Abstract

Mutual trapping of the fundamental and second-harmonic waves propagating in a material with cascaded second-order nonlinearity is investigated. Formation of solitonlike waves under a variety of excitation conditions is numerically observed, consistent with the robustness hypothesis of solitons.

© 1994 Optical Society of America

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References

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  1. G. I. Stegeman, M. Sheik-Bahae, E. Van Stryland, G. Assanto, Opt. Lett. 18, 13 (1993).
    [CrossRef] [PubMed]
  2. N. R. Belashenkov, S. V. Gagarskii, M. V. Inochkin, Opt. Spectrosc. (USSR) 66, 806 (1989); R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, E. W. Van Stryland, H. Vanherzeele, Opt. Lett. 17,28 (1992); M. L. Sundheimer, Ch. Bosshard, E. W. Van Stryland, G. I. Stegeman, J. D. Bierlein, Opt. Lett. 18, 1397 (1993).
    [CrossRef] [PubMed]
  3. G. Assanto, G. Stegeman, M. Sheik-Bahae, E. Van Stryland, Appl. Phys. Lett. 62, 1323 (1993); C. N. Ironside, J. S. Aitchison, J. M. Arnold, IEEE J. Quantum Electron. 29, 2650 (1993); P. St. J. Russell, Electron. Lett. 29, 1228 (1993).
    [CrossRef]
  4. R. Schiek, J. Opt. Soc. Am. B 10, 1848 (1993).
    [CrossRef]
  5. Q. Guo, Quantum Opt. 5, 133 (1993); A. Kalocsai, J. Haus, Phys. Rev. A 49, 574 (1994).
    [CrossRef] [PubMed]
  6. C. R. Menyuk, R. Schiek, L. Torner, “Solitary waves due to χ(2): χ(2) cascading,” J. Opt. Soc. Am. B (to be published).
  7. M. J. Ablowitz, H. Segur, Solitons and the Inverse Scattering Transform (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1981).
    [CrossRef]
  8. Yu. N. Karamzin, A. P. Sukhorukov, JETP Lett. 20, 339 (1974); M. J. Werner, P. D. Drummond, J. Opt. Soc. Am. B 10, 2390 (1993); Opt. Lett. 19, 613 (1994); K. Hayata, M. Koshiba, Phys. Rev. Lett. 71, 3275 (1993).
    [CrossRef] [PubMed]
  9. C. R. Menyuk, J. Opt. Soc. Am. B 10, 1585 (1993).
    [CrossRef]

1993 (5)

G. Assanto, G. Stegeman, M. Sheik-Bahae, E. Van Stryland, Appl. Phys. Lett. 62, 1323 (1993); C. N. Ironside, J. S. Aitchison, J. M. Arnold, IEEE J. Quantum Electron. 29, 2650 (1993); P. St. J. Russell, Electron. Lett. 29, 1228 (1993).
[CrossRef]

Q. Guo, Quantum Opt. 5, 133 (1993); A. Kalocsai, J. Haus, Phys. Rev. A 49, 574 (1994).
[CrossRef] [PubMed]

G. I. Stegeman, M. Sheik-Bahae, E. Van Stryland, G. Assanto, Opt. Lett. 18, 13 (1993).
[CrossRef] [PubMed]

C. R. Menyuk, J. Opt. Soc. Am. B 10, 1585 (1993).
[CrossRef]

R. Schiek, J. Opt. Soc. Am. B 10, 1848 (1993).
[CrossRef]

1989 (1)

N. R. Belashenkov, S. V. Gagarskii, M. V. Inochkin, Opt. Spectrosc. (USSR) 66, 806 (1989); R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, E. W. Van Stryland, H. Vanherzeele, Opt. Lett. 17,28 (1992); M. L. Sundheimer, Ch. Bosshard, E. W. Van Stryland, G. I. Stegeman, J. D. Bierlein, Opt. Lett. 18, 1397 (1993).
[CrossRef] [PubMed]

1974 (1)

Yu. N. Karamzin, A. P. Sukhorukov, JETP Lett. 20, 339 (1974); M. J. Werner, P. D. Drummond, J. Opt. Soc. Am. B 10, 2390 (1993); Opt. Lett. 19, 613 (1994); K. Hayata, M. Koshiba, Phys. Rev. Lett. 71, 3275 (1993).
[CrossRef] [PubMed]

Ablowitz, M. J.

M. J. Ablowitz, H. Segur, Solitons and the Inverse Scattering Transform (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1981).
[CrossRef]

Assanto, G.

