Abstract

Parametric amplification in fibers with dispersion fluctuations is analyzed. The fluctuations are modelled as a stochastic process, with their size at a given position modelled as a Gaussian, and the autocorrelation decreasing exponentially. Two models are studied: in one the dispersion is piecewise constant, while in the other it is continuous. We find that the amplification does not depend on the models’ details and that only fluctuations with long correlation lengths affect the amplification significantly.

© 2004 Optical Society of America

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References

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  2. S. Kinoshita et al. Eds., Optical amplifiers and their application (Optical Society of America, Washington, DC 1999).
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    [CrossRef]
  4. M. Karlsson, �??Four-wave mixing in fibers with randomly varying zero-dispersion wavelength,�?? J. Opt. Soc. Am. B, 15, 2269-2275 (1998). It is noted that in the Appendix in this paper the matrices G and H are implicitly, and incorrectly, assumed to commute.
    [CrossRef]
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  7. M. Eiselt, R.M. Jopson, and R.H. Stolen, �??Non-destructive position-resolved measurement of the zero-dispersion wavelength in an optical fiber,�?? J. Lightwave Technol. 15, 135-142 (1997).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  10. J.M. Chávez-Boggio, P. Dainese, and H.L. Fragnito, �??Performance of a two-pump fiber optical parametric amplifier in a 10 Gb/s�?64 channel dense wavelength division multiplexing system,�?? Opt. Commun. 218, 303-310 (2003).
    [CrossRef]
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    [CrossRef]
  13. A. Papoulis, Probability, random variables, and stochastic processes(McGraw-Hill, New York, 1965).
  14. P.K.A. Wai and C.R. Menyuk, �??Anisotropic diffusion of the state of polarization in optical fibers with randomly varying birefringence,�?? Opt. Lett. 24, 2493-2495 (1995).
    [CrossRef]

J. Lightwave Technol.

M-C Ho, K. Uesaka, M. Marhic, Y. Akasaka, and L.G. Kazovsky, �??200-nm-bandwidth fiber optical amplifier combining parametric an Raman gain,�?? J. Lightwave Technol. 19, 977-980 (2001).
[CrossRef]

M. Eiselt, R.M. Jopson, and R.H. Stolen, �??Non-destructive position-resolved measurement of the zero-dispersion wavelength in an optical fiber,�?? J. Lightwave Technol. 15, 135-142 (1997).
[CrossRef]

N. Kuwaki and M. Ohashi, �??Evolution of longitudinal chromatic dispersion,�?? J. Lightwave Technol. 8, 1476-1480 (1990).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Commun.

J.M. Chávez-Boggio, P. Dainese, and H.L. Fragnito, �??Performance of a two-pump fiber optical parametric amplifier in a 10 Gb/s�?64 channel dense wavelength division multiplexing system,�?? Opt. Commun. 218, 303-310 (2003).
[CrossRef]

Opt. Lett.

OSA TOPS Series

J.S. Pereira et al, �??Measurement of zero-dispersion wavelength using a novel method based on four-wave mixing,�?? in Optical Fiber Communications Conference, Vol. 2, 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 345-346.

Phys. Lett. A

F. Kh. Abdullaev, S.A. Darmanyan, A. Kobyakov, and F. Lederer, �??Modulational instability in optical fibers with variable dispersion,�?? Phys. Lett. A 220, 213-218 (1996).
[CrossRef]

Other

A. Papoulis, Probability, random variables, and stochastic processes(McGraw-Hill, New York, 1965).

G. P.Agrawal, Nonlinear Fiber Optics (Academic Press, 1995)

S. Kinoshita et al. Eds., Optical amplifiers and their application (Optical Society of America, Washington, DC 1999).

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Figures (2)

Fig. 1.
Fig. 1.

(a) Example of dispersion fluctuations according to Model I. (b) Same as (a), but for Model II.

Fig. 2.
Fig. 2.

Numerical results for the expectation value of the gain versus γP 0 Lc , for γP 0 L=4. The horizontal solid line refers to result (5) whereas the dotted line indicates result (10). The red coloring refers to Model I, whereas green refers to Model II. The error bars indicate the variance of the distribution. In (a) and (b) Δ/(γP 0)=0.25; in (c) and (d) Δ/(γP 0)=2.00; in (e) and (f) Δ/(γP 0)=1.00. Further, in (a), (c) and (e) σ/(γP 0)=0.50, while in (b), (d) and (f) σ/(γP 0)=1.00.

Equations (10)

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Δ β = 2 β p β s β i ,
A p = P 0 exp ( i γ P 0 z ) ,
d A dz = ( i Δ k i γ P 0 i γ P 0 i Δ k ) A .
A ( z ) = MA ( 0 ) [ cosh α z + i Δ k α sinh α z i γ P 0 α sinh α z i γ P 0 α sinh α z cosh α z i Δ k α sinh α z ] A ( 0 ) ,
G = cosh 2 α L + ( Δ k ) 2 α 2 sinh 2 α L ,
f G ( δ k ) = 1 σ 2 π exp [ 1 2 ( δ k σ 2 ) 2 ] ,
C ( z ) = σ 2 exp ( z L c ) ,
P ( L s ) e L s L c .
f ( δ k ( z 1 ) δ k ( z 0 ) ) = 1 σ 2 π ( 1 r 2 ) e 1 2 σ 2 ( 1 r 2 ) ( δ k ( z 1 ) r δ k ( z 0 ) ) 2 ,
G ( L c L ) = 1 2 π σ + d ( Δ k ) e ( Δ k Δ ) 2 2 σ 2 log [ cosh 2 α L + ( Δ k ) 2 α 2 sinh 2 α L ] .

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