Abstract

We investigate nonlinear pulse propagation in a twin-core fiber whose birefringent axes have been periodically rocked at the beat length of the cores. We find that the four coupled-mode equations that describe this system can be reduced to a pair of coupled nonlinear Schrödinger equations under suitable conditions. Consequently we find two new types of compound soliton: one that propagates down both cores of the fiber simultaneously and another that couples completely between the cores of this structure without degradation. These solitons typically have a peak power of ~1 W and a length of ~10 ps.

© 1993 Optical Society of America

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References

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  1. R. H. Stolen, A. Ashkin, W. Pleibel, J. M. Dziedzic, Opt. Lett. 9, 200 (1984).
    [CrossRef]
  2. K. O. Hill, F. Bilodeau, B. Malo, D. C. Johnson, Electron. Lett. 27, 1548 (1991).
    [CrossRef]
  3. S. Wabnitz, Opt. Lett. 14, 1071 (1989).
    [CrossRef] [PubMed]
  4. A. B. Aceves, S. Wabnitz, Phys. Lett. A 141, 37 (1989).
    [CrossRef]
  5. C. M. de Sterke, J. E. Sipe, Phys. Rev. A 42, 550 (1990).
    [CrossRef]
  6. R. K. Dodd, J. C. Eilbeck, J. D. Gibbon, H. C. Morris, Solitons and Nonlinear Wave Equations (Academic, London, 1982).
  7. G. P. Agrawal, Nonlinear Fiber Optics (Academic, London, 1989), Chap. 7, p. 177.
  8. S. Trillo, S. Wabnitz, J. Opt. Soc. Am. B 5, 483 (1988).
    [CrossRef]
  9. Coupled gap solitons have been reported in a contrapropagating geometry by S. Lee, S.-T. Ho, Opt. Lett. 18, 962 (1993).
    [CrossRef] [PubMed]
  10. N. J. Doran, D. Wood, Opt. Lett. 13, 56 (1988).
    [CrossRef] [PubMed]
  11. G. D. Peng, T. Tjugiarto, P. L. Chu, Appl. Opt. 30, 632 (1991).
    [CrossRef] [PubMed]
  12. M. N. Islam, Ultrafast Fiber Switching Devices and Systems (Cambridge U. Press, New York, 1992), Chap. 3, p. 60.

1993 (1)

1991 (2)

G. D. Peng, T. Tjugiarto, P. L. Chu, Appl. Opt. 30, 632 (1991).
[CrossRef] [PubMed]

K. O. Hill, F. Bilodeau, B. Malo, D. C. Johnson, Electron. Lett. 27, 1548 (1991).
[CrossRef]

1990 (1)

C. M. de Sterke, J. E. Sipe, Phys. Rev. A 42, 550 (1990).
[CrossRef]

1989 (2)

S. Wabnitz, Opt. Lett. 14, 1071 (1989).
[CrossRef] [PubMed]

A. B. Aceves, S. Wabnitz, Phys. Lett. A 141, 37 (1989).
[CrossRef]

1988 (2)

1984 (1)

R. H. Stolen, A. Ashkin, W. Pleibel, J. M. Dziedzic, Opt. Lett. 9, 200 (1984).
[CrossRef]

Aceves, A. B.

A. B. Aceves, S. Wabnitz, Phys. Lett. A 141, 37 (1989).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, London, 1989), Chap. 7, p. 177.

Ashkin, A.

R. H. Stolen, A. Ashkin, W. Pleibel, J. M. Dziedzic, Opt. Lett. 9, 200 (1984).
[CrossRef]

Bilodeau, F.

K. O. Hill, F. Bilodeau, B. Malo, D. C. Johnson, Electron. Lett. 27, 1548 (1991).
[CrossRef]

Chu, P. L.

de Sterke, C. M.

C. M. de Sterke, J. E. Sipe, Phys. Rev. A 42, 550 (1990).
[CrossRef]

Dodd, R. K.

R. K. Dodd, J. C. Eilbeck, J. D. Gibbon, H. C. Morris, Solitons and Nonlinear Wave Equations (Academic, London, 1982).

Doran, N. J.

Dziedzic, J. M.

R. H. Stolen, A. Ashkin, W. Pleibel, J. M. Dziedzic, Opt. Lett. 9, 200 (1984).
[CrossRef]

Eilbeck, J. C.

R. K. Dodd, J. C. Eilbeck, J. D. Gibbon, H. C. Morris, Solitons and Nonlinear Wave Equations (Academic, London, 1982).

Gibbon, J. D.

R. K. Dodd, J. C. Eilbeck, J. D. Gibbon, H. C. Morris, Solitons and Nonlinear Wave Equations (Academic, London, 1982).

Hill, K. O.

K. O. Hill, F. Bilodeau, B. Malo, D. C. Johnson, Electron. Lett. 27, 1548 (1991).
[CrossRef]

Ho, S.-T.

Islam, M. N.

M. N. Islam, Ultrafast Fiber Switching Devices and Systems (Cambridge U. Press, New York, 1992), Chap. 3, p. 60.

Johnson, D. C.

K. O. Hill, F. Bilodeau, B. Malo, D. C. Johnson, Electron. Lett. 27, 1548 (1991).
[CrossRef]

Lee, S.

Malo, B.

K. O. Hill, F. Bilodeau, B. Malo, D. C. Johnson, Electron. Lett. 27, 1548 (1991).
[CrossRef]

Morris, H. C.

