Abstract

We demonstrate numerically that a frequency-degenerate process through type  II downconversion in a quadratic nonlinear waveguide leads to the formation of spatial simultons and all-optical switching in the presence of a control signal. This novel effect is phase independent, generally insensitive to polarization, and weakly affected by the magnitude of the control input. Multiple solitary waves can also be obtained, depending on the details of the interaction.

© 1997 Optical Society of America

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  1. Y. N. Karamzin and A. P. Sukhorukov, Sov. Phys. JETP 41, 414 (1976).
  2. G. Assanto, G. I. Stegeman, M. Sheik-Bahae, and E. W. Van Stryland, IEEE J. Quantum Electron. 31, 673 (1995).
    [CrossRef]
  3. G. Assanto, Opt. Lett. 20, 1595 (1995); A. Kobyakov, U. Peschel, R. Muschall, G. Assanto, V. P. Torchigin, and F. Lederer, Opt. Lett. 20, 1686 (1995).
    [CrossRef] [PubMed]
  4. K. Hayata and M. Koshiba, Phys. Rev. Lett. 71, 3275 (1993).
    [CrossRef] [PubMed]
  5. C. R. Menyuk, R. Schiek, and L. Torner, J. Opt. Soc. Am. B 11, 2434 (1994).
    [CrossRef]
  6. A. V. Buryak, Y. S. Kivshar, and S. Trillo, Phys. Rev. Lett. 77, 5210 (1995).
    [CrossRef]
  7. L. Lefort and A. Barthelemy, Electron. Lett. 31, 910 (1995).
    [CrossRef]
  8. G. Assanto, Z. Wang, D. J. Hagan, and E. W. Van Stryland, Appl. Phys. Lett. 67, 2120 (1995).
    [CrossRef]
  9. 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]
  10. W. E. Torruellas, G. Assanto, B. L. Lawrence, R. A. Fuerst, and G. I. Stegeman, Appl. Phys. Lett. 68, 1149 (1996).
    [CrossRef]
  11. D. C. Hutchings, J. S. Aitchison, and C. N. Ironside, Opt. Lett. 18, 793 (1993).
    [CrossRef] [PubMed]
  12. L. Torner, D. Mazilu, and D. Mihalache, Phys. Rev. Lett. 77, 2455 (1996).
    [CrossRef] [PubMed]
  13. P. Agin and G. I. Stegeman, Appl. Phys. Lett. 69, 3996 (1996).
    [CrossRef]
  14. L. Torner, J. P. Torres, and C. R. Menyuk, Opt. Lett. 21, 462 (1996).
    [CrossRef]
  15. G. Leo, G. Assanto, and W. E. Torruellas, “Bidimensional spatial solitary waves in quadratically nonlinear bulk media,” J. Opt. Soc. Am. B (to be published).

1996 (4)

W. E. Torruellas, G. Assanto, B. L. Lawrence, R. A. Fuerst, and G. I. Stegeman, Appl. Phys. Lett. 68, 1149 (1996).
[CrossRef]

L. Torner, D. Mazilu, and D. Mihalache, Phys. Rev. Lett. 77, 2455 (1996).
[CrossRef] [PubMed]

P. Agin and G. I. Stegeman, Appl. Phys. Lett. 69, 3996 (1996).
[CrossRef]

L. Torner, J. P. Torres, and C. R. Menyuk, Opt. Lett. 21, 462 (1996).
[CrossRef]

1995 (6)

G. Assanto, G. I. Stegeman, M. Sheik-Bahae, and E. W. Van Stryland, IEEE J. Quantum Electron. 31, 673 (1995).
[CrossRef]

G. Assanto, Opt. Lett. 20, 1595 (1995); A. Kobyakov, U. Peschel, R. Muschall, G. Assanto, V. P. Torchigin, and F. Lederer, Opt. Lett. 20, 1686 (1995).
[CrossRef] [PubMed]

A. V. Buryak, Y. S. Kivshar, and S. Trillo, Phys. Rev. Lett. 77, 5210 (1995).
[CrossRef]

L. Lefort and A. Barthelemy, Electron. Lett. 31, 910 (1995).
[CrossRef]

G. Assanto, Z. Wang, D. J. Hagan, and E. W. Van Stryland, Appl. Phys. Lett. 67, 2120 (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]

1994 (1)

1993 (2)

1976 (1)

Y. N. Karamzin and A. P. Sukhorukov, Sov. Phys. JETP 41, 414 (1976).

Agin, P.

P. Agin and G. I. Stegeman, Appl. Phys. Lett. 69, 3996 (1996).
[CrossRef]

Aitchison, J. S.

Assanto, G.

