Abstract

The interaction between two one-dimensional quadratic solitons has been investigated experimentally in lithium niobate planar waveguides for both parallel- and crossing-launched solitons.

© 1997 Optical Society of America

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  1. G. I. Stegeman, Opt. Appl. 26, 239 (1997).
  2. J. U. Kang, G. I. Stegeman, J. S. Aitchison, and N. Akhmediev, Phys. Rev. Lett. 76, 3699 (1996).
    [Crossref] [PubMed]
  3. G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993).
    [Crossref]
  4. R. Schiek, Y. Baek, and G. I. Stegeman, Phys. Rev. E 53, 1138 (1996).
    [Crossref]
  5. Yu. N. Karamzin and A. P. Sukhorukov, Zh. Eksp. Teor. Fiz. 68, 834 (1975) [Sov. Phys. JETP 41, 414 (1976)].
  6. D. E. Pelinovsky, A. V. Buryak, and Y. S. Kivshar, Phys. Rev. Lett. 75, 591 (1995).
    [Crossref] [PubMed]
  7. L. Torner, C. R. Menyuk, W. E. Torruellas, and G. I. Stegeman, Opt. Lett. 20, 13 (1995).
    [Crossref] [PubMed]
  8. 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]
  9. J. S. Aitchison, A. M. Weiner, Y. Silberberg, D. E. Leaird, M. K. Oliver, J. L. Jackel, and P. W. E. Smith, Opt. Lett. 16, 15 (1991).
    [Crossref] [PubMed]
  10. A. V. Buryak, Y. S. Kivshar, and V. V. Stelbina, Phys. Rev. A 52, 1670 (1995).
    [Crossref] [PubMed]
  11. D.-M. Baboiu, G. I. Stegeman, and L. Torner, Opt. Lett. 20, 2282 (1995).
    [Crossref]
  12. C. Etrich, U. Peschel, F. Lederer, and B. Malomed, Phys. Rev. A 52, 3444 (1995).
    [Crossref]
  13. M. Shalaby, F. Reynaud, and A. Barthelemy, Opt. Lett. 17, 778 (1992).
    [Crossref] [PubMed]
  14. A. W. Snyder and A. P. Sheppard, Opt. Lett. 18, 482 (1993).
    [Crossref] [PubMed]

1997 (1)

G. I. Stegeman, Opt. Appl. 26, 239 (1997).

1996 (2)

J. U. Kang, G. I. Stegeman, J. S. Aitchison, and N. Akhmediev, Phys. Rev. Lett. 76, 3699 (1996).
[Crossref] [PubMed]

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

1995 (6)

D. E. Pelinovsky, A. V. Buryak, and Y. S. Kivshar, Phys. Rev. Lett. 75, 591 (1995).
[Crossref] [PubMed]

L. Torner, C. R. Menyuk, W. E. Torruellas, and G. I. Stegeman, Opt. Lett. 20, 13 (1995).
[Crossref] [PubMed]

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]

A. V. Buryak, Y. S. Kivshar, and V. V. Stelbina, Phys. Rev. A 52, 1670 (1995).
[Crossref] [PubMed]

D.-M. Baboiu, G. I. Stegeman, and L. Torner, Opt. Lett. 20, 2282 (1995).
[Crossref]

C. Etrich, U. Peschel, F. Lederer, and B. Malomed, Phys. Rev. A 52, 3444 (1995).
[Crossref]

1993 (2)

A. W. Snyder and A. P. Sheppard, Opt. Lett. 18, 482 (1993).
[Crossref] [PubMed]

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993).
[Crossref]

1992 (1)

1991 (1)

1975 (1)

Yu. N. Karamzin and A. P. Sukhorukov, Zh. Eksp. Teor. Fiz. 68, 834 (1975) [Sov. Phys. JETP 41, 414 (1976)].

Aitchison, J. S.

Akhmediev, N.

J. U. Kang, G. I. Stegeman, J. S. Aitchison, and N. Akhmediev, Phys. Rev. Lett. 76, 3699 (1996).
[Crossref] [PubMed]

Baboiu, D.-M.

Baek, Y.

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

Barthelemy, A.

Buryak, A. V.

D. E. Pelinovsky, A. V. Buryak, and Y. S. Kivshar, Phys. Rev. Lett. 75, 591 (1995).
[Crossref] [PubMed]

A. V. Buryak, Y. S. Kivshar, and V. V. Stelbina, Phys. Rev. A 52, 1670 (1995).
[Crossref] [PubMed]

Crosignani, B.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993).
[Crossref]

Di Porto, P.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993).
[Crossref]

Duree, G. C.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993).
[Crossref]

Etrich, C.

C. Etrich, U. Peschel, F. Lederer, and B. Malomed, Phys. Rev. A 52, 3444 (1995).
[Crossref]

Hagan, D. J.

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]

Jackel, J. L.

Kang, J. U.

J. U. Kang, G. I. Stegeman, J. S. Aitchison, and N. Akhmediev, Phys. Rev. Lett. 76, 3699 (1996).
[Crossref] [PubMed]

Karamzin, Yu. N.

Yu. N. Karamzin and A. P. Sukhorukov, Zh. Eksp. Teor. Fiz. 68, 834 (1975) [Sov. Phys. JETP 41, 414 (1976)].

Kivshar, Y. S.

D. E. Pelinovsky, A. V. Buryak, and Y. S. Kivshar, Phys. Rev. Lett. 75, 591 (1995).
[Crossref] [PubMed]

A. V. Buryak, Y. S. Kivshar, and V. V. Stelbina, Phys. Rev. A 52, 1670 (1995).
[Crossref] [PubMed]

Leaird, D. E.

Lederer, F.

