Abstract

Three- and four-wave spatial Bragg solitons in the form of weakly coupled states, originating with one- and two-phonon non-collinear scattering of light in anisotropic medium, are uncovered. The spatial-frequency distributions of their optical components are investigated both theoretically and experimentally.

© 2002 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, Moscow, 1988).
  2. A. S. Shcherbakov, A three-wave interaction. Stationary coupled states, (Saint-Petersburg Technical University, St. Petersburg, 1998).
  3. A. I. Maimistov, Nonlinear Optical Waves, (Kluwer, Boston, 1999).
  4. A. S. Shcherbakov, “Properties of solitary three-wave coupled states in a two-mode optical waveguide,” in Nonlinear Guided Waves and Their applications, OSA Technical Digest (Optical Society of America, Washington DC, 2001), pp. 100–102.
  5. A. S. Shcherbakov, “Shaping the optical components of solitary three-wave weakly coupled states in a two-mode crystalline waveguide,” in Nonlinear Guided Waves and Their Applications, OSA Technical Digest (Optical Society of America, Washington DC, 2002), NLMD7, pp.1–3.
  6. V. I. Balakshy, V. N. Parygin, and L. I. Chirkov, Physical Principles of Acousto-Optics, (Radio i Svyaz, Moscow, 1985).
  7. A. Korpel, Acousto-Optics, (Marcel Dekker, New-York, 1988).
  8. F. Yu, Introduction to Information Optics, (Academic Press, San Diego, 2001).
  9. D. E. Pelinovsky and Yu. S. Kivshar, “Stability criterion for multicomponent solitary waves,” Phys. Rev. E 62, 8668–8676 (2000).
    [Crossref]

2000 (1)

D. E. Pelinovsky and Yu. S. Kivshar, “Stability criterion for multicomponent solitary waves,” Phys. Rev. E 62, 8668–8676 (2000).
[Crossref]

Balakshy, V. I.

V. I. Balakshy, V. N. Parygin, and L. I. Chirkov, Physical Principles of Acousto-Optics, (Radio i Svyaz, Moscow, 1985).

Chirkov, L. I.

V. I. Balakshy, V. N. Parygin, and L. I. Chirkov, Physical Principles of Acousto-Optics, (Radio i Svyaz, Moscow, 1985).

Kivshar, Yu. S.

D. E. Pelinovsky and Yu. S. Kivshar, “Stability criterion for multicomponent solitary waves,” Phys. Rev. E 62, 8668–8676 (2000).
[Crossref]

Korpel, A.

A. Korpel, Acousto-Optics, (Marcel Dekker, New-York, 1988).

Maimistov, A. I.

A. I. Maimistov, Nonlinear Optical Waves, (Kluwer, Boston, 1999).

Parygin, V. N.

V. I. Balakshy, V. N. Parygin, and L. I. Chirkov, Physical Principles of Acousto-Optics, (Radio i Svyaz, Moscow, 1985).

Pelinovsky, D. E.

D. E. Pelinovsky and Yu. S. Kivshar, “Stability criterion for multicomponent solitary waves,” Phys. Rev. E 62, 8668–8676 (2000).
[Crossref]

Shcherbakov, A. S.

A. S. Shcherbakov, “Properties of solitary three-wave coupled states in a two-mode optical waveguide,” in Nonlinear Guided Waves and Their applications, OSA Technical Digest (Optical Society of America, Washington DC, 2001), pp. 100–102.

A. S. Shcherbakov, “Shaping the optical components of solitary three-wave weakly coupled states in a two-mode crystalline waveguide,” in Nonlinear Guided Waves and Their Applications, OSA Technical Digest (Optical Society of America, Washington DC, 2002), NLMD7, pp.1–3.

A. S. Shcherbakov, A three-wave interaction. Stationary coupled states, (Saint-Petersburg Technical University, St. Petersburg, 1998).

Sukhorukov, A. P.

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

Yu, F.

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

Phys. Rev. E (1)

D. E. Pelinovsky and Yu. S. Kivshar, “Stability criterion for multicomponent solitary waves,” Phys. Rev. E 62, 8668–8676 (2000).
[Crossref]

Other (8)

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

A. S. Shcherbakov, A three-wave interaction. Stationary coupled states, (Saint-Petersburg Technical University, St. Petersburg, 1998).