G. I. Stegeman, M. Sheik-Bahae, E. Van Stryland, G. Assanto, Opt. Lett. 18, 13 (1993).
[CrossRef] [PubMed]

G. Assanto, G. Stegeman, M. Sheik-Bahae, E. Van Stryland, Appl. Phys. Lett. 62, 1323 (1993); C. N. Ironside, J. S. Aitchison, J. M. Arnold, IEEE J. Quantum Electron. 29, 2650 (1993); P. St. J. Russell, Electron. Lett. 29, 1228 (1993).
[CrossRef]

Belashenkov, N. R.

N. R. Belashenkov, S. V. Gagarskii, M. V. Inochkin, Opt. Spectrosc. (USSR) 66, 806 (1989); R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, E. W. Van Stryland, H. Vanherzeele, Opt. Lett. 17,28 (1992); M. L. Sundheimer, Ch. Bosshard, E. W. Van Stryland, G. I. Stegeman, J. D. Bierlein, Opt. Lett. 18, 1397 (1993).
[CrossRef] [PubMed]

Gagarskii, S. V.

N. R. Belashenkov, S. V. Gagarskii, M. V. Inochkin, Opt. Spectrosc. (USSR) 66, 806 (1989); R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, E. W. Van Stryland, H. Vanherzeele, Opt. Lett. 17,28 (1992); M. L. Sundheimer, Ch. Bosshard, E. W. Van Stryland, G. I. Stegeman, J. D. Bierlein, Opt. Lett. 18, 1397 (1993).
[CrossRef] [PubMed]

Guo, Q.

Q. Guo, Quantum Opt. 5, 133 (1993); A. Kalocsai, J. Haus, Phys. Rev. A 49, 574 (1994).
[CrossRef] [PubMed]

Inochkin, M. V.

N. R. Belashenkov, S. V. Gagarskii, M. V. Inochkin, Opt. Spectrosc. (USSR) 66, 806 (1989); R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, E. W. Van Stryland, H. Vanherzeele, Opt. Lett. 17,28 (1992); M. L. Sundheimer, Ch. Bosshard, E. W. Van Stryland, G. I. Stegeman, J. D. Bierlein, Opt. Lett. 18, 1397 (1993).
[CrossRef] [PubMed]

Karamzin, Yu. N.

Yu. N. Karamzin, A. P. Sukhorukov, JETP Lett. 20, 339 (1974); M. J. Werner, P. D. Drummond, J. Opt. Soc. Am. B 10, 2390 (1993); Opt. Lett. 19, 613 (1994); K. Hayata, M. Koshiba, Phys. Rev. Lett. 71, 3275 (1993).
[CrossRef] [PubMed]

Menyuk, C. R.

C. R. Menyuk, J. Opt. Soc. Am. B 10, 1585 (1993).
[CrossRef]

C. R. Menyuk, R. Schiek, L. Torner, “Solitary waves due to χ(2): χ(2) cascading,” J. Opt. Soc. Am. B (to be published).

Schiek, R.

R. Schiek, J. Opt. Soc. Am. B 10, 1848 (1993).
[CrossRef]

C. R. Menyuk, R. Schiek, L. Torner, “Solitary waves due to χ(2): χ(2) cascading,” J. Opt. Soc. Am. B (to be published).

Segur, H.

M. J. Ablowitz, H. Segur, Solitons and the Inverse Scattering Transform (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1981).
[CrossRef]

Sheik-Bahae, M.

G. I. Stegeman, M. Sheik-Bahae, E. Van Stryland, G. Assanto, Opt. Lett. 18, 13 (1993).
[CrossRef] [PubMed]

G. Assanto, G. Stegeman, M. Sheik-Bahae, E. Van Stryland, Appl. Phys. Lett. 62, 1323 (1993); C. N. Ironside, J. S. Aitchison, J. M. Arnold, IEEE J. Quantum Electron. 29, 2650 (1993); P. St. J. Russell, Electron. Lett. 29, 1228 (1993).
[CrossRef]

Stegeman, G.

G. Assanto, G. Stegeman, M. Sheik-Bahae, E. Van Stryland, Appl. Phys. Lett. 62, 1323 (1993); C. N. Ironside, J. S. Aitchison, J. M. Arnold, IEEE J. Quantum Electron. 29, 2650 (1993); P. St. J. Russell, Electron. Lett. 29, 1228 (1993).
[CrossRef]

Stegeman, G. I.

Sukhorukov, A. P.

