Abstract

We investigate analytically and numerically the existence and stability properties of three-wave solitons resulting from double-resonance (type I plus type II) parametric interaction in a purely quadratic nonlinear medium. The existence of a family of stable solitons for the double-resonance model is demonstrated in a broad parameter range. Moreover, these solitons are shown to exhibit multistability, a feature that is potentially useful for optical switching applications. Finally, we find and present a novel family of quasi solitons.

© 1999 Optical Society of America

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  1. J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. E 6, 1918 (1962).
  2. A. V. Buryak and Yu. S. Kivshar, Phys. Lett. A 197, 407 (1995); D. E. Pelinovsky, A. V. Buryak, and Yu. S. Kivshar, Phys. Rev. Lett. 75, 591 (1995).
    [CrossRef] [PubMed]
  3. H. T. Tran, Opt. Commun. 118, 581 (1995); D. Anderson, M. Lisak, and B. A. Malomed, Opt. Commun. 126, 251 (1996).
    [CrossRef]
  4. A. V. Buryak, Yu. S. Kivshar, and S. Trillo, J. Opt. Soc. Am. B 14, 3110 (1997).
    [CrossRef]
  5. A. D. Boardman, P. Bontemps, and K. Xie, Opt. Quantum Electron. 30, 891 (1998).
    [CrossRef]
  6. Yu. S. Kivshar, T. J. Alexander, and S. Saltiel, Opt. Lett. 24, 759 (1999); S. Saltiel, A. A. Sukhorukov, and S. M. Saltiel, in Nonlinear Guided Waves and Their Applications, 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), pp. 82–84.
    [CrossRef]
  7. M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, IEEE J. Quantum Electron. 28, 2631 (1992); G. D. Miller, R. G. Batchko, W. M. Tulloch, D. R. Weise, M. M. Fejer, and R. L. Byer, Opt. Lett. 22, 1834 (1997).
    [CrossRef]
  8. S. Trillo and G. Assanto, Opt. Lett. 19, 1825 (1994).
    [CrossRef]
  9. A. V. Buryak and Yu. S. Kivshar, Phys. Rev. Lett. 77, 3286 (1997).
    [CrossRef]
  10. Yu. S. Kivshar, D. E. Pelinovsky, T. Cretegny, and M. Peyrard, Phys. Rev. Lett. 80, 5032 (1998).
    [CrossRef]
  11. P. K. A. Wai, H. H. Chen, and Y. C. Lee, Phys. Rev. A 41, 426 (1990); D. J. Kaup, T. I. Lakoba, and B. A. Malomed, J. Opt. Soc. Am. B 14, 1199 (1997); V. E. Zakharov and E. A. Kuznetsov, JETP 86, 1035 (1998).
    [CrossRef] [PubMed]

1999 (1)

1998 (2)

A. D. Boardman, P. Bontemps, and K. Xie, Opt. Quantum Electron. 30, 891 (1998).
[CrossRef]

Yu. S. Kivshar, D. E. Pelinovsky, T. Cretegny, and M. Peyrard, Phys. Rev. Lett. 80, 5032 (1998).
[CrossRef]

1997 (2)

A. V. Buryak and Yu. S. Kivshar, Phys. Rev. Lett. 77, 3286 (1997).
[CrossRef]

A. V. Buryak, Yu. S. Kivshar, and S. Trillo, J. Opt. Soc. Am. B 14, 3110 (1997).
[CrossRef]

1995 (2)

A. V. Buryak and Yu. S. Kivshar, Phys. Lett. A 197, 407 (1995); D. E. Pelinovsky, A. V. Buryak, and Yu. S. Kivshar, Phys. Rev. Lett. 75, 591 (1995).
[CrossRef] [PubMed]

H. T. Tran, Opt. Commun. 118, 581 (1995); D. Anderson, M. Lisak, and B. A. Malomed, Opt. Commun. 126, 251 (1996).
[CrossRef]

1994 (1)

1992 (1)

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, IEEE J. Quantum Electron. 28, 2631 (1992); G. D. Miller, R. G. Batchko, W. M. Tulloch, D. R. Weise, M. M. Fejer, and R. L. Byer, Opt. Lett. 22, 1834 (1997).
[CrossRef]

1990 (1)

P. K. A. Wai, H. H. Chen, and Y. C. Lee, Phys. Rev. A 41, 426 (1990); D. J. Kaup, T. I. Lakoba, and B. A. Malomed, J. Opt. Soc. Am. B 14, 1199 (1997); V. E. Zakharov and E. A. Kuznetsov, JETP 86, 1035 (1998).
[CrossRef] [PubMed]

1962 (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. E 6, 1918 (1962).

