Abstract

We discuss the propagation of nonlinear optical pulses in fibers. The wave equation is solved taking the radial dependence in an average way. The radius versus wavelength curves for “no dispersion” in SiO2 glass are calculated and plotted. These no-dispersion curves separate the regions of light and dark solitons supported by the fibers.

© 1978 Optical Society of America

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References

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  1. D. Gloge, Appl. Opt. 10, 2442 (1971).
    [Crossref] [PubMed]
  2. R. Y. Chiao, E. Garmire, C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
    [Crossref]
  3. A. Hasigawa, F. Tappert, Appl. Phys. Lett. 23, 142, (1973).A. Hasigawa, F. Tappert, Appl. Phys. Lett. 23, 171 (1973).
    [Crossref]
  4. N. Tzoar, J. I. Gersten, in Optical Properties of Highly Transparent Solids, S. Mitra, B. Bendow, eds. (Plenum, New York, 1976).
  5. M. Jain, N. Tzoar, J. Appl. Phys. 49, 4649, 1978.
    [Crossref]
  6. The no-dispersion condition is defined (to make contact with the linear case) as the condition for stable pulse propagation at vanishing intensity. One also notes from Fig. 2 that the no-dispersion condition represents the boundary between light and dark solitons.

1978 (1)

M. Jain, N. Tzoar, J. Appl. Phys. 49, 4649, 1978.
[Crossref]

1973 (1)

A. Hasigawa, F. Tappert, Appl. Phys. Lett. 23, 142, (1973).A. Hasigawa, F. Tappert, Appl. Phys. Lett. 23, 171 (1973).
[Crossref]

1971 (1)

1964 (1)

R. Y. Chiao, E. Garmire, C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
[Crossref]

Chiao, R. Y.

R. Y. Chiao, E. Garmire, C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
[Crossref]

Garmire, E.

R. Y. Chiao, E. Garmire, C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
[Crossref]

Gersten, J. I.

N. Tzoar, J. I. Gersten, in Optical Properties of Highly Transparent Solids, S. Mitra, B. Bendow, eds. (Plenum, New York, 1976).

Gloge, D.

Hasigawa, A.

A. Hasigawa, F. Tappert, Appl. Phys. Lett. 23, 142, (1973).A. Hasigawa, F. Tappert, Appl. Phys. Lett. 23, 171 (1973).
[Crossref]

Jain, M.

M. Jain, N. Tzoar, J. Appl. Phys. 49, 4649, 1978.
[Crossref]

Tappert, F.

A. Hasigawa, F. Tappert, Appl. Phys. Lett. 23, 142, (1973).A. Hasigawa, F. Tappert, Appl. Phys. Lett. 23, 171 (1973).
[Crossref]

Townes, C. H.

R. Y. Chiao, E. Garmire, C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
[Crossref]

Tzoar, N.

M. Jain, N. Tzoar, J. Appl. Phys. 49, 4649, 1978.
[Crossref]

N. Tzoar, J. I. Gersten, in Optical Properties of Highly Transparent Solids, S. Mitra, B. Bendow, eds. (Plenum, New York, 1976).

Appl. Opt. (1)

Appl. Phys. Lett. (1)

A. Hasigawa, F. Tappert, Appl. Phys. Lett. 23, 142, (1973).A. Hasigawa, F. Tappert, Appl. Phys. Lett. 23, 171 (1973).
[Crossref]

J. Appl. Phys. (1)

M. Jain, N. Tzoar, J. Appl. Phys. 49, 4649, 1978.
[Crossref]

Phys. Rev. Lett. (1)

R. Y. Chiao, E. Garmire, C. H. Townes, Phys. Rev. Lett. 13, 479 (1964).
[Crossref]

Other (2)

The no-dispersion condition is defined (to make contact with the linear case) as the condition for stable pulse propagation at vanishing intensity. One also notes from Fig. 2 that the no-dispersion condition represents the boundary between light and dark solitons.

N. Tzoar, J. I. Gersten, in Optical Properties of Highly Transparent Solids, S. Mitra, B. Bendow, eds. (Plenum, New York, 1976).

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Figures (2)

Fig. 1
Fig. 1

Plot of k0R/l1 versus k0R for various values of Δ.

Fig. 2
Fig. 2

R versus λ curves for no dispersion in SiO2 glass for various values of Δ.

Equations (21)

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2 E - 1 c 2 2 D L t 2 = 2 n 0 n 2 c 2 2 t 2 ( E 2 E ) ,
n ( r , ω , E ) = n ( r , ω ) + n 2 E 2 ,
E ( r , z , t ) = e ^ A ( r , z , t ) exp [ i ( q z - ω 0 t ) ] ,
[ 2 + 2 z 2 + 2 i q z - q 2 + k 0 2 + 2 i k 0 k 0 t + ( k 0 2 + k 0 k 0 ) 2 t 2 ] A ( r , z , t ) = - 2 n 2 n 0 k 0 2 A 2 A ( r , z , t ) ,
k 0 2 = ω 0 2 c 2 n 0 2 ,             k 0 = k ω | ω 0 ,             k 0 = 2 k ω 2 | ω 0 .
A ( r , z , t ) = U ( r ) ϕ ( z , t )
ϕ 2 U ( r ) + U [ 2 z 2 + 2 i q z - q 2 + k 0 2 + 2 i k 0 k 0 t - ( k 0 2 + k 0 k 0 ) 2 t 2 ] ϕ ( z , t ) = - 2 n 2 n 0 k 0 2 U ϕ 2 U ( r ) ϕ ( z , t ) .
( 2 - p 2 + k 0 2 ) ψ ( r ) = 0.
ψ m ( r ) = J 0 ( l m r / R )
p m 2 = k 0 2 - ( l m / R ) 2 ,
J 1 ( x ) x J 0 ( x ) + ( 1 - Δ ) K 1 ( Δ k 0 2 R 2 - x 2 ) 1 / 2 ( Δ k 0 2 R 2 - x 2 ) 1 / 2 K 0 ( Δ k 0 2 R 2 - x 2 ) 1 / 2 = 0.
ψ 1 ( r ) = J 0 ( l 1 r / R ) ,
p 1 2 = k 0 2 - ( l 1 / R ) 2 .
[ p 1 2 - q 2 + 2 z 2 + 2 i q z + 2 i k 0 k 0 t - ( k 0 + k 0 k 0 ) 2 t 2 ] ϕ ( z , t ) = - 2 α n 2 n 0 k 0 2 ϕ ϕ 2 ( z , t ) ,
α = 0 1 d x x [ J 0 ( l 1 x ) ] 4 0 1 d x x [ J 0 ( l 1 x ) ] 2 .
v g = q / k 0 k 0 .
[ k 0 k 0 - ( l 1 k 0 R ) k 0 2 ] 1 ϕ d 2 ϕ d ξ 2 + ( q 2 - p 0 2 ) τ 2 = 2 n 2 n 0 τ 2 k 0 2 ϕ 2 α .
q 2 = k 0 2 [ 1 - l 1 2 k 0 2 R 2 + n 2 n 0 α ϕ 0 2 ] ,
ϕ 0 2 = - k 0 k 0 + l 1 2 k 0 2 R 2 k 0 2 n 2 n 0 k 0 2 τ 2 α .
q 2 = k 0 2 ( 1 - l 1 2 k 0 2 R 2 + 2 n 2 n 0 α ϕ 0 2 ) ,
ϕ 0 2 = k 0 k 0 - l 1 2 k 0 2 k 0 2 R 2 n 2 n 0 k 0 2 τ 2 α .

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