Abstract

A physical mechanism for a non-Kerr-like nonlinear refractive-index change in double-doped fibers is proposed, which shows for realistic material parameters a bistable (or two-valued) soliton regime with a large bistability range. The collision of two bistable solitons with a frequency difference in such materials is investigated. Solitons of the lower solution branch retain their shape after the collision. In contrast, two solitons of the upper solution branch with a low-frequency difference fuse to a single high-energy soliton after the collision. The possible applications of this effect for nonlinear photonic switching are discussed.

© 1992 Optical Society of America

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References

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  1. S. Gatz, J. Herrmann, J. Opt. Soc. Am. B 8, 2296 (1991).
    [CrossRef]
  2. J. Herrmann, “Bistable bright solitons in dispersive media with a linear and quadratic intensity-dependent refraction index change,” Opt. Commun. (to be published).
  3. A. I. Kaplan, Phys. Rev. Lett. 55, 1291 (1985).
    [CrossRef] [PubMed]
  4. R. A. Enns, S. S. Rangnekar, A. E. Kaplan, Phys. Rev. A 35, 466 (1987).
    [CrossRef] [PubMed]
  5. L. Coutaz, M. Kull, J. Opt. Soc. Am. B 8, 99 (1991).
    [CrossRef]

1991 (2)

1987 (1)

R. A. Enns, S. S. Rangnekar, A. E. Kaplan, Phys. Rev. A 35, 466 (1987).
[CrossRef] [PubMed]

1985 (1)

A. I. Kaplan, Phys. Rev. Lett. 55, 1291 (1985).
[CrossRef] [PubMed]

Coutaz, L.

Enns, R. A.

R. A. Enns, S. S. Rangnekar, A. E. Kaplan, Phys. Rev. A 35, 466 (1987).
[CrossRef] [PubMed]

Gatz, S.

Herrmann, J.

S. Gatz, J. Herrmann, J. Opt. Soc. Am. B 8, 2296 (1991).
[CrossRef]

J. Herrmann, “Bistable bright solitons in dispersive media with a linear and quadratic intensity-dependent refraction index change,” Opt. Commun. (to be published).

Kaplan, A. E.

R. A. Enns, S. S. Rangnekar, A. E. Kaplan, Phys. Rev. A 35, 466 (1987).
[CrossRef] [PubMed]

Kaplan, A. I.

A. I. Kaplan, Phys. Rev. Lett. 55, 1291 (1985).
[CrossRef] [PubMed]

Kull, M.

Rangnekar, S. S.

R. A. Enns, S. S. Rangnekar, A. E. Kaplan, Phys. Rev. A 35, 466 (1987).
[CrossRef] [PubMed]

J. Opt. Soc. Am. B (2)

Phys. Rev. A (1)

R. A. Enns, S. S. Rangnekar, A. E. Kaplan, Phys. Rev. A 35, 466 (1987).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

A. I. Kaplan, Phys. Rev. Lett. 55, 1291 (1985).
[CrossRef] [PubMed]

Other (1)

J. Herrmann, “Bistable bright solitons in dispersive media with a linear and quadratic intensity-dependent refraction index change,” Opt. Commun. (to be published).

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Figures (3)

Fig. 1
Fig. 1

(a) Dependence of the soliton amplitude B on the parameter α for different γ values. Parameters: curve 1, γ = 0.5α; curve 2, γ = α; curve 3, γ = 2α; curve 4, γ = 10α; curve 5, γ = 0. (b) Dependence of the normalized inner energy HI/P on the invariant P.

Fig. 2
Fig. 2

Collision of two solitons of the upper solution branch with the same duration and shape with parameters α = 0.1, γ = 0.1, B = 2.3, and |Ω| = 0.5. (a) Evolution of the amplitude |q(s, ξ)| along the fiber. (b) Intensity |q(s)|2 and phase ϕ(s) of the outgoing pulse.

Fig. 3
Fig. 3

(Collision of two solitons of the upper solution branch with parameters α = 0.1, γ = 0.1, B = 2.3, and |Ω| = 1.5.

Equations (11)

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- i 1 ξ q + 1 2 2 s 2 q + f ( q 2 ) q = 0 ,
A = P 0 q ( ξ , s ) ,             ξ = z / z c ,             s = 1.76 η / τ 0 ,
P 0 = ( 1.76 ) 2 k 1 k 1 / τ 0 2 n 0 n 2 , z c = τ 0 2 ( 1.76 ) 2 k 1 ,             1 = - sgn ( k 1 ) .
f ( q 2 ) = q 2 - α q 4 1 + γ q 2 ,
α = ( 1.76 ) 2 k 1 n 2 ( a ) c I sat ( b ) ω 1 τ 0 2 [ n 2 ( a ) - n 2 ( b ) ] 2 , γ = ( 1.76 ) 2 k 1 c I sat ( b ) ω 1 τ 0 2 [ n 2 ( b ) - n 2 ( a ) ] .
q ( ξ , s ) = [ ρ ( s ) ] 1 / 2 exp ( i β ξ ) ,
( d ρ d s ) 2 = 8 ρ 2 { α 2 γ ( ρ - ρ 0 ) + 1 γ 2 ( 1 + α γ ) × [ 1 ρ ln ( 1 + γ p ) - 1 ρ 0 ln ( 1 + γ ρ 0 ) ] } ,
β = - α 2 γ ρ 0 + 1 γ ( 1 + α γ ) [ 1 - 1 γ ρ 0 ln ( 1 + γ ρ 0 ) ]
P = - q ( s ) 2 d s ,             Θ = i - q q * s d s , H = 1 P Θ 2 + H I ,
H I = - [ ( s q ) 2 - 2 0 I f ( x ) d x ] d s .
q ( ξ = 0 , s ) = q 1 ( s - s 0 ) exp [ - i Ω ( s - s 0 ) ] + q r ( s + s 0 ) exp [ i Ω ( s + s 0 ) ] .

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