Abstract

The noise of spontaneous emission of a short pulse propagating in a fiber with losses is translated into frequency jitter, causing exponential growth of jitter. This is in contrast with a classical treatment in which the jitter remains constant. Absorption-induced frequency noise continuously affects timing through group-velocity dispersion, and the accumulated timing jitter is therefore always larger than when it is evaluated classically. This numerical discrepancy is demonstrated to be considerable and points to the importance of including quantum effects in estimations of noise in high-bit-rate communications.

© 2002 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]

2001 (1)

2000 (1)

A. B. Matsko and V. V. Kozlov, Phys. Rev. A 62, 033811 (2000).
[CrossRef]

1992 (1)

B. Huttner and S. M. Barnett, Phys. Rev. A 46, 4306 (1992).
[CrossRef] [PubMed]

1986 (1)

1985 (1)

J. N. Elgin, Phys. Lett. A 110, 441 (1985).
[CrossRef]

1980 (1)

1951 (1)

H. B. Callen and T. A. Welton, Phys. Rev. 83, 34 (1951).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 2001).

Barnett, S. M.

B. Huttner and S. M. Barnett, Phys. Rev. A 46, 4306 (1992).
[CrossRef] [PubMed]

Callen, H. B.

H. B. Callen and T. A. Welton, Phys. Rev. 83, 34 (1951).
[CrossRef]

Cohen, L. G.

Elgin, J. N.

J. N. Elgin, Phys. Lett. A 110, 441 (1985).
[CrossRef]

Gordon, J. P.

Haus, H. A.

Huttner, B.

B. Huttner and S. M. Barnett, Phys. Rev. A 46, 4306 (1992).
[CrossRef] [PubMed]

Kogelnik, H.

Kozlov, V. V.

Lin, C.

Matsko, A. B.

A. B. Matsko and V. V. Kozlov, Phys. Rev. A 62, 033811 (2000).
[CrossRef]

Welton, T. A.

H. B. Callen and T. A. Welton, Phys. Rev. 83, 34 (1951).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Phys. Lett. A (1)

J. N. Elgin, Phys. Lett. A 110, 441 (1985).
[CrossRef]

Phys. Rev. (1)

H. B. Callen and T. A. Welton, Phys. Rev. 83, 34 (1951).
[CrossRef]

Phys. Rev. A (2)

B. Huttner and S. M. Barnett, Phys. Rev. A 46, 4306 (1992).
[CrossRef] [PubMed]

A. B. Matsko and V. V. Kozlov, Phys. Rev. A 62, 033811 (2000).
[CrossRef]

Other (1)

G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 2001).

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Figures (1)

Fig. 1
Fig. 1

(top) Sketch of the pulse shapes and a fiber line with dispersion compensation, consisting of two fibers of equal lengths, z1=z2-z1, equal absorption coefficients, α1=α2α, and dispersions equal in magnitude but opposite in sign, k1=-k2k. (middle) Normalized frequency jitter σW/σW0 and (bottom) normalized timing jitter σX/σX0 as functions of distance. The parameters are z2=20 km. α=0.2 dB/km, k=1 ps2/km, and τp=4 ps. Note that, apart from the reduced peak amplitude, the output pulse shape is identical to the input, whereas the input and output jitters are different. The two sets of curves correspond to classical versus quantum treatment of dispersive fibers with losses. A “classical” treatment implies that a stochastic input of any origin (quantum mechanical in our case) in then propagating in an otherwise noiseless fiber.

Equations (12)

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XˆtϕˆϕˆdtNˆ, Pˆi2ϕˆtϕˆ-H.c.dt,
kω=k0+i2α+kω-ω0+12kω-ω02,
ϕˆz=-12αϕˆ-i2k2ϕˆτ2+αsˆ.
ϕˆz,τ,ϕˆz,τ=δτ-τ.
Wˆz=αsˆP-WˆsˆNNˆ,
Xˆz=-kWˆ+αsˆX-XˆsˆNNˆ,
wˆ=wˆ0, w2ˆ=wˆ02+pˆ02nˆ02eαz-1,
xˆ=xˆ0-kzwˆ0, x2ˆ=xˆ0-kzwˆ02+F.
F=xˆ02nˆ02eZ-1+kαgˆ02nˆ02Z-1+ZeZ-1+kα2pˆ02nˆ02Z22+2Z-3eZ-1-Z22+3Z,
σW02=p02n02=τp-22n0, σX02=x02n02=τp22n0.
σW2=σW02eZ,
σX2=σX02eZ+σW02kα2Z2+σW02kα2×Z22+2Z-3eZ-1-Z22+3Z.

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