Abstract

Evaluating the relative time displacement of the two orthogonally polarized components of a pulse propagating down a birefringent optical fiber is considered. A method that provides analytical expressions for this time displacement is described and generalizes analytical results already published.

© 2002 Optical Society of America

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References

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  1. G. P. Agrawal, Fiber-Optic Communication Systems (Wiley-Interscience, New York, 1997).
  2. Y. Chen and H. A. Haus, Opt. Lett. 25, 290 (2000).
    [CrossRef]
  3. S. Boscolo, A. Pavan, and M. Midrio, J. Opt. Soc. Am. B 19, 1 (2002).
    [CrossRef]
  4. T. I. Lakoba and D. J. Kaup, Phys. Rev. E 56, 6147 (1997).
    [CrossRef]
  5. T. P. Horikis and J. N. Elgin, paper submitted to Phys. Rev. E.
  6. J. P. Gordon, J. Opt. Soc. Am. 9, 91 (1992).
    [CrossRef]
  7. S. V. Manakov, Sov. Phys. JETP 8, 248 (1974).
  8. T. P. Horikis and J. N. Elgin, J. Opt. Soc. Am. B 18, 913 (2001).
    [CrossRef]
  9. T. P. Horikis and J. N. Elgin, “Perturbed solitons in birefringent fibers.”

2002 (1)

2001 (1)

2000 (1)

1997 (1)

T. I. Lakoba and D. J. Kaup, Phys. Rev. E 56, 6147 (1997).
[CrossRef]

1992 (1)

1974 (1)

S. V. Manakov, Sov. Phys. JETP 8, 248 (1974).

Agrawal, G. P.

G. P. Agrawal, Fiber-Optic Communication Systems (Wiley-Interscience, New York, 1997).

Boscolo, S.

Chen, Y.

Elgin, J. N.

T. P. Horikis and J. N. Elgin, J. Opt. Soc. Am. B 18, 913 (2001).
[CrossRef]

T. P. Horikis and J. N. Elgin, paper submitted to Phys. Rev. E.

T. P. Horikis and J. N. Elgin, “Perturbed solitons in birefringent fibers.”

Gordon, J. P.

Haus, H. A.

Horikis, T. P.

T. P. Horikis and J. N. Elgin, J. Opt. Soc. Am. B 18, 913 (2001).
[CrossRef]

T. P. Horikis and J. N. Elgin, “Perturbed solitons in birefringent fibers.”

T. P. Horikis and J. N. Elgin, paper submitted to Phys. Rev. E.

Kaup, D. J.

T. I. Lakoba and D. J. Kaup, Phys. Rev. E 56, 6147 (1997).
[CrossRef]

Lakoba, T. I.

T. I. Lakoba and D. J. Kaup, Phys. Rev. E 56, 6147 (1997).
[CrossRef]

Manakov, S. V.

S. V. Manakov, Sov. Phys. JETP 8, 248 (1974).

Midrio, M.

Pavan, A.

J. Opt. Soc. Am. (1)

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

Opt. Lett. (1)

Phys. Rev. E (1)

T. I. Lakoba and D. J. Kaup, Phys. Rev. E 56, 6147 (1997).
[CrossRef]

Sov. Phys. JETP (1)

S. V. Manakov, Sov. Phys. JETP 8, 248 (1974).

Other (3)

T. P. Horikis and J. N. Elgin, “Perturbed solitons in birefringent fibers.”

T. P. Horikis and J. N. Elgin, paper submitted to Phys. Rev. E.

G. P. Agrawal, Fiber-Optic Communication Systems (Wiley-Interscience, New York, 1997).

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Figures (1)

Fig. 1
Fig. 1

Time displacement corresponding to Eq. (19), with birefringence parameter μ=0.01 and polarization angles θ=π/4 (top) and θ=5π/12 (bottom).

Equations (24)

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iq1x-q1tt-2q1q12+q22=-iμq1t,
iq2x-q2tt-2q2q22+q12=iμq2t,
qsx,t=q1sq2s=qsx,tcos θsin θ,
qs=2η1 exp-2iξ1t+4iξ12-η12x×sech2η1t-4ξ1t.
qx,t=qsx,t+δqx,t,
-if1f2x=f1f2tt+iμf1-f2t-iμ2sin2θsin θ-cos θqsh,
ht=0t<0exp-tt>0,
-δq1=M-N sin2 θf1+½ sin2θNf2-qs2 cos θf1* cos θ+f2* sin θ,
-δq2=M-N cos2 θf2+½ sin2θNf1-qs2 sin θf1* cos θ+f2* sin θ.
M=2t2-2 tanh tt+tanh2 t,
N=1-tanh tt+tanh2 t-tanh t.
Δtx=Re-+tδq2q2s*dt-Re-+tδq1q1s*dt=Δt2x-Δt1x.
ΔT1=Δt1 tan θ-Δt2 cot θ,
ΔT2=Δt1+Δt2.
Δtx=-sin2θΔT1-cos2θΔT2,
ΔT1=-Re-+t-δq1 sin θ+δq2 cos θqs*dt,
ΔT2=Re-+tδq1 cos θ+δq2 sin θqs*dt.
Δtx=sin2θΔT1=sin2θReexpix×-+exp-tsech2tFx,tdt,
ΔT2=Reexpix-+t sech3 tG dt-exp-ix-+t sech3 tG* dt,
δq=-MG+qs2G*.
Δtx=sin2θRei expix2-+ω-i×sechπω/2Fˆx,ωdω,
-+ftg*tdt=12π-+fˆωgˆ*ωdω.
Fˆx,ω=-2 µπsin2θsechπω/2ω-isin2 θω2+μω+1×expiω2+μωx-exp-ix+cos2 θω2-μω+1expiω2-μωx-exp-ix.
Δtx-sin22θμπ-+sech2πω/21+ω2×sin1+ω2xdω,

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