Abstract

We address the important problem of excitation of gap solitons of a parametric nature, which are sustained in periodically corrugated frequency-doubling media near Bragg resonance with both the fundamental frequency and its second harmonic. We demonstrate that a zero-velocity soliton can be trapped in a finite Bragg structure by the quiescence of two counterpropagating moving solitons, which in turn might be formed by injection of appropriate light pulses at a single carrier frequency.

© 1998 Optical Society of America

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References

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  1. C. M. De Sterke and J. E. Sipe, in Progress in Optics XXXIII, E. Wolf, ed. (Elsevier, Amsterdam, 1994), Chap. III; Phys. Rev. A 39, 5163 (1989).
    [Crossref]
  2. B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, Phys. Rev. Lett. 76, 1627 (1996).
    [Crossref] [PubMed]
  3. C. Conti, S. Trillo, and G. Assanto, Phys. Rev. Lett. 78, 2341 (1997); Opt. Lett. 22, 445 (1997).
    [Crossref]
  4. H. He and P. D. Drummond, Phys. Rev. Lett. 78, 4311 (1997).
    [Crossref]
  5. T. Peschel, U. Peschel, F. Lederer, and B. A. Malomed, Phys. Rev. E 55, 4730 (1997).
    [Crossref]
  6. C. Conti, S. Trillo, and G. Assanto, “Optical gap solitons via second-harmonic generation:?exact solitary solutions,” Phys. Rev. E (to be published).
  7. C. Conti, G. Assanto, and S. Trillo, Opt. Lett. 22, 1350 (1997).
    [Crossref]
  8. A. V. Buryak and Y. S. Kivshar, Opt. Lett. 19, 1612 (1994); Phys. Lett. A 197, 407 (1995).
    [Crossref] [PubMed]
  9. D. Baboiu, G. I. Stegeman, and L. Torner, Opt. Lett. 20, 2282 (1995).
    [Crossref]
  10. C. Etrich, U. Peschel, F. Lederer, and B. A. Malomed, Phys. Rev. A 52, 3444 (1995).
    [Crossref]
  11. C. Etrich, U. Peschel, F. Lederer, B. A. Malomed, and Y. S. Kivshar, Phys. Rev. A 54, 4321 (1996).
  12. J. Söchtig, R. Grob, I. Baumann, W. Sohler, H. Shultz, and R. Widmer, Electron. Lett. 31, 551 (1995).
    [Crossref]

1997 (4)

C. Conti, S. Trillo, and G. Assanto, Phys. Rev. Lett. 78, 2341 (1997); Opt. Lett. 22, 445 (1997).
[Crossref]

H. He and P. D. Drummond, Phys. Rev. Lett. 78, 4311 (1997).
[Crossref]

T. Peschel, U. Peschel, F. Lederer, and B. A. Malomed, Phys. Rev. E 55, 4730 (1997).
[Crossref]

C. Conti, G. Assanto, and S. Trillo, Opt. Lett. 22, 1350 (1997).
[Crossref]

1996 (2)

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

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, Phys. Rev. Lett. 76, 1627 (1996).
[Crossref] [PubMed]

1995 (3)

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

J. Söchtig, R. Grob, I. Baumann, W. Sohler, H. Shultz, and R. Widmer, Electron. Lett. 31, 551 (1995).
[Crossref]

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

1994 (1)

Assanto, G.

C. Conti, S. Trillo, and G. Assanto, Phys. Rev. Lett. 78, 2341 (1997); Opt. Lett. 22, 445 (1997).
[Crossref]

C. Conti, G. Assanto, and S. Trillo, Opt. Lett. 22, 1350 (1997).
[Crossref]

C. Conti, S. Trillo, and G. Assanto, “Optical gap solitons via second-harmonic generation:?exact solitary solutions,” Phys. Rev. E (to be published).

Baboiu, D.

Baumann, I.

J. Söchtig, R. Grob, I. Baumann, W. Sohler, H. Shultz, and R. Widmer, Electron. Lett. 31, 551 (1995).
[Crossref]

Buryak, A. V.

Conti, C.

C. Conti, S. Trillo, and G. Assanto, Phys. Rev. Lett. 78, 2341 (1997); Opt. Lett. 22, 445 (1997).
[Crossref]

C. Conti, G. Assanto, and S. Trillo, Opt. Lett. 22, 1350 (1997).
[Crossref]

C. Conti, S. Trillo, and G. Assanto, “Optical gap solitons via second-harmonic generation:?exact solitary solutions,” Phys. Rev. E (to be published).

de Sterke, C. M.

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, Phys. Rev. Lett. 76, 1627 (1996).
[Crossref] [PubMed]

C. M. De Sterke and J. E. Sipe, in Progress in Optics XXXIII, E. Wolf, ed. (Elsevier, Amsterdam, 1994), Chap. III; Phys. Rev. A 39, 5163 (1989).
[Crossref]

Drummond, P. D.

H. He and P. D. Drummond, Phys. Rev. Lett. 78, 4311 (1997).
[Crossref]

Eggleton, B. J.

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, Phys. Rev. Lett. 76, 1627 (1996).
[Crossref] [PubMed]

Etrich, C.

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

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

Grob, R.

J. Söchtig, R. Grob, I. Baumann, W. Sohler, H. Shultz, and R. Widmer, Electron. Lett. 31, 551 (1995).
[Crossref]

He, H.

H. He and P. D. Drummond, Phys. Rev. Lett. 78, 4311 (1997).
[Crossref]

Kivshar, Y. S.

