Abstract

The propagation of nonlinear optical pulses in fibers is discussed, taking into account physical effects arising from nonlinearity, dispersion, and transverse confinement. The wave equation is solved by treating the radial dependence of the field in an exact way. The conditions supporting bright solitary waves are presented and compared with previous results.

© 1984 Optical Society of America

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References

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  1. A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 142 (1973); Appl. Phys. Lett. 23, 171 (1973).
    [CrossRef]
  2. M. Jain, N. Tzoar, J. Appl. Phys. 49, 4649 (1978).
    [CrossRef]
  3. M. Jain, N. Tzoar, Opt. Lett. 3, 202 (1978).
    [CrossRef] [PubMed]
  4. B. Bendow, P. Gianino, N. Tzoar, M. Jain, J. Opt. Soc. Am. 70, 539 (1980).
    [CrossRef]
  5. A. Hasegawa, Y. Kodama, Proc. IEEE 69, 1145 (1981).
    [CrossRef]
  6. B. Crosignani, P. Di Porto, C. H. Papas, Opt. Lett. 6, 61 (1981).
    [CrossRef] [PubMed]
  7. B. Crosignani, P. Di Porto, Opt. Lett. 6, 329 (1981).
    [CrossRef] [PubMed]
  8. B. Crosignani, A. Cutolo, P. Di Porto, J. Opt. Soc. Am. 72, 1136 (1982).
    [CrossRef]

1982 (1)

1981 (3)

1980 (1)

1978 (2)

M. Jain, N. Tzoar, J. Appl. Phys. 49, 4649 (1978).
[CrossRef]

M. Jain, N. Tzoar, Opt. Lett. 3, 202 (1978).
[CrossRef] [PubMed]

1973 (1)

A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 142 (1973); Appl. Phys. Lett. 23, 171 (1973).
[CrossRef]

Bendow, B.

Crosignani, B.

Cutolo, A.

Di Porto, P.

Gianino, P.

Hasegawa, A.

A. Hasegawa, Y. Kodama, Proc. IEEE 69, 1145 (1981).
[CrossRef]

A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 142 (1973); Appl. Phys. Lett. 23, 171 (1973).
[CrossRef]

Jain, M.

Kodama, Y.

A. Hasegawa, Y. Kodama, Proc. IEEE 69, 1145 (1981).
[CrossRef]

Papas, C. H.

Tappert, F.

A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 142 (1973); Appl. Phys. Lett. 23, 171 (1973).
[CrossRef]

Tzoar, N.

Appl. Phys. Lett. (1)

A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 142 (1973); Appl. Phys. Lett. 23, 171 (1973).
[CrossRef]

J. Appl. Phys. (1)

M. Jain, N. Tzoar, J. Appl. Phys. 49, 4649 (1978).
[CrossRef]

J. Opt. Soc. Am. (2)

Opt. Lett. (3)

Proc. IEEE (1)

A. Hasegawa, Y. Kodama, Proc. IEEE 69, 1145 (1981).
[CrossRef]

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Figures (1)

Fig. 1
Fig. 1

Plot of F(σ) [defined in Eq. (18)] versus σ [defined in Eq. (19)].

Equations (29)

