Abstract

We consider stationary soliton states in a birefringent optical fiber with two components locked in phase. Two values of the phase difference between the two components of the soliton states are studied: 0 and π/2. These cases allow us to find composite soliton states in a simple way. The bifurcation diagrams for the coupled soliton states in these two cases are constructed. The stability of these soliton states is examined also.

© 1995 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |

  1. H. G. Winful, Appl. Phys. Lett. 47, 213 (1985).
    [CrossRef]
  2. K. J. Blow, N. J. Doran, and D. Wood, Opt. Lett. 12, 202 (1987).
    [CrossRef] [PubMed]
  3. C. R. Menyuk, Opt. Lett. 12, 614 (1987).
    [CrossRef] [PubMed]
  4. S. Wabnitz, Phys. Rev. A 38, 2018 (1988).
    [CrossRef] [PubMed]
  5. D. N. Christodoulides and R. I. Joseph, Opt. Lett. 13, 53 (1988).
    [CrossRef] [PubMed]
  6. S. Trillo, S. Wabnitz, E. M. Wright, and G. I. Stegeman. Opt. Lett. 13, 672 (1988).
    [CrossRef]
  7. C. R. Menyuk, IEEE J. Quantum Electron. 25, 2674 (1989).
    [CrossRef]
  8. E. M. Wright, G. I. Stegeman, and S. Wabnitz, Phys. Rev. A 40, 4455 (1989).
    [CrossRef] [PubMed]
  9. M. Haelterman and A. P. Sheppard, Electron. Lett. 29, 1176 (1993).
    [CrossRef]
  10. C. J. Chen, P. K. A. Wai, and C. R. Menyuk, Opt. Lett. 15, 477 (1990).
    [CrossRef] [PubMed]
  11. S. G. Evangelides, Jr., L. F. Mollenauer, J. P. Gordon, and N. S. Bergano, J. Lightwave Technol. 10, 28 (1992).
    [CrossRef]
  12. N. N. Akhmediev, V. M. Eleonskii, N. E. Kulagin, and L. P. Shil'nikov, Pis'ma Zh. Tekh. Fiz. 15, 19 (1989) [Sov. Tech. Phys. Lett. 15, 587 (1989)].
  13. M. V. Tratnik and J. E. Sipe, Phys. Rev. A 38, 2011 (1988).
    [CrossRef] [PubMed]
  14. N. N. Akhmediev and A. Ankiewicz, Phys. Rev. Lett. 70, 2395 (1993).
    [CrossRef] [PubMed]
  15. J. M. Soto-Crespo and N. N. Akhmediev, Phys. Rev. E 48, 4710 (1993).
    [CrossRef]
  16. A. A. Kolokolov, J. Appl. Mech. Tech. Phys. (USSR) 11, 426 (1975).
    [CrossRef]
  17. C. K. R. T. Jones and J. V. Moloney, Phys. Lett. A 117, 175 (1986).
    [CrossRef]
  18. D. J. Mitchell and A. W. Snyder, J. Opt. Soc. Am. B 10, 1572 (1993).
    [CrossRef]
  19. N. N. Akhmediev, "The problem of stability and excitation of nonlinear surface waves," in Nonlinear Surface Electromagnetic Phenomena, Vol. 29 of Modern Problems in Condensed Matter Sciences, H.-E. Ponath and G. I. Stegeman, eds. (North-Holland, Amsterdam, 1991), p. 289.
    [CrossRef]
  20. N. N. Akhmediev, V. I. Korneev, and Yu. V. Kuz'menko, Zh. Eksp. Teor. Fiz. 88, 107 (1985) [Sov. Phys. JETP 61, 62 (1985)].

Akhmediev, N. N.

N. N. Akhmediev, V. M. Eleonskii, N. E. Kulagin, and L. P. Shil'nikov, Pis'ma Zh. Tekh. Fiz. 15, 19 (1989) [Sov. Tech. Phys. Lett. 15, 587 (1989)].

