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]

Phys. Rev. E

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

Other

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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