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n ( ω , E ) = n ( ω ) + n 2 | E | 2 , r R .
2 E 1 c 2 2 D L t 2 = 2 n 0 n 2 c 2 2 t 2 ( | E | 2 E ) ,
E ( r , t ) = e ˆ A ( r , z , t ) exp [ i ( q z ω 0 t ) ] ,
[ 2 r 2 + 1 r r + 2 z 2 + 2 i q z + k 0 2 q 2 + 2 i k 0 k 0 t ( k 0 2 + k 0 k 0 ) 2 t 2 ] A = 2 n 2 n 0 k 0 2 | A | 2 A ,
[ 2 r 2 + 1 r r + ν 2 ξ 2 + k 0 2 q 2 ] A + 2 β A 3 = 0 ,
A ( r , ξ ) = 0 for r R , all ξ .
A ( r , ξ ) = sech p ξ n = 0 R n ( r ) sech 2 n p ξ ,
n = 0 S 2 n [ R n + 1 r R n + γ n 2 R n ] 2 ν p 2 S 2 n = 0 ( n + 1 ) ( 2 n + 1 ) S 2 n R n + 2 β S 2 i = 0 j = 0 k = 0 S 2 ( i + j + k ) R i R j R k = 0 ,
R 0 + 1 r R 0 + γ 0 2 R 0 = 0 ,
R 1 + 1 r R 1 + γ 1 2 R 1 = 2 R 0 ( ν p 2 β R 0 2 ) ,
R 2 + 1 r R 2 + γ 2 2 R 2 = 6 R 1 ( 2 ν p 2 β R 0 2 ) .
R n = 0 , r = R R n finite , r = 0 } for all n .
R 0 ( r ) = A 0 J 0 ( γ 0 r ) + B 0 Y 0 ( γ 0 r ) ,
( q / k 0 ) 2 = 1 + ( p / k 0 ) 2 ( j 01 / k 0 R ) 2 1 + ( 1 + K ) ( p / k 0 ) 2 .
R 1 ( r ) = A 1 J 0 ( γ 1 r ) + B 1 Y 0 ( γ 1 r ) + π ν p 2 A 0 [ J 0 ( γ 1 r ) U ( r ) Y 0 ( γ 1 r ) V ( r ) ] ,
[ U ( r ) V ( r ) ] = r r ˆ d η η J 0 ( γ 0 η ) [ 1 ( β A 0 2 ν p 2 ) × J 0 2 ( γ 0 η ) ] [ Y 0 ( γ 1 η ) J 0 ( γ 1 η ) ] .
A 0 2 = ν p 2 β F ( σ ) = ( j 01 / k 0 R ) 2 8 n 2 / n 0 ( σ 2 1 ) F ( σ ) ,
F ( σ ) = 0 j 01 d x x J 0 ( x ) J 0 ( σ x ) 0 j 01 d x x J 0 3 ( x ) J 0 ( σ x )
σ 2 = γ 1 2 γ 0 2 = 1 + 8 ( p / k 0 ) 2 [ 1 + K K ( k 0 R / j 01 ) 2 ] 1 + ( 1 + K ) ( p / k 0 ) 2 .
1 + K K ( k 0 R / j 01 ) 2 1 + ( 1 + K ) ( p / k 0 ) 2 > 0 .
1 > K [ ( k 0 R / j 01 ) 2 1 ] ,
A 0 2 1 . 768 k 0 c / n 2 ω 0 τ 2 ,
R 2 ( r ) = 3 ( π 8 ) 2 A 0 ( σ 2 1 ) 2 { A ˆ 2 J 0 ( μ j 01 r / R ) + 0 j 0 I r / R d x x [ J 0 ( μ x ) Y 0 ( μ j 01 r / R ) Y 0 ( μ x ) J 0 ( μ j 01 r / R ) ] × [ 2 F ( σ ) J 0 2 ( x ) ] W ( x ) } ,
W ( x ) = x j 01 d y y J 0 ( y ) [ 1 F ( σ ) J 0 2 ( y ) ] × [ J 0 ( σ x ) Y 0 ( σ y ) Y 0 ( σ x ) J 0 ( σ y ) ] ,
A ˆ 2 = 0 j 01 d x x [ 2 F ( σ ) J 0 2 ( x ) ] W ( x ) × [ Y 0 ( μ x ) Y 0 ( μ j 01 ) J 0 ( μ j 01 ) J 0 ( μ x ) ] ,
μ 2 = γ 2 2 γ 0 2 = 3 σ 2 2 .
H ( ξ ) 2 R 2 0 R d r r H ( r , ξ ) .
A = 2 A 0 sech p ξ J 1 ( j 01 ) j 01 { 1 + ( σ 2 1 ) 4 σ 2 × [ 1 F ( σ ) F ( 0 ) ] sech 2 p ξ + } .
A 2 = A 0 2 J 1 2 ( j 01 ) sech 2 p ξ [ 1 + C ( σ ) sech 2 p ξ + ] ,

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