Alexander, T. J.

Armstrong, J. A.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. E 6, 1918 (1962).

Assanto, G.

Bloembergen, N.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. E 6, 1918 (1962).

Boardman, A. D.

A. D. Boardman, P. Bontemps, and K. Xie, Opt. Quantum Electron. 30, 891 (1998).
[CrossRef]

Bontemps, P.

A. D. Boardman, P. Bontemps, and K. Xie, Opt. Quantum Electron. 30, 891 (1998).
[CrossRef]

Buryak, A. V.

A. V. Buryak and Yu. S. Kivshar, Phys. Rev. Lett. 77, 3286 (1997).
[CrossRef]

A. V. Buryak, Yu. S. Kivshar, and S. Trillo, J. Opt. Soc. Am. B 14, 3110 (1997).
[CrossRef]

A. V. Buryak and Yu. S. Kivshar, Phys. Lett. A 197, 407 (1995); D. E. Pelinovsky, A. V. Buryak, and Yu. S. Kivshar, Phys. Rev. Lett. 75, 591 (1995).
[CrossRef] [PubMed]

Byer, R. L.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, IEEE J. Quantum Electron. 28, 2631 (1992); G. D. Miller, R. G. Batchko, W. M. Tulloch, D. R. Weise, M. M. Fejer, and R. L. Byer, Opt. Lett. 22, 1834 (1997).
[CrossRef]

Chen, H. H.

P. K. A. Wai, H. H. Chen, and Y. C. Lee, Phys. Rev. A 41, 426 (1990); D. J. Kaup, T. I. Lakoba, and B. A. Malomed, J. Opt. Soc. Am. B 14, 1199 (1997); V. E. Zakharov and E. A. Kuznetsov, JETP 86, 1035 (1998).
[CrossRef] [PubMed]

Cretegny, T.

Yu. S. Kivshar, D. E. Pelinovsky, T. Cretegny, and M. Peyrard, Phys. Rev. Lett. 80, 5032 (1998).
[CrossRef]

Ducuing, J.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. E 6, 1918 (1962).

Fejer, M. M.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, IEEE J. Quantum Electron. 28, 2631 (1992); G. D. Miller, R. G. Batchko, W. M. Tulloch, D. R. Weise, M. M. Fejer, and R. L. Byer, Opt. Lett. 22, 1834 (1997).
[CrossRef]

Jundt, D. H.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, IEEE J. Quantum Electron. 28, 2631 (1992); G. D. Miller, R. G. Batchko, W. M. Tulloch, D. R. Weise, M. M. Fejer, and R. L. Byer, Opt. Lett. 22, 1834 (1997).
[CrossRef]

Kivshar, Yu. S.

Yu. S. Kivshar, T. J. Alexander, and S. Saltiel, Opt. Lett. 24, 759 (1999); S. Saltiel, A. A. Sukhorukov, and S. M. Saltiel, in Nonlinear Guided Waves and Their Applications, 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), pp. 82–84.
[CrossRef]

Yu. S. Kivshar, D. E. Pelinovsky, T. Cretegny, and M. Peyrard, Phys. Rev. Lett. 80, 5032 (1998).
[CrossRef]

A. V. Buryak, Yu. S. Kivshar, and S. Trillo, J. Opt. Soc. Am. B 14, 3110 (1997).
[CrossRef]

A. V. Buryak and Yu. S. Kivshar, Phys. Rev. Lett. 77, 3286 (1997).
[CrossRef]

A. V. Buryak and Yu. S. Kivshar, Phys. Lett. A 197, 407 (1995); D. E. Pelinovsky, A. V. Buryak, and Yu. S. Kivshar, Phys. Rev. Lett. 75, 591 (1995).
[CrossRef] [PubMed]

Lee, Y. C.

P. K. A. Wai, H. H. Chen, and Y. C. Lee, Phys. Rev. A 41, 426 (1990); D. J. Kaup, T. I. Lakoba, and B. A. Malomed, J. Opt. Soc. Am. B 14, 1199 (1997); V. E. Zakharov and E. A. Kuznetsov, JETP 86, 1035 (1998).
[CrossRef] [PubMed]

Magel, G. A.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, IEEE J. Quantum Electron. 28, 2631 (1992); G. D. Miller, R. G. Batchko, W. M. Tulloch, D. R. Weise, M. M. Fejer, and R. L. Byer, Opt. Lett. 22, 1834 (1997).
[CrossRef]

Pelinovsky, D. E.