Yu. N. Karamzin, A. P. Sukhorukov, JETP Lett. 20, 339 (1974); M. J. Werner, P. D. Drummond, J. Opt. Soc. Am. B 10, 2390 (1993); Opt. Lett. 19, 613 (1994); K. Hayata, M. Koshiba, Phys. Rev. Lett. 71, 3275 (1993).
[CrossRef] [PubMed]

Torner, L.

C. R. Menyuk, R. Schiek, L. Torner, “Solitary waves due to χ(2): χ(2) cascading,” J. Opt. Soc. Am. B (to be published).

Van Stryland, E.

G. Assanto, G. Stegeman, M. Sheik-Bahae, E. Van Stryland, Appl. Phys. Lett. 62, 1323 (1993); C. N. Ironside, J. S. Aitchison, J. M. Arnold, IEEE J. Quantum Electron. 29, 2650 (1993); P. St. J. Russell, Electron. Lett. 29, 1228 (1993).
[CrossRef]

G. I. Stegeman, M. Sheik-Bahae, E. Van Stryland, G. Assanto, Opt. Lett. 18, 13 (1993).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

G. Assanto, G. Stegeman, M. Sheik-Bahae, E. Van Stryland, Appl. Phys. Lett. 62, 1323 (1993); C. N. Ironside, J. S. Aitchison, J. M. Arnold, IEEE J. Quantum Electron. 29, 2650 (1993); P. St. J. Russell, Electron. Lett. 29, 1228 (1993).
[CrossRef]

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

JETP Lett. (1)

Yu. N. Karamzin, A. P. Sukhorukov, JETP Lett. 20, 339 (1974); M. J. Werner, P. D. Drummond, J. Opt. Soc. Am. B 10, 2390 (1993); Opt. Lett. 19, 613 (1994); K. Hayata, M. Koshiba, Phys. Rev. Lett. 71, 3275 (1993).
[CrossRef] [PubMed]

Opt. Lett. (1)

Opt. Spectrosc. (1)

N. R. Belashenkov, S. V. Gagarskii, M. V. Inochkin, Opt. Spectrosc. (USSR) 66, 806 (1989); R. DeSalvo, D. J. Hagan, M. Sheik-Bahae, G. Stegeman, E. W. Van Stryland, H. Vanherzeele, Opt. Lett. 17,28 (1992); M. L. Sundheimer, Ch. Bosshard, E. W. Van Stryland, G. I. Stegeman, J. D. Bierlein, Opt. Lett. 18, 1397 (1993).
[CrossRef] [PubMed]

Quantum Opt. (1)

Q. Guo, Quantum Opt. 5, 133 (1993); A. Kalocsai, J. Haus, Phys. Rev. A 49, 574 (1994).
[CrossRef] [PubMed]

Other (2)

C. R. Menyuk, R. Schiek, L. Torner, “Solitary waves due to χ(2): χ(2) cascading,” J. Opt. Soc. Am. B (to be published).

M. J. Ablowitz, H. Segur, Solitons and the Inverse Scattering Transform (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1981).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Evolution of the amplitude of the fundamental wave: (a) β = 10, (b) β = 1. The dashed curves show the evolution of the corresponding linear waves. All values are scaled to the input amplitudes.

Fig. 2
Fig. 2

Same as in Fig. 1, with (a) β = 3, (b) β = −3.

Fig. 3
Fig. 3

Amplitudes at large distances (averaged over one oscillation period) as a function of the input second-harmonic amplitude. Solid curves, fundamental wave; dashed curves, second harmonic. All values are scaled to the solitary wave amplitudes A0 and B0.

Fig. 4
Fig. 4

Detail of the wave evolution. Dotted curves, ξ = 0; solid curves, ξ = 50. (a) a = 1, A = 2, B = 0; (b) a = 2, A = 3, B = 3; (c) a = 1, A = 2, B = 0, δ = 0.5; (d) a = 2, A = 3, B = 3, δ = 0.3.

Equations (3)

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i a 1 ξ - r 2 2 a 1 s 2 + a 1 * a 2 exp ( - i β ξ ) = 0 , i a 2 ξ - α 2 2 a 2 s 2 - i δ a 2 s + a 1 2 exp ( + i β ξ ) = 0 ,
a 1 ( ξ = 0 ) = A sech a ( s ) , a 2 ( ξ = 0 ) = B sech 2 ( s ) .
i a 1 ξ + 1 2 2 a 1 s 2 + 1 β a 1 2 a 1 0 ,

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