W. E. Torruellas, G. Assanto, B. L. Lawrence, R. A. Fuerst, and G. I. Stegeman, Appl. Phys. Lett. 68, 1149 (1996).
[CrossRef]

G. Assanto, Z. Wang, D. J. Hagan, and E. W. Van Stryland, Appl. Phys. Lett. 67, 2120 (1995).
[CrossRef]

G. Assanto, Opt. Lett. 20, 1595 (1995); A. Kobyakov, U. Peschel, R. Muschall, G. Assanto, V. P. Torchigin, and F. Lederer, Opt. Lett. 20, 1686 (1995).
[CrossRef] [PubMed]

G. Assanto, G. I. Stegeman, M. Sheik-Bahae, and E. W. Van Stryland, IEEE J. Quantum Electron. 31, 673 (1995).
[CrossRef]

G. Leo, G. Assanto, and W. E. Torruellas, “Bidimensional spatial solitary waves in quadratically nonlinear bulk media,” J. Opt. Soc. Am. B (to be published).

Barthelemy, A.

L. Lefort and A. Barthelemy, Electron. Lett. 31, 910 (1995).
[CrossRef]

Buryak, A. V.

A. V. Buryak, Y. S. Kivshar, and S. Trillo, Phys. Rev. Lett. 77, 5210 (1995).
[CrossRef]

Fuerst, R. A.

W. E. Torruellas, G. Assanto, B. L. Lawrence, R. A. Fuerst, and G. I. Stegeman, Appl. Phys. Lett. 68, 1149 (1996).
[CrossRef]

Hagan, D. J.

G. Assanto, Z. Wang, D. J. Hagan, and E. W. Van Stryland, Appl. Phys. Lett. 67, 2120 (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]

Hayata, K.

K. Hayata and M. Koshiba, Phys. Rev. Lett. 71, 3275 (1993).
[CrossRef] [PubMed]

Hutchings, D. C.

Ironside, C. N.

Karamzin, Y. N.

Y. N. Karamzin and A. P. Sukhorukov, Sov. Phys. JETP 41, 414 (1976).

Kivshar, Y. S.

A. V. Buryak, Y. S. Kivshar, and S. Trillo, Phys. Rev. Lett. 77, 5210 (1995).
[CrossRef]

Koshiba, M.

K. Hayata and M. Koshiba, Phys. Rev. Lett. 71, 3275 (1993).
[CrossRef] [PubMed]

Lawrence, B. L.

W. E. Torruellas, G. Assanto, B. L. Lawrence, R. A. Fuerst, and G. I. Stegeman, Appl. Phys. Lett. 68, 1149 (1996).
[CrossRef]

Lefort, L.

L. Lefort and A. Barthelemy, Electron. Lett. 31, 910 (1995).
[CrossRef]

Leo, G.

G. Leo, G. Assanto, and W. E. Torruellas, “Bidimensional spatial solitary waves in quadratically nonlinear bulk media,” J. Opt. Soc. Am. B (to be published).

Mazilu, D.

L. Torner, D. Mazilu, and D. Mihalache, Phys. Rev. Lett. 77, 2455 (1996).
[CrossRef] [PubMed]

Menyuk, C. R.

L. Torner, J. P. Torres, and C. R. Menyuk, Opt. Lett. 21, 462 (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]

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

Mihalache, D.

L. Torner, D. Mazilu, and D. Mihalache, Phys. Rev. Lett. 77, 2455 (1996).
[CrossRef] [PubMed]

Schiek, R.

Sheik-Bahae, M.

G. Assanto, G. I. Stegeman, M. Sheik-Bahae, and E. W. Van Stryland, IEEE J. Quantum Electron. 31, 673 (1995).
[CrossRef]

Stegeman, G. I.

P. Agin and G. I. Stegeman, Appl. Phys. Lett. 69, 3996 (1996).
[CrossRef]

W. E. Torruellas, G. Assanto, B. L. Lawrence, R. A. Fuerst, and G. I. Stegeman, Appl. Phys. Lett. 68, 1149 (1996).
[CrossRef]

G. Assanto, G. I. Stegeman, M. Sheik-Bahae, and E. W. Van Stryland, IEEE J. Quantum Electron. 31, 673 (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]

Sukhorukov, A. P.

Y. N. Karamzin and A. P. Sukhorukov, Sov. Phys. JETP 41, 414 (1976).

Torner, L.

L. Torner, J. P. Torres, and C. R. Menyuk, Opt. Lett. 21, 462 (1996).
[CrossRef]

L. Torner, D. Mazilu, and D. Mihalache, Phys. Rev. Lett. 77, 2455 (1996).
[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]

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

Torres, J. P.

Torruellas, W. E.

W. E. Torruellas, G. Assanto, B. L. Lawrence, R. A. Fuerst, and G. I. Stegeman, Appl. Phys. Lett. 68, 1149 (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]

G. Leo, G. Assanto, and W. E. Torruellas, “Bidimensional spatial solitary waves in quadratically nonlinear bulk media,” J. Opt. Soc. Am. B (to be published).

