Abstract

Recently it was shown that in quasi-phase-matched quadratic media the average intensities are subject to an induced Kerr effect. We analytically study the influence of this induced cubic nonlinearity on the amplitude and phase modulation of the fundamental wave and predict efficient all-optical switching.

© 1998 Optical Society of America

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References

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  1. For a general review see G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum Electron. 28, 1691 (1996).
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    [CrossRef]
  4. J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918 (1962).
    [CrossRef]
  5. E. J. Lim, M. M. Fejer, and R. L. Byer, Electron. Lett. 25, 174 (1989); K. Mizuuchi, K. Yamamoto, and T. Taniuchi, Appl. Phys. Lett. 58, 2732 (1991); T. Fujimura, T. Suhara, and H. Nishihara, Electron. Lett. 27, 1207 (1991).
    [CrossRef]
  6. C. B. Clausen, O. Bang, and Yu. S. Kivshar, Phys. Rev. Lett. 78, 4749 (1997).
    [CrossRef]
  7. L. Torner and G. I. Stegeman, J. Opt. Soc. Am. B 14, 3127 (1997).
    [CrossRef]
  8. A. Kobyakov and F. Lederer, Phys. Rev. A 54, 3455 (1996).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  12. C. N. Ironside, J. S. Aitchison, and J. M. Arnold, IEEE J. Quantum Electron. 29, 2650 (1993).
    [CrossRef]
  13. M. Asobe, I. Yokohama, H. Itoh, and T. Kaino, Opt. Lett. 22, 274 (1997).
    [CrossRef] [PubMed]

1997 (3)

1996 (2)

For a general review see G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum Electron. 28, 1691 (1996).
[CrossRef]

A. Kobyakov and F. Lederer, Phys. Rev. A 54, 3455 (1996).
[CrossRef] [PubMed]

1995 (2)

1993 (1)

C. N. Ironside, J. S. Aitchison, and J. M. Arnold, IEEE J. Quantum Electron. 29, 2650 (1993).
[CrossRef]

1992 (1)

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, IEEE J. Quantum Electron. 28, 2631 (1992).
[CrossRef]

1991 (1)

1989 (1)

E. J. Lim, M. M. Fejer, and R. L. Byer, Electron. Lett. 25, 174 (1989); K. Mizuuchi, K. Yamamoto, and T. Taniuchi, Appl. Phys. Lett. 58, 2732 (1991); T. Fujimura, T. Suhara, and H. Nishihara, Electron. Lett. 27, 1207 (1991).
[CrossRef]

1962 (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Abramowitz, M.

M. Abramowitz and I. Stegun, Handbook of Mathematical Functions, 9th ed. (Dover, New York, 1972), p. 599.

Aitchison, J. S.

C. N. Ironside, J. S. Aitchison, and J. M. Arnold, IEEE J. Quantum Electron. 29, 2650 (1993).
[CrossRef]

Armstrong, J. A.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Arnold, J. M.

C. N. Ironside, J. S. Aitchison, and J. M. Arnold, IEEE J. Quantum Electron. 29, 2650 (1993).
[CrossRef]

Asobe, M.

Baek, Y.

Banerjee, P. P.

Bang, O.

C. B. Clausen, O. Bang, and Yu. S. Kivshar, Phys. Rev. Lett. 78, 4749 (1997).
[CrossRef]

Bloembergen, N.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Byer, R. L.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, IEEE J. Quantum Electron. 28, 2631 (1992).
[CrossRef]

E. J. Lim, M. M. Fejer, and R. L. Byer, Electron. Lett. 25, 174 (1989); K. Mizuuchi, K. Yamamoto, and T. Taniuchi, Appl. Phys. Lett. 58, 2732 (1991); T. Fujimura, T. Suhara, and H. Nishihara, Electron. Lett. 27, 1207 (1991).
[CrossRef]

Caimi, F. C.

Choe, W.

Clausen, C. B.

C. B. Clausen, O. Bang, and Yu. S. Kivshar, Phys. Rev. Lett. 78, 4749 (1997).
[CrossRef]

Ducuing, J.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Fejer, M. M.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, IEEE J. Quantum Electron. 28, 2631 (1992).
[CrossRef]

E. J. Lim, M. M. Fejer, and R. L. Byer, Electron. Lett. 25, 174 (1989); K. Mizuuchi, K. Yamamoto, and T. Taniuchi, Appl. Phys. Lett. 58, 2732 (1991); T. Fujimura, T. Suhara, and H. Nishihara, Electron. Lett. 27, 1207 (1991).
[CrossRef]

Hagan, D. J.

For a general review see G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum Electron. 28, 1691 (1996).
[CrossRef]

Ironside, C. N.

C. N. Ironside, J. S. Aitchison, and J. M. Arnold, IEEE J. Quantum Electron. 29, 2650 (1993).
[CrossRef]

Itoh, H.

Jundt, D. H.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, IEEE J. Quantum Electron. 28, 2631 (1992).
[CrossRef]

Kaino, T.

Kivshar, Yu. S.