A. I. Maimistov, Nonlinear Optical Waves, (Kluwer, Boston, 1999).

A. S. Shcherbakov, “Properties of solitary three-wave coupled states in a two-mode optical waveguide,” in Nonlinear Guided Waves and Their applications, OSA Technical Digest (Optical Society of America, Washington DC, 2001), pp. 100–102.

A. S. Shcherbakov, “Shaping the optical components of solitary three-wave weakly coupled states in a two-mode crystalline waveguide,” in Nonlinear Guided Waves and Their Applications, OSA Technical Digest (Optical Society of America, Washington DC, 2002), NLMD7, pp.1–3.

V. I. Balakshy, V. N. Parygin, and L. I. Chirkov, Physical Principles of Acousto-Optics, (Radio i Svyaz, Moscow, 1985).

A. Korpel, Acousto-Optics, (Marcel Dekker, New-York, 1988).

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

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Figures (5)

Fig. 1.
Fig. 1.

Spatial-frequency distributions for optical components in a two-pulse three-wave weakly coupled state with q = 1, I = 1, n = 2, and L = 2π : (a) the zero-th order of scattering; (b) the first order of scattering. The distribution (b) is locked with η = 0 .

Fig. 2.
Fig. 2.

Distributions for the triplet of optical components in a multi-pulse four-wave weakly coupled state with q = 1, I = 1, and x = 2π : a five-pulse component of incident light in the zero-th order of scattering (a); a ten-pulse component in the first order (b); a five-pulse component in the second order (c). The distributions (b) and (c) are completely locked with η1 = 0 .

Fig. 3.
Fig. 3.

Schematic arrangement of the experiment (a) and the simplest distribution of optical components inside the rectangular acoustic pulse for a non-collinear four-wave weakly coupled state (b), see Eqs. (7) with n = 1.

Fig. 4.
Fig. 4.

Oscilloscope traces for the intensities of the optical components in three-wave coupled states (m = 1, 2) versus the product qx at various values of the frequency detuning Δf.

Fig. 5.
Fig. 5.

Oscilloscope traces for the intensities of the optical components in four-wave coupled states versus the product qx at various values of the frequency detuning Δf.

Equations (11)

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d C 0 dx = q 1 C 1 exp ( 2 iηx ) , d C 1 dx = q 0 C 0 exp ( 2 iηx ) .
C 0 2 = η 2 q 2 + η 2 + q 2 q 2 + η 2 cos 2 ( x q 2 + η 2 ) , C 1 2 = q 2 q 2 + η 2 sin 2 ( x q 2 + η 2 ) .
d C 0 dx = q C 1 exp ( i η 0 x ) ,
d C 1 dx = q [ C 0 exp ( i η 0 x ) C 2 exp ( i η 1 x ] ,
d C 2 dx = q C 1 exp ( i η 1 x ) .
C 0 ( x ) = iI { 1 + q 2 ( η a 0 ) a 0 ( a 0 a 1 ) ( a 0 a 2 ) [ 1 exp ( i a 0 x ) ]
q 2 ( η a 1 ) a 1 ( a 2 a 1 ) ( a 0 a 1 ) [ 1 exp ( i a 1 x ) ] + q 2 ( η a 2 ) a 2 ( a 2 a 1 ) ( a 0 a 2 ) [ 1 exp ( i a 2 x ) ] } ,
C 1 ( x ) = qI ( η a 0 ) ( a 0 a 1 ) ( a 0 a 2 ) exp [ i ( η 0 a 1 ) x ]
qI ( η a 1 ) ( a 2 a 1 ) ( a 0 a 1 ) exp [ i ( η 0 a 1 ) x ] + qI ( η a 2 ) ( a 2 a 1 ) ( a 0 a 2 ) exp [ i ( η 0 a 2 ) x ] } ,
C 2 ( x ) = i q 2 I { 1 exp [ i ( η a 0 ) x ] ( a 0 a 1 ) ( a 0 a 2 ) + 1 exp [ i ( η a 0 ) x ] ( a 2 a 1 ) ( a 0 a 1 ) 1 exp [ i ( η a 0 ) x ] ( a 2 a 1 ) ( a 0 a 2 ) } .
C 0 ( x ) 2 = cos 4 ( qx 2 ) , C 1 ( x ) 2 = 1 2 sin 2 ( qx 2 ) , C 2 ( x ) 2 = sin 4 ( qx 2 ) .

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