N. N. Akhmediev and A. Ankiewicz, Phys. Rev. Lett. 70, 2395 (1993).
[CrossRef] [PubMed]

J. M. Soto-Crespo and N. N. Akhmediev, Phys. Rev. E 48, 4710 (1993).
[CrossRef]

N. N. Akhmediev, "The problem of stability and excitation of nonlinear surface waves," in Nonlinear Surface Electromagnetic Phenomena, Vol. 29 of Modern Problems in Condensed Matter Sciences, H.-E. Ponath and G. I. Stegeman, eds. (North-Holland, Amsterdam, 1991), p. 289.
[CrossRef]

N. N. Akhmediev, V. I. Korneev, and Yu. V. Kuz'menko, Zh. Eksp. Teor. Fiz. 88, 107 (1985) [Sov. Phys. JETP 61, 62 (1985)].

Ankiewicz, A.

N. N. Akhmediev and A. Ankiewicz, Phys. Rev. Lett. 70, 2395 (1993).
[CrossRef] [PubMed]

Bergano, N. S.

S. G. Evangelides, Jr., L. F. Mollenauer, J. P. Gordon, and N. S. Bergano, J. Lightwave Technol. 10, 28 (1992).
[CrossRef]

Blow, K. J.

K. J. Blow, N. J. Doran, and D. Wood, Opt. Lett. 12, 202 (1987).
[CrossRef] [PubMed]

Chen, C. J.

C. J. Chen, P. K. A. Wai, and C. R. Menyuk, Opt. Lett. 15, 477 (1990).
[CrossRef] [PubMed]

Christodoulides, D. N.

D. N. Christodoulides and R. I. Joseph, Opt. Lett. 13, 53 (1988).
[CrossRef] [PubMed]

Doran, N. J.

K. J. Blow, N. J. Doran, and D. Wood, Opt. Lett. 12, 202 (1987).
[CrossRef] [PubMed]

Eleonskii, V. M.

N. N. Akhmediev, V. M. Eleonskii, N. E. Kulagin, and L. P. Shil'nikov, Pis'ma Zh. Tekh. Fiz. 15, 19 (1989) [Sov. Tech. Phys. Lett. 15, 587 (1989)].

Evangelides, S. G.

S. G. Evangelides, Jr., L. F. Mollenauer, J. P. Gordon, and N. S. Bergano, J. Lightwave Technol. 10, 28 (1992).
[CrossRef]

Gordon, J. P.

S. G. Evangelides, Jr., L. F. Mollenauer, J. P. Gordon, and N. S. Bergano, J. Lightwave Technol. 10, 28 (1992).
[CrossRef]

Haelterman, M.

M. Haelterman and A. P. Sheppard, Electron. Lett. 29, 1176 (1993).
[CrossRef]

Jones, C. K. R. T.

C. K. R. T. Jones and J. V. Moloney, Phys. Lett. A 117, 175 (1986).
[CrossRef]

Joseph, R. I.

D. N. Christodoulides and R. I. Joseph, Opt. Lett. 13, 53 (1988).
[CrossRef] [PubMed]

Kolokolov, A. A.

A. A. Kolokolov, J. Appl. Mech. Tech. Phys. (USSR) 11, 426 (1975).
[CrossRef]

Korneev, V. I.

N. N. Akhmediev, V. I. Korneev, and Yu. V. Kuz'menko, Zh. Eksp. Teor. Fiz. 88, 107 (1985) [Sov. Phys. JETP 61, 62 (1985)].

Kulagin, N. E.

N. N. Akhmediev, V. M. Eleonskii, N. E. Kulagin, and L. P. Shil'nikov, Pis'ma Zh. Tekh. Fiz. 15, 19 (1989) [Sov. Tech. Phys. Lett. 15, 587 (1989)].

Kuz'menko, Yu. V.

N. N. Akhmediev, V. I. Korneev, and Yu. V. Kuz'menko, Zh. Eksp. Teor. Fiz. 88, 107 (1985) [Sov. Phys. JETP 61, 62 (1985)].