C. B. Clausen, O. Bang, and Yu. S. Kivshar, Phys. Rev. Lett. 78, 4749 (1997).
[CrossRef]

Kobyakov, A.

A. Kobyakov and F. Lederer, Phys. Rev. A 54, 3455 (1996).
[CrossRef] [PubMed]

Lederer, F.

A. Kobyakov and F. Lederer, Phys. Rev. A 54, 3455 (1996).
[CrossRef] [PubMed]

Lim, E. J.

E. J. Lim, M. M. Fejer, and R. L. Byer, Electron. Lett. 25, 174 (1989); K. Mizuuchi, K. Yamamoto, and T. Taniuchi, Appl. Phys. Lett. 58, 2732 (1991); T. Fujimura, T. Suhara, and H. Nishihara, Electron. Lett. 27, 1207 (1991).
[CrossRef]

Magel, G. A.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, IEEE J. Quantum Electron. 28, 2631 (1992).
[CrossRef]

Pershan, P. S.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Sceats, M.

Y. Zhao, G. Town, and M. Sceats, Opt. Commun. 115, 129 (1995).
[CrossRef]

Schiek, R.

Stegeman, G. I.

Stegun, I.

M. Abramowitz and I. Stegun, Handbook of Mathematical Functions, 9th ed. (Dover, New York, 1972), p. 599.

Torner, L.

L. Torner and G. I. Stegeman, J. Opt. Soc. Am. B 14, 3127 (1997).
[CrossRef]

For a general review see G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum Electron. 28, 1691 (1996).
[CrossRef]

Town, G.

Y. Zhao, G. Town, and M. Sceats, Opt. Commun. 115, 129 (1995).
[CrossRef]

Yokohama, I.

Zhao, Y.

Y. Zhao, G. Town, and M. Sceats, Opt. Commun. 115, 129 (1995).
[CrossRef]

Electron. Lett. (1)

E. J. Lim, M. M. Fejer, and R. L. Byer, Electron. Lett. 25, 174 (1989); K. Mizuuchi, K. Yamamoto, and T. Taniuchi, Appl. Phys. Lett. 58, 2732 (1991); T. Fujimura, T. Suhara, and H. Nishihara, Electron. Lett. 27, 1207 (1991).
[CrossRef]

IEEE J. Quantum Electron. (2)

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, IEEE J. Quantum Electron. 28, 2631 (1992).
[CrossRef]

C. N. Ironside, J. S. Aitchison, and J. M. Arnold, IEEE J. Quantum Electron. 29, 2650 (1993).
[CrossRef]

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

Opt. Commun. (1)

Y. Zhao, G. Town, and M. Sceats, Opt. Commun. 115, 129 (1995).
[CrossRef]

Opt. Lett. (2)

Opt. Quantum Electron. (1)

For a general review see G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum Electron. 28, 1691 (1996).
[CrossRef]

Phys. Rev. (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Phys. Rev. A (1)

A. Kobyakov and F. Lederer, Phys. Rev. A 54, 3455 (1996).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

C. B. Clausen, O. Bang, and Yu. S. Kivshar, Phys. Rev. Lett. 78, 4749 (1997).
[CrossRef]

Other (1)

M. Abramowitz and I. Stegun, Handbook of Mathematical Functions, 9th ed. (Dover, New York, 1972), p. 599.

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Figures (3)

Fig. 1
Fig. 1

Domains in the parameter plane σ, q with different characteristics of the polynomial fu: I, Δ<0; II, Δ>0. The separatrix is marked by the dashed line, and the inset is a magnification of the region near the separatrix.

Fig. 2
Fig. 2

Analytically calculated spatial evolution of the intensity ρ2ξ and the phase ϕξ of the FW (thick curves). A, q=-0.0195, σ=0.04; B, q=-0.02, σ=0.0388 (see Fig.  1). Thin curves, the corresponding results of direct numerical integration of Eqs.  (1).

Fig. 3
Fig. 3

Normalized FW irradiance and phase shift ϕ versus normalized input intensity I/Isep=Γ/Γsep2, with Γsep=15.8, σsep=6.3×10-3.

Equations (9)

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

idWdz+gzW*V exp-iβz=0, idVdz+gzW2 expiβz=0.
idw0dz-iχw0*v0+αw02-v02w0=0, idv0dz-β~v0+iχw02-2αw02v0=0,
ρ·=Γρμ cos θ, μ·=-Γρ2 cos θ, θ·=2κ+Γρ2/μ-2 µsin θ+2γ2ρ2-μ2,
ϕ·=-Γμ sin θ+γρ2-μ2.
Δ27D2+22C2+9CD-C2-40.
uξ=u3 sn2(rξ|m)/[sn2(rξ|m)-1/p],
p=u1u1-u3, m=u1u3-u2u2u3-u1, r=32σu2u3-u11/2.
ϕξ=a0ξ+a1Π(p; Φ|m)+a2Π[p1-u3; Φ|m],
ϕT=π1+2q/σ[1-Λ0(ϑ1|m)]31-u1u2-1u3-11/2+π3[1-Λ0(ϑ2|m)]+σ2-u1rKm,

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