Trillo, S.

A. V. Buryak, Y. S. Kivshar, and S. Trillo, Phys. Rev. Lett. 77, 5210 (1995).
[CrossRef]

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]

G. Assanto, G. I. Stegeman, M. Sheik-Bahae, and E. W. Van Stryland, IEEE J. Quantum Electron. 31, 673 (1995).
[CrossRef]

G. Assanto, Z. Wang, D. J. Hagan, and E. W. Van Stryland, Appl. Phys. Lett. 67, 2120 (1995).
[CrossRef]

Wang, Z.

G. Assanto, Z. Wang, D. J. Hagan, and E. W. Van Stryland, Appl. Phys. Lett. 67, 2120 (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]

Appl. Phys. Lett. (3)

G. Assanto, Z. Wang, D. J. Hagan, and E. W. Van Stryland, Appl. Phys. Lett. 67, 2120 (1995).
[CrossRef]

W. E. Torruellas, G. Assanto, B. L. Lawrence, R. A. Fuerst, and G. I. Stegeman, Appl. Phys. Lett. 68, 1149 (1996).
[CrossRef]

P. Agin and G. I. Stegeman, Appl. Phys. Lett. 69, 3996 (1996).
[CrossRef]

Electron. Lett. (1)

L. Lefort and A. Barthelemy, Electron. Lett. 31, 910 (1995).
[CrossRef]

IEEE J. Quantum Electron. (1)

G. Assanto, G. I. Stegeman, M. Sheik-Bahae, and E. W. Van Stryland, IEEE J. Quantum Electron. 31, 673 (1995).
[CrossRef]

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

Opt. Lett. (3)

Phys. Rev. Lett. (4)

L. Torner, D. Mazilu, and D. Mihalache, Phys. Rev. Lett. 77, 2455 (1996).
[CrossRef] [PubMed]

K. Hayata and M. Koshiba, Phys. Rev. Lett. 71, 3275 (1993).
[CrossRef] [PubMed]

A. V. Buryak, Y. S. Kivshar, and S. Trillo, Phys. Rev. Lett. 77, 5210 (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]

Sov. Phys. JETP (1)

Y. N. Karamzin and A. P. Sukhorukov, Sov. Phys. JETP 41, 414 (1976).

Other (1)

G. Leo, G. Assanto, and W. E. Torruellas, “Bidimensional spatial solitary waves in quadratically nonlinear bulk media,” J. Opt. Soc. Am. B (to be published).

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Figures (5)

Fig. 1
Fig. 1

Intensity ujx, z2 of the components (a), (b) at 2ω and (c), (d) at ω in the xz plane. For δ2=δ3=0 and Gaussian input distributions with peak amplitudes Uj ( j=1–3): (a) 2ω field, with U3=5.4, U1=U2=0; (b) 2ω field, with U3=5.4, U1=6×10-5, and U2=0; (c) ωe field; and (d) ωo field for the same inputs as in (b). Here β=0.07, α1=1, α2=1.05, α3=0.51. Peak intensities in (c) and (d) are 23% and 21% of the input, respectively, but the total output intensity at ω exceeds by 50% the output at 2ω. Notice that, in ζ=10, more than 85% of the input power is trapped in the SSW.

Fig. 2
Fig. 2

Normalized peak intensity (left axis) and total power (right axis) at ω in ζ=z/zd1=10 versus input control power normalized to the 2ω pump for various wave-vector mismatches: β=0 (solid curves), β=0.07 (short-dashed curves), β=-0.07 (long-dashed curves), β=0.7 (long-dashed–short-dashed curve), β=-0.7 (dotted curve).

Fig. 3
Fig. 3

Contour profile of the total intensity at ω in the presence of walk-off ρ2=0.18° and ρ2=0.28°,9 for U1=6×10-5, U2=0, and U3=5.4. The other parameters are as in Fig.  1.

Fig. 4
Fig. 4

Contour maps of total e+o intensity at ω for the same values as in Fig.  1 but with one parameter altered: (a) β=3.5, (b) U3=8.8. The peak intensity of each channel at ω with respect to the input is (a) >18%, (b) 41% in the central SSW and 4.1% in each lateral beam.

Fig. 5
Fig. 5

Output lateral displacement of either split-off SSW with respect to the central solitary wave [see Fig.  4(b)] versus control input U1, for U3=6.2 (circles), U3=7.6 (triangles), and U3=8.8 (squares).

Equations (1)

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ζ(u1u2u3* )-ξ(0δ2u2δ3u3* )+14i2ξ2(α1u1α2u2-α3u3* )=i(u2*u3u1* u3-u1*u2* )exp-iβζ,

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