Abstract

It is demonstrated theoretically that a nonlinear medium with a spatially periodic refractive index can support solitons of the nonlinear Schrödinger equation.

© 1988 Optical Society of America

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References

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  1. H. G. Winful, Appl. Phys. Lett. 46, 527 (1985).
    [CrossRef]
  2. See, e.g., R. K. Dodd, J. C. Eilbeck, J. D. Gibbon, H. C. Morris, Solitons and Nonlinear Wave Equations (Academic, New York, 1982).
  3. N. W. Ashcroft, N. D. Mermin, Solid State Physics (Holt, Rinehart and Winston, New York, 1976).
  4. W. Chen, D. L. Mills, Phys. Rev. Lett. 58, 160 (1987).
    [CrossRef] [PubMed]

1987 (1)

W. Chen, D. L. Mills, Phys. Rev. Lett. 58, 160 (1987).
[CrossRef] [PubMed]

1985 (1)

H. G. Winful, Appl. Phys. Lett. 46, 527 (1985).
[CrossRef]

Ashcroft, N. W.

N. W. Ashcroft, N. D. Mermin, Solid State Physics (Holt, Rinehart and Winston, New York, 1976).

Chen, W.

W. Chen, D. L. Mills, Phys. Rev. Lett. 58, 160 (1987).
[CrossRef] [PubMed]

Dodd, R. K.

See, e.g., R. K. Dodd, J. C. Eilbeck, J. D. Gibbon, H. C. Morris, Solitons and Nonlinear Wave Equations (Academic, New York, 1982).

Eilbeck, J. C.

See, e.g., R. K. Dodd, J. C. Eilbeck, J. D. Gibbon, H. C. Morris, Solitons and Nonlinear Wave Equations (Academic, New York, 1982).

Gibbon, J. D.

See, e.g., R. K. Dodd, J. C. Eilbeck, J. D. Gibbon, H. C. Morris, Solitons and Nonlinear Wave Equations (Academic, New York, 1982).

Mermin, N. D.

N. W. Ashcroft, N. D. Mermin, Solid State Physics (Holt, Rinehart and Winston, New York, 1976).

Mills, D. L.

W. Chen, D. L. Mills, Phys. Rev. Lett. 58, 160 (1987).
[CrossRef] [PubMed]

Morris, H. C.

See, e.g., R. K. Dodd, J. C. Eilbeck, J. D. Gibbon, H. C. Morris, Solitons and Nonlinear Wave Equations (Academic, New York, 1982).

Winful, H. G.

H. G. Winful, Appl. Phys. Lett. 46, 527 (1985).
[CrossRef]

Appl. Phys. Lett. (1)

H. G. Winful, Appl. Phys. Lett. 46, 527 (1985).
[CrossRef]

Phys. Rev. Lett. (1)

W. Chen, D. L. Mills, Phys. Rev. Lett. 58, 160 (1987).
[CrossRef] [PubMed]

Other (2)

See, e.g., R. K. Dodd, J. C. Eilbeck, J. D. Gibbon, H. C. Morris, Solitons and Nonlinear Wave Equations (Academic, New York, 1982).

N. W. Ashcroft, N. D. Mermin, Solid State Physics (Holt, Rinehart and Winston, New York, 1976).

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Equations (15)

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c 2 2 x 2 E ( x , t ) + ( x ) 2 t 2 E ( x , t ) = 4 π 2 t 2 P NL ( x , t ) ,
c 2 d 2 d x 2 ϕ m ( x ) = ( x ) ω m 2 ϕ m ( x ) .
ϕ m ( x ) = u n k ( x ) e i k x ,
m | | m = 0 L ϕ m * ( x ) ( x ) ϕ m ( x ) d x
E = μ e 1 + μ 2 e 2 + μ 3 e 3 + ,
x = x 0 + μ x 1 + μ 2 x 2 , t = t 0 + μ t 1 + μ 2 t 2 ,
L e i = F i ,
e 1 = a ( x 1 , x 2 , ; t 1 , t 2 , ) ϕ m ( x 0 ) exp ( i ω m t 0 ) + c . c .
e 2 = l b l ( x 1 , x 2 , ; t 0 , t 1 , t 2 , ) ϕ l ( x 0 ) + c . c .,
( 2 t 0 2 + ω l 2 ) b l = 2 i ( c l | Ω | m a x 1 + ω m δ l m a t 1 ) × exp ( i ω m t 0 ) ,
ω m = c ω m 1 m | Ω | m .
e 2 = 2 i c a z 1 l m ϕ ( x 0 ) l | Ω | m ω 2 ω m 2 exp ( i ω m t 0 ) + c . c .
i a ¯ t + 1 2 ω m 2 a ¯ z 2 + α m | a ¯ | 2 a ¯ = 0 ,
ω m = c 2 ω m m | m ( ω m ) 2 ω m + l m 4 c 2 | l | Ω | m | 2 ω m ( ω m 2 ω l 2 ) ,
α m = 6 π ω m L 0 L χ ( 3 ) ( x 0 ) | ϕ m ( x 0 ) | 4 d x 0 ,

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