiβz=0,
if1Z-k1f1+rκ22f1-r22f1X2+U1f2+U2f1*=0, if2Z-k2f2+ακ22f2-α22f2X2+2U1f1=0.
iγf1-k1-rκ22f1-r22f1X2+U1f2+U2f1*=0, iγf2-k2-ακ22f2-α22f2X2+2U1f1=0.

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