Menyuk, C. R.

C. J. Chen, P. K. A. Wai, and C. R. Menyuk, Opt. Lett. 15, 477 (1990).
[CrossRef] [PubMed]

C. R. Menyuk, Opt. Lett. 12, 614 (1987).
[CrossRef] [PubMed]

C. R. Menyuk, IEEE J. Quantum Electron. 25, 2674 (1989).
[CrossRef]

Mitchell, D. J.

D. J. Mitchell and A. W. Snyder, J. Opt. Soc. Am. B 10, 1572 (1993).
[CrossRef]

Mollenauer, L. F.

S. G. Evangelides, Jr., L. F. Mollenauer, J. P. Gordon, and N. S. Bergano, J. Lightwave Technol. 10, 28 (1992).
[CrossRef]

Moloney, J. V.

C. K. R. T. Jones and J. V. Moloney, Phys. Lett. A 117, 175 (1986).
[CrossRef]

Sheppard, A. P.

M. Haelterman and A. P. Sheppard, Electron. Lett. 29, 1176 (1993).
[CrossRef]

Shil'nikov, L. P.

N. N. Akhmediev, V. M. Eleonskii, N. E. Kulagin, and L. P. Shil'nikov, Pis'ma Zh. Tekh. Fiz. 15, 19 (1989) [Sov. Tech. Phys. Lett. 15, 587 (1989)].

Sipe, J. E.

M. V. Tratnik and J. E. Sipe, Phys. Rev. A 38, 2011 (1988).
[CrossRef] [PubMed]

Snyder, A. W.

D. J. Mitchell and A. W. Snyder, J. Opt. Soc. Am. B 10, 1572 (1993).
[CrossRef]

Soto-Crespo, J. M.

J. M. Soto-Crespo and N. N. Akhmediev, Phys. Rev. E 48, 4710 (1993).
[CrossRef]

Stegeman, G. I.

E. M. Wright, G. I. Stegeman, and S. Wabnitz, Phys. Rev. A 40, 4455 (1989).
[CrossRef] [PubMed]

Tratnik, M. V.

M. V. Tratnik and J. E. Sipe, Phys. Rev. A 38, 2011 (1988).
[CrossRef] [PubMed]

Trillo, S.

S. Trillo, S. Wabnitz, E. M. Wright, and G. I. Stegeman. Opt. Lett. 13, 672 (1988).
[CrossRef]

Wabnitz, S.

S. Trillo, S. Wabnitz, E. M. Wright, and G. I. Stegeman. Opt. Lett. 13, 672 (1988).
[CrossRef]

S. Wabnitz, Phys. Rev. A 38, 2018 (1988).
[CrossRef] [PubMed]

E. M. Wright, G. I. Stegeman, and S. Wabnitz, Phys. Rev. A 40, 4455 (1989).
[CrossRef] [PubMed]

Wai, P. K. A.

C. J. Chen, P. K. A. Wai, and C. R. Menyuk, Opt. Lett. 15, 477 (1990).
[CrossRef] [PubMed]

Winful, H. G.

H. G. Winful, Appl. Phys. Lett. 47, 213 (1985).
[CrossRef]

Wood, D.

K. J. Blow, N. J. Doran, and D. Wood, Opt. Lett. 12, 202 (1987).
[CrossRef] [PubMed]

Wright, E. M.

