Abstract

Temporal Bragg solitary waves in the form of collinear three-wave weakly coupled states are studied theoretically and experimentally in a two-mode optical waveguide, exhibiting square-law nonlinearity. The dynamics of shaping their optical components, bright and dark, is studied, and the roles of localizing pulse width and phase mismatch are revealed.

© 2003 Optical Society of America

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References

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  1. A.P.Sukhorukov. Nonlinear Wave Interactions in Optics and Radiophysics. (Nauka Press, Moscow. 1988).
  2. A. S.Shcherbakov. A three-wave interaction. Stationary coup led states. (St. Petersburg State Technical University Press, St. Petersburg. 1998).
  3. A.S.Shcherbakov and A.Aguirre Lopez. �??Observation of the optical components inherent in multi-wave non-collinear acousto-optical coupled states.�?? Opt. Express 10, 1398-1403 (2002), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-24-1398">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-10-24-1398</a>.
    [CrossRef] [PubMed]
  4. R.K.Dodd, J.C.Eilbeck, J.D.Gibbon, and H.C.Morris. Solitons and Nonlinear Wave Equations. (Academic Press, Orlando. 1984).
  5. R. Rajaraman. Solitons and Instantons, North-Holland Publishing Company, Amsterdam (1982).
  6. E.Kamke. Differentialgleichungen. Losungmethoden und Losungen. Part I (Chelsea Co. NY. 1974).
  7. F.Yu. Introduction to Information Optics. (Academic Press, San Diego. 2001).
  8. D.E.Pelinovsky and Yu.S.Kivshar, �??Stability criterion for multi-component solitary waves,�?? Phys. Rev. E 62, 8668-8676 (2000).
    [CrossRef]

Opt. Express (1)

Phys. Rev. E (1)

D.E.Pelinovsky and Yu.S.Kivshar, �??Stability criterion for multi-component solitary waves,�?? Phys. Rev. E 62, 8668-8676 (2000).
[CrossRef]

Other (6)

A.P.Sukhorukov. Nonlinear Wave Interactions in Optics and Radiophysics. (Nauka Press, Moscow. 1988).

A. S.Shcherbakov. A three-wave interaction. Stationary coup led states. (St. Petersburg State Technical University Press, St. Petersburg. 1998).

R.K.Dodd, J.C.Eilbeck, J.D.Gibbon, and H.C.Morris. Solitons and Nonlinear Wave Equations. (Academic Press, Orlando. 1984).

R. Rajaraman. Solitons and Instantons, North-Holland Publishing Company, Amsterdam (1982).

E.Kamke. Differentialgleichungen. Losungmethoden und Losungen. Part I (Chelsea Co. NY. 1974).

F.Yu. Introduction to Information Optics. (Academic Press, San Diego. 2001).

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Figures (3)

Fig. 1.
Fig. 1.

Intensity of the scattered optical component (vertical axis) versus the time τ=x/v and the waveguide length L0: a. τ0C/2; b. τ0C; c. 3τC/4<τ0<2τC; d. τ0=2τC.

Fig. 2
Fig. 2

The incident (upper lines) and scattered (bottom lines) light intensities with Δf=0.4 MHz in a two-mode waveguide: a. τ0=0.8 µs; b. τ0C=2.5 µs; c. τ0=4.2 µs; d. τ0=2τC=5.0 µs.

Fig. 3.
Fig. 3.

The incident (upper lines) and scattered (bottom lines) light intensities in a two-mode waveguide: a. τ0C=2.5 µs; Δf=0.4 MHz; N=1, b. τ0=3 τC=7.5 µs; Δf=0.4 MHz; N=3 c. τ0C=2.5 µs; Δf=1.2 MHz; N=3 (the amplitude scale is enlarged nine times).

Equations (12)

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d C 0 dx = C 1 C 2 * exp ( 2 i q x ) , d C 1 dx = C 0 C 2 exp ( 2 i q x ) , d C 2 dx = C 1 C 0 * exp ( 2 i q x ) ,
1 4 [ d ( a k 2 ) dx ] 2 + ζ k 2 + a k 4 ( E k + q 2 ) + ( 1 ) k a k 6 + λ k a k 2 = 0 , d φ k dx = ζ k a k 2 + ( 1 ) k q .
a k 2 = α k 2 + b k 2 , b 0 2 = β 2 cn 2 [ η ( x x 0 ) ; κ ] , b 1 2 = β 2 sn 2 [ η ( x x 0 ) ; κ ] , b 2 2 = η 2 dn 2 [ η ( x x 0 ) ; κ ] .
d b k dx = ( 1 ) k + 1 b n b m , b 1 2 b 2 2 + 2 b 0 2 = F 0 , b 0 2 + b 2 2 + 2 b 1 2 = F 1 , b 0 2 b 1 2 2 b 2 2 = F 2 ,
( a ) d 2 b k d x 2 = 2 q k b k 3 + p k b k , ( b ) U k ( b k ) = q k 2 b k 4 p k 2 b k 2 + H k ,
C 0 x = C 1 U * ( x vt ) exp ( 2 iq x ) , C 1 x = C 0 U ( x vt ) exp ( 2 iq x ) .
2 a 0,1 x 2 ( 1 u u x ) a 0,1 x + ( u 2 γ 0,1 2 ± 2 q γ 0,1 ) a 0,1 = 0 ,
2 ( γ 0,1 q ) a 0,1 x + ( γ 0,1 x γ 0,1 u u x ) a 0,1 = 0 .
C 0 2 = q 2 U 0 2 + q 2 + U 0 2 U 0 2 + q 2 cos 2 ( x U 0 2 + q 2 ) ,
C 1 2 = U 0 2 U 0 2 + q 2 sin 2 ( x U 0 2 + q 2 ) .
C 0 2 = q 2 U 0 2 + q 2 + U 0 2 U 0 2 + q 2 cos 2 ( α x 2 2 U 0 2 + q 2 ) ,
C 1 2 = U 0 2 U 0 2 + q 2 sin 2 ( α x 2 2 U 0 2 + q 2 ) .

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