R. K. Dodd, J. C. Eilbeck, J. D. Gibbon, H. C. Morris, Solitons and Nonlinear Wave Equations (Academic, London, 1982).

Peng, G. D.

Pleibel, W.

R. H. Stolen, A. Ashkin, W. Pleibel, J. M. Dziedzic, Opt. Lett. 9, 200 (1984).
[CrossRef]

Sipe, J. E.

C. M. de Sterke, J. E. Sipe, Phys. Rev. A 42, 550 (1990).
[CrossRef]

Stolen, R. H.

R. H. Stolen, A. Ashkin, W. Pleibel, J. M. Dziedzic, Opt. Lett. 9, 200 (1984).
[CrossRef]

Tjugiarto, T.

Trillo, S.

Wabnitz, S.

Wood, D.

Appl. Opt. (1)

Electron. Lett. (1)

K. O. Hill, F. Bilodeau, B. Malo, D. C. Johnson, Electron. Lett. 27, 1548 (1991).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Lett. (4)

Phys. Lett. A (1)

A. B. Aceves, S. Wabnitz, Phys. Lett. A 141, 37 (1989).
[CrossRef]

Phys. Rev. A (1)

C. M. de Sterke, J. E. Sipe, Phys. Rev. A 42, 550 (1990).
[CrossRef]

Other (3)

R. K. Dodd, J. C. Eilbeck, J. D. Gibbon, H. C. Morris, Solitons and Nonlinear Wave Equations (Academic, London, 1982).

G. P. Agrawal, Nonlinear Fiber Optics (Academic, London, 1989), Chap. 7, p. 177.

M. N. Islam, Ultrafast Fiber Switching Devices and Systems (Cambridge U. Press, New York, 1992), Chap. 3, p. 60.

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Figures (2)

Fig. 1
Fig. 1

Schematic diagram of a twin elliptical-core optical fiber.

Fig. 2
Fig. 2

Results of a numerical simulation of Eq. (3) of a soliton with the parameters given in the text. The solid curve gives the initial intensity profile in each of the two cores, while the dashed curve shows the profiles after 100 core-to-core couplings.

Equations (12)

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E ( r , z , t ) = { [ A 1 x ( z , t ) 1 x ( r ) + A 2 x ( z , t ) 2 x ( r ) ] exp ( i β x z ) x ˆ + [ A 1 y ( z , t ) 1 y ( r ) + A 2 y ( z , t ) 2 y ( r ) ] exp ( i β y z ) y ˆ } × exp ( i ω t ) + c . c . ,
i A 1 x , y z + i V x , y A 1 x , y t + κ g A 1 y , x exp ( 2 i ν z ) + κ c A 2 x , y + Γ a | A 1 x , y | 2 A 1 x , y + Γ b | A 1 y , x | 2 A 1 x , y = 0 ,
i 1 x , y ζ ± i 1 x , y τ + κ g 1 y , x + κ c 2 x , y + Γ a | 1 x , y | 2 1 x , y + Γ b | 1 y , x | 2 1 x , y = 0
ζ = ζ 0 + μ ζ 1 + μ 2 ζ 2 + ,
= { μ [ a 1 exp ( i κ c ζ 0 ) | 1 + a 3 exp ( i κ c ζ 0 ) | 3 ] + μ 2 [ b 2 exp ( i κ c ζ 0 ) | 2 + b 4 exp ( i κ c ζ 0 ) | 4 ] } × exp [ i ( Q 0 ζ 0 Ω 0 τ ) ] ,
| 1 = ( 1 1 1 1 ) , | 2 = ( 1 1 1 1 ) , | 3 = ( 1 1 1 1 ) , | 4 = ( 1 1 1 1 ) .
i a 1 ζ + 1 2 κ g 2 a 1 τ 2 + ( Γ a + Γ b ) [ | a 1 | 2 a 1 + 2 | a 3 | 2 a 1 + a 3 2 a 1 * exp ( 4 i κ c ζ ) ] = 0 , i a 3 ζ + 1 2 κ g 2 a 3 τ 2 + ( Γ a + Γ b ) [ | a 3 | 2 a 3 + 2 | a 1 | 2 a 3 + a 1 2 a 3 * exp ( + 4 i κ c ζ ) ] = 0 .
a 1 ( ζ , τ ) = [ κ g ( Γ a + Γ b ) ] 1 / 2 p exp ( i ϕ ) sech ( θ ) ,
ϕ = κ g [ q τ + ζ 2 ( p 2 q 2 ) ] , θ = κ g p ( τ q ζ ) .
= [ κ g ( Γ a + Γ b ) ] 1 / 2 p exp ( i σ ) sech ( θ ) { | 1 + [ q + i p tanh ( θ ) ] | 2 } ,
σ = κ g [ q τ ( κ g κ c ) ζ + ζ 2 ( p 2 q 2 ) ] .
= [ 4 κ g 3 ( Γ a + Γ b ) ] 1 / 2 p exp ( i ϕ ) sech ( θ ) [ ( cos ( κ c ζ ) cos ( κ c ζ ) i sin ( κ c ζ ) i sin ( κ c ζ ) ) + [ q + i p tanh ( θ ) ] ( cos ( κ c ζ ) cos ( κ c ζ ) i sin ( κ c ζ ) i sin ( κ c ζ ) ) ] .

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