S. Trillo, S. Wabnitz, E. M. Wright, and G. I. Stegeman. Opt. Lett. 13, 672 (1988).
[CrossRef]

E. M. Wright, G. I. Stegeman, and S. Wabnitz, Phys. Rev. A 40, 4455 (1989).
[CrossRef] [PubMed]

Other (20)

H. G. Winful, Appl. Phys. Lett. 47, 213 (1985).
[CrossRef]

K. J. Blow, N. J. Doran, and D. Wood, Opt. Lett. 12, 202 (1987).
[CrossRef] [PubMed]

C. R. Menyuk, Opt. Lett. 12, 614 (1987).
[CrossRef] [PubMed]

S. Wabnitz, Phys. Rev. A 38, 2018 (1988).
[CrossRef] [PubMed]

D. N. Christodoulides and R. I. Joseph, Opt. Lett. 13, 53 (1988).
[CrossRef] [PubMed]

S. Trillo, S. Wabnitz, E. M. Wright, and G. I. Stegeman. Opt. Lett. 13, 672 (1988).
[CrossRef]

C. R. Menyuk, IEEE J. Quantum Electron. 25, 2674 (1989).
[CrossRef]

E. M. Wright, G. I. Stegeman, and S. Wabnitz, Phys. Rev. A 40, 4455 (1989).
[CrossRef] [PubMed]

M. Haelterman and A. P. Sheppard, Electron. Lett. 29, 1176 (1993).
[CrossRef]

C. J. Chen, P. K. A. Wai, and C. R. Menyuk, Opt. Lett. 15, 477 (1990).
[CrossRef] [PubMed]

S. G. Evangelides, Jr., L. F. Mollenauer, J. P. Gordon, and N. S. Bergano, J. Lightwave Technol. 10, 28 (1992).
[CrossRef]

N. N. Akhmediev, V. M. Eleonskii, N. E. Kulagin, and L. P. Shil'nikov, Pis'ma Zh. Tekh. Fiz. 15, 19 (1989) [Sov. Tech. Phys. Lett. 15, 587 (1989)].

M. V. Tratnik and J. E. Sipe, Phys. Rev. A 38, 2011 (1988).
[CrossRef] [PubMed]

N. N. Akhmediev and A. Ankiewicz, Phys. Rev. Lett. 70, 2395 (1993).
[CrossRef] [PubMed]

J. M. Soto-Crespo and N. N. Akhmediev, Phys. Rev. E 48, 4710 (1993).
[CrossRef]

A. A. Kolokolov, J. Appl. Mech. Tech. Phys. (USSR) 11, 426 (1975).
[CrossRef]

C. K. R. T. Jones and J. V. Moloney, Phys. Lett. A 117, 175 (1986).
[CrossRef]

D. J. Mitchell and A. W. Snyder, J. Opt. Soc. Am. B 10, 1572 (1993).
[CrossRef]

N. N. Akhmediev, "The problem of stability and excitation of nonlinear surface waves," in Nonlinear Surface Electromagnetic Phenomena, Vol. 29 of Modern Problems in Condensed Matter Sciences, H.-E. Ponath and G. I. Stegeman, eds. (North-Holland, Amsterdam, 1991), p. 289.
[CrossRef]

N. N. Akhmediev, V. I. Korneev, and Yu. V. Kuz'menko, Zh. Eksp. Teor. Fiz. 88, 107 (1985) [Sov. Phys. JETP 61, 62 (1985)].

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

Bifurcation diagram for polarized and composite soliton states in a birefringent optical fiber: (a) γ = 1, (b) γ = 1/3.

Fig. 2
Fig. 2

Examples of functions u and υ for the C-branch soliton states at q/β = 2.0: (a) Δτ = 0, (b) Δ τ β = 2.0.

Fig. 3
Fig. 3

Example of functions u and v for the A-branch soliton states at q/β = 2.0.

Fig. 4
Fig. 4

Instability growth rates for the fast soliton (solid curves), for the A-type soliton states (lower dashed curve), and for the C-type soliton states at Δτ = 0 (leftmost dashed curve) at Δτ = 2 (dotted curve). The curve for Δτ = 6 practically coincides with the curve for the fast soliton.

Fig. 5
Fig. 5

Perspective plot for propagation of the A-type soliton states with a small initial perturbation. Parameters of the simulation are A = 2/3 and q/β = 10.