C. Etrich, U. Peschel, F. Lederer, and B. Malomed, Phys. Rev. A 52, 3444 (1995).
[Crossref]

Malomed, B.

C. Etrich, U. Peschel, F. Lederer, and B. Malomed, Phys. Rev. A 52, 3444 (1995).
[Crossref]

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]

L. Torner, C. R. Menyuk, W. E. Torruellas, and G. I. Stegeman, Opt. Lett. 20, 13 (1995).
[Crossref] [PubMed]

Neurgaonkar, R. R.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993).
[Crossref]

Oliver, M. K.

Pelinovsky, D. E.

D. E. Pelinovsky, A. V. Buryak, and Y. S. Kivshar, Phys. Rev. Lett. 75, 591 (1995).
[Crossref] [PubMed]

Peschel, U.

C. Etrich, U. Peschel, F. Lederer, and B. Malomed, Phys. Rev. A 52, 3444 (1995).
[Crossref]

Reynaud, F.

Salamo, G. J.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993).
[Crossref]

Schiek, R.

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

Segev, M.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993).
[Crossref]

Shalaby, M.

Sharp, E. J.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993).
[Crossref]

Sheppard, A. P.

Shultz, J. L.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993).
[Crossref]

Silberberg, Y.

Smith, P. W. E.

Snyder, A. W.

Stegeman, G. I.

G. I. Stegeman, Opt. Appl. 26, 239 (1997).

J. U. Kang, G. I. Stegeman, J. S. Aitchison, and N. Akhmediev, Phys. Rev. Lett. 76, 3699 (1996).
[Crossref] [PubMed]

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

D.-M. Baboiu, G. I. Stegeman, and L. Torner, Opt. Lett. 20, 2282 (1995).
[Crossref]

L. Torner, C. R. Menyuk, W. E. Torruellas, and G. I. Stegeman, Opt. Lett. 20, 13 (1995).
[Crossref] [PubMed]

Stelbina, V. V.

A. V. Buryak, Y. S. Kivshar, and V. V. Stelbina, Phys. Rev. A 52, 1670 (1995).
[Crossref] [PubMed]

Sukhorukov, A. P.

Yu. N. Karamzin and A. P. Sukhorukov, Zh. Eksp. Teor. Fiz. 68, 834 (1975) [Sov. Phys. JETP 41, 414 (1976)].

Torner, L.

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]

D.-M. Baboiu, G. I. Stegeman, and L. Torner, Opt. Lett. 20, 2282 (1995).
[Crossref]

L. Torner, C. R. Menyuk, W. E. Torruellas, and G. I. Stegeman, Opt. Lett. 20, 13 (1995).
[Crossref] [PubMed]

Torruellas, W. E.

L. Torner, C. R. Menyuk, W. E. Torruellas, and G. I. Stegeman, Opt. Lett. 20, 13 (1995).
[Crossref] [PubMed]

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]

Weiner, A. M.

Yariv, A.

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993).
[Crossref]

Opt. Appl. (1)

G. I. Stegeman, Opt. Appl. 26, 239 (1997).

Opt. Lett. (5)

Phys. Rev. A (2)

C. Etrich, U. Peschel, F. Lederer, and B. Malomed, Phys. Rev. A 52, 3444 (1995).
[Crossref]

A. V. Buryak, Y. S. Kivshar, and V. V. Stelbina, Phys. Rev. A 52, 1670 (1995).
[Crossref] [PubMed]

Phys. Rev. E (1)

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

Phys. Rev. Lett. (4)

J. U. Kang, G. I. Stegeman, J. S. Aitchison, and N. Akhmediev, Phys. Rev. Lett. 76, 3699 (1996).
[Crossref] [PubMed]

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993).
[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]

D. E. Pelinovsky, A. V. Buryak, and Y. S. Kivshar, Phys. Rev. Lett. 75, 591 (1995).
[Crossref] [PubMed]

Zh. Eksp. Teor. Fiz. (1)

Yu. N. Karamzin and A. P. Sukhorukov, Zh. Eksp. Teor. Fiz. 68, 834 (1975) [Sov. Phys. JETP 41, 414 (1976)].

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Figures (5)

Fig. 1
Fig. 1

Measured output beam profiles of the two-solitary-wave interaction for the parallel-launching case for large phase mismatch T=335.05 °C. The relative phase difference between the two beams is (a) 0, (b) π/2, (c) π, (d) 3π/2.

Fig. 2
Fig. 2

Numerical simulations of the two-solitary-wave interaction for the parallel-launching case for large phase mismatch T=335.05 °C. The relative phase difference between the two beams is (a) 0, (b) π/2, (c) π, (d) 3π/2.

Fig. 3
Fig. 3

(a), (c) Measured and (b), (d) simulated output beam profiles of the two-solitary-wave interaction for the parallel-launching case for small phase mismatch T=335.35 °C. The relative phase difference between the two beams is (a), (b) 0 and (c), (d) π.

Fig. 4
Fig. 4

(a), (c) Measured and (b), (d) simulated output beam profiles of the two-solitary-wave interaction for the parallel-launching case for small phase mismatch T=335.35 °C. The relative phase difference between the beams is (a), (b) π/2 and (c), (d) 3π/2.

Fig. 5
Fig. 5

Measured output beam profiles for the two-solitary-wave interaction in the cross-launching case for large net phase mismatch T=335.05 °C. The relative phase difference between the two beams is (a) 0, (b) π/2, (c) π, (d) 3π/2.

Equations (2)

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ddxA1βz+iβ1xA1βz=-iω1K22χ2β18πp0β1x×dβzA2βz-βzA1*-βz,
ddxA2βz+iβ2xA2βz=-iω1K22χ2β28πp0β2x×dβzA1βz-βzA1βz.

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