Yu. S. Kivshar, D. E. Pelinovsky, T. Cretegny, and M. Peyrard, Phys. Rev. Lett. 80, 5032 (1998).
[CrossRef]

Pershan, P. S.

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. E 6, 1918 (1962).

Peyrard, M.

Yu. S. Kivshar, D. E. Pelinovsky, T. Cretegny, and M. Peyrard, Phys. Rev. Lett. 80, 5032 (1998).
[CrossRef]

Saltiel, S.

Tran, H. T.

H. T. Tran, Opt. Commun. 118, 581 (1995); D. Anderson, M. Lisak, and B. A. Malomed, Opt. Commun. 126, 251 (1996).
[CrossRef]

Trillo, S.

Wai, P. K. A.

P. K. A. Wai, H. H. Chen, and Y. C. Lee, Phys. Rev. A 41, 426 (1990); D. J. Kaup, T. I. Lakoba, and B. A. Malomed, J. Opt. Soc. Am. B 14, 1199 (1997); V. E. Zakharov and E. A. Kuznetsov, JETP 86, 1035 (1998).
[CrossRef] [PubMed]

Xie, K.

A. D. Boardman, P. Bontemps, and K. Xie, Opt. Quantum Electron. 30, 891 (1998).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, IEEE J. Quantum Electron. 28, 2631 (1992); G. D. Miller, R. G. Batchko, W. M. Tulloch, D. R. Weise, M. M. Fejer, and R. L. Byer, Opt. Lett. 22, 1834 (1997).
[CrossRef]

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

Opt. Commun. (1)

H. T. Tran, Opt. Commun. 118, 581 (1995); D. Anderson, M. Lisak, and B. A. Malomed, Opt. Commun. 126, 251 (1996).
[CrossRef]

Opt. Lett. (2)

Opt. Quantum Electron. (1)

A. D. Boardman, P. Bontemps, and K. Xie, Opt. Quantum Electron. 30, 891 (1998).
[CrossRef]

Phys. Lett. A (1)

A. V. Buryak and Yu. S. Kivshar, Phys. Lett. A 197, 407 (1995); D. E. Pelinovsky, A. V. Buryak, and Yu. S. Kivshar, Phys. Rev. Lett. 75, 591 (1995).
[CrossRef] [PubMed]

Phys. Rev. A (1)

P. K. A. Wai, H. H. Chen, and Y. C. Lee, Phys. Rev. A 41, 426 (1990); D. J. Kaup, T. I. Lakoba, and B. A. Malomed, J. Opt. Soc. Am. B 14, 1199 (1997); V. E. Zakharov and E. A. Kuznetsov, JETP 86, 1035 (1998).
[CrossRef] [PubMed]

Phys. Rev. E (1)

J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. E 6, 1918 (1962).

Phys. Rev. Lett. (2)

A. V. Buryak and Yu. S. Kivshar, Phys. Rev. Lett. 77, 3286 (1997).
[CrossRef]

Yu. S. Kivshar, D. E. Pelinovsky, T. Cretegny, and M. Peyrard, Phys. Rev. Lett. 80, 5032 (1998).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Soliton solutions from the lower family for various values of χ1e. Within this parameter range, solitons exhibit multistability. Left, χ2=1.0, Δ=-1, r=-1; right, χ2=0.1, Δ=-1, r=-1.

Fig. 2
Fig. 2

Change in local propagation constant β for a stable soliton before and after a collision with another soliton. Note the rapid jump of the β value after the collision. χ2=0.1, χ1e=0.2, Δ=-1, r=-1, C=0.2, δ=π/30.

Fig. 3
Fig. 3

Example of stable quasi-soliton generation. Equations (3) are modeled with the initial conditions V=1.5exp-x2/a2, a3.55, and U=W=0 for Δ=-10.0, r=+1, χ1e=0.0, and χ2=1.0.

Equations (5)

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

ivz+2vx2-β˜v+χ1ov*w+χ2u*w=0,iuz+2ux2-α˜u+χ1eu*w+χ2v*w=0,2iwz+2wx2-γ˜w+χ1ov22+χ1eu22+χ2vu=0,
Q=-+4w2+v2+u2dx.
iVZ+2VX2-βV+χ1oV*W+χ2U*W=0,iUZ+2UX2-αU+χ1eU*W+χ2V*W=0,2iWZ+2WX2-γW+χ1oV22+χ1oU22+χ2VU=0,
V=a sech2x/λ, U=b sech2x/λ,W=c sech2x/λ,
VX,Z=V0X-CZexpiCX/2-iC2Z/4,UX,Z=U0X-CZexpiCX/2-iC2Z/4,WX,Z=W0X-CZexpiCX-iC2Z/2,

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