Fig. 6
Fig. 6

Perspective plot for propagation of the C-type soliton states with a small initial perturbation. Parameters of the simulation are A = 2/3, Δτ = 0, and q/β = 100.

Fig. 7
Fig. 7

Trajectories in the complex plane of variables U and V of the right (R) and the left (L) pulses of Fig. 6 after the C-type state splits into two pulses. Variables Yi,j denote U or V for the right or left pulses at the point of maximum amplitude.

Equations (18)

Equations on this page are rendered with MathJax. Learn more.

i ( U ξ + δ U τ ) + 1 2 2 U τ 2 + β U + ( | U | 2 + A | V | 2 ) U + ( 1 A ) V 2 U * = 0 ,
i ( V ξ δ V τ ) + 1 2 2 V τ 2 β V + ( A | U | 2 + | V | 2 ) V + ( 1 A ) V 2 V * = 0 ,
U ( ξ , τ ) = u ( τ , ξ ) exp ( i β ξ ) , V ( ξ , τ ) = υ ( τ , ξ ) exp ( i β ξ ) .
i ( u ξ + δ u τ ) + 1 2 2 u τ 2 + ( | u | 2 + A | υ | 2 ) u + ( 1 A ) υ 2 u * exp ( i 4 β ξ ) = 0 , i ( υ ξ + δ υ τ ) + 1 2 2 υ τ 2 + ( A | u | 2 + | υ | 2 ) υ + ( 1 A ) u 2 υ * exp ( i 4 β ξ ) = 0 ,
U ( ξ , τ ) = u ( τ , q ) exp ( i q ξ ) , V ( ξ , τ ) = υ ( τ , q ) exp ( i q ξ + i ϕ ) ,
U ( ξ , τ ) = u ( τ , q ) exp ( i q ξ ) , V ( ξ , τ ) = υ ( τ , q ) exp ( i q ξ ) .
U ( ξ , τ ) = u ( τ , q ) exp ( i q ξ ) , V ( ξ , τ ) = i υ ( τ , q ) exp ( i q ξ ) ,
1 2 2 u τ 2 ( q β ) u + ( u 2 + γ υ 2 ) u = 0 , 1 2 2 υ τ 2 ( q + β ) υ + ( γ u 2 + υ 2 ) υ = 0 ,
x = 1 + γ 2 ( u + υ ) , y = 1 + γ 2 ( u υ ) ,
1 2 2 x τ 2 q x + β y + ( x 2 + 3 γ 1 + γ y 2 ) x = 0 , 1 2 2 y τ 2 q y + β x + ( 3 γ 1 + γ x 2 + y 2 ) y = 0 .
u = 2 ( q β ) sech [ 2 ( q β ) τ ] , υ = 0 ;
u = 0 , υ = 2 ( q + β ) sech [ 2 ( q + β ) τ ] .
u = λ 2 λ 1 2 λ 2 2 sinh [ λ 1 ( τ τ 1 ) ] λ 1 cosh [ λ 1 ( τ τ 1 ) ] cosh [ λ 2 ( τ τ 2 ) ] λ 2 sinh [ λ 1 ( τ τ 1 ) ] sinh [ λ 2 ( τ τ 2 ) ] , υ = λ 1 λ 1 2 λ 2 2 cosh [ λ 2 ( τ τ 2 ) ] λ 1 cosh [ λ 1 ( τ τ 1 ) ] cosh [ λ 2 ( τ τ 2 ) ] λ 2 sinh [ λ 1 ( τ τ 1 ) ] sinh [ λ 2 ( τ τ 2 ) ] ,
Q = ( | U | 2 + | V | 2 ) d τ = ( u 2 + υ 2 ) d τ = 2 1 + γ ( x 2 + y 2 ) d τ .
Q = 2 2 ( q β ) + 2 2 ( q + β ) .
u = G , υ = α sech ( α t ) + 2 F ,
G ¨ μ 2 α 2 G + 2 γ α 2 cosh 2 α t G = 0 ,
2 γ = μ ( μ + 1 )

Metrics