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

A. V. Buryak and Y. S. Kivshar, Opt. Lett. 19, 1612 (1994); Phys. Lett. A 197, 407 (1995).
[Crossref] [PubMed]

Krug, P. A.

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, Phys. Rev. Lett. 76, 1627 (1996).
[Crossref] [PubMed]

Lederer, F.

T. Peschel, U. Peschel, F. Lederer, and B. A. Malomed, Phys. Rev. E 55, 4730 (1997).
[Crossref]

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

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

Malomed, B. A.

T. Peschel, U. Peschel, F. Lederer, and B. A. Malomed, Phys. Rev. E 55, 4730 (1997).
[Crossref]

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

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

Peschel, T.

T. Peschel, U. Peschel, F. Lederer, and B. A. Malomed, Phys. Rev. E 55, 4730 (1997).
[Crossref]

Peschel, U.

T. Peschel, U. Peschel, F. Lederer, and B. A. Malomed, Phys. Rev. E 55, 4730 (1997).
[Crossref]

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

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

Shultz, H.

J. Söchtig, R. Grob, I. Baumann, W. Sohler, H. Shultz, and R. Widmer, Electron. Lett. 31, 551 (1995).
[Crossref]

Sipe, J. E.

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, Phys. Rev. Lett. 76, 1627 (1996).
[Crossref] [PubMed]

C. M. De Sterke and J. E. Sipe, in Progress in Optics XXXIII, E. Wolf, ed. (Elsevier, Amsterdam, 1994), Chap. III; Phys. Rev. A 39, 5163 (1989).
[Crossref]

Slusher, R. E.

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, Phys. Rev. Lett. 76, 1627 (1996).
[Crossref] [PubMed]

Söchtig, J.

J. Söchtig, R. Grob, I. Baumann, W. Sohler, H. Shultz, and R. Widmer, Electron. Lett. 31, 551 (1995).
[Crossref]

Sohler, W.

J. Söchtig, R. Grob, I. Baumann, W. Sohler, H. Shultz, and R. Widmer, Electron. Lett. 31, 551 (1995).
[Crossref]

Stegeman, G. I.

Torner, L.

Trillo, S.

C. Conti, G. Assanto, and S. Trillo, Opt. Lett. 22, 1350 (1997).
[Crossref]

C. Conti, S. Trillo, and G. Assanto, Phys. Rev. Lett. 78, 2341 (1997); Opt. Lett. 22, 445 (1997).
[Crossref]

C. Conti, S. Trillo, and G. Assanto, “Optical gap solitons via second-harmonic generation:?exact solitary solutions,” Phys. Rev. E (to be published).

Widmer, R.

J. Söchtig, R. Grob, I. Baumann, W. Sohler, H. Shultz, and R. Widmer, Electron. Lett. 31, 551 (1995).
[Crossref]

Electron. Lett. (1)

J. Söchtig, R. Grob, I. Baumann, W. Sohler, H. Shultz, and R. Widmer, Electron. Lett. 31, 551 (1995).
[Crossref]

Opt. Lett. (3)

Phys. Rev. A (2)

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

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

Phys. Rev. E (1)

T. Peschel, U. Peschel, F. Lederer, and B. A. Malomed, Phys. Rev. E 55, 4730 (1997).
[Crossref]

Phys. Rev. Lett. (3)

B. J. Eggleton, R. E. Slusher, C. M. de Sterke, P. A. Krug, and J. E. Sipe, Phys. Rev. Lett. 76, 1627 (1996).
[Crossref] [PubMed]

C. Conti, S. Trillo, and G. Assanto, Phys. Rev. Lett. 78, 2341 (1997); Opt. Lett. 22, 445 (1997).
[Crossref]

H. He and P. D. Drummond, Phys. Rev. Lett. 78, 4311 (1997).
[Crossref]

Other (2)

C. Conti, S. Trillo, and G. Assanto, “Optical gap solitons via second-harmonic generation:?exact solitary solutions,” Phys. Rev. E (to be published).

C. M. De Sterke and J. E. Sipe, in Progress in Optics XXXIII, E. Wolf, ed. (Elsevier, Amsterdam, 1994), Chap. III; Phys. Rev. A 39, 5163 (1989).
[Crossref]

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Figures (4)

Fig. 1
Fig. 1

Scheme of the double-bandgap structure.

Fig. 2
Fig. 2

Injection of a FF pulse in a semi-infinite nonlinear grating κ2=1, v2=0.5. (a), (b) Excitation of a two-color gap soliton propagating at low velocity in the LB–LB case. (c), (d) Dispersive propagation in the UB–UB case, in which the soliton is not supported. We show the contour levels of the total FF [(a), (b)] and SH [(c), (d)] intensities.

Fig. 3
Fig. 3

Formation of a stationary gap soliton by inelastic collision of two counterpropagating low-velocity solitons: (a) FF, (b) generated SH.

Fig. 4
Fig. 4

SHG in a transparent grating at FF (FF out of gap). The collision generates a SH dispersive wave: (a) FF, (b) SH.

Equations (4)

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

i±u1, z±+v1-1u1, t±+δ1u1±+κ1u1+u1±*u2±=0, i±u2, z±+v2-1u2, t±+δ2u2±+κ2u2+u1±2/2=0,
[um+z, tum-z, t]=amz, tfm±expiQmz+iνmt,
ita1-ω1z2a1+γ1a1*a2 exp-iβt=0, ita2-ω2z2a2+γ2a12/2expiβt=0,
(um+um-)=Am(1ρm)Umζ+(ρm-1)12mVUmζ+izUmζexpimVz,

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