Abstract

Frequency and timing noise added in a linear optical amplifier of gain G grows as G-1/G. Provided that the pulse is initially in a coherent state, the output frequency and timing noise cannot exceed twice the input value. It is also shown that, in a transmission line with zero net gain and loss, the frequency and timing noise added in the lossy medium is equal to or larger than the noise added in the amplifier.

© 2002 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. N. Elgin, Phys. Lett. 110A, 441 (1985).
    [CrossRef]
  2. J. P. Gordon and H. A. Haus, Opt. Lett. 11, 665 (1986).
    [CrossRef] [PubMed]
  3. G. P. Agrawal, Applications of Nonlinear Fiber Optics (Academic, San Diego, Calif., 2001).
  4. V. V. Kozlov, Opt. Lett. 27, 760 (2002).
    [CrossRef]
  5. V. V. Kozlov, Opt. Express 8, 688 (2001), http://www.opticsexpress.org .
    [CrossRef] [PubMed]
  6. H. A. Haus and J. A. Mullen, Phys. Rev. 128, 2407 (1962).
    [CrossRef]
  7. C. M. Caves, Phys. Rev. D 26, 1817 (1982).
    [CrossRef]

2002 (1)

2001 (1)

1986 (1)

1985 (1)

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

1982 (1)

C. M. Caves, Phys. Rev. D 26, 1817 (1982).
[CrossRef]

1962 (1)

H. A. Haus and J. A. Mullen, Phys. Rev. 128, 2407 (1962).
[CrossRef]

Agrawal, G. P.

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

Caves, C. M.

C. M. Caves, Phys. Rev. D 26, 1817 (1982).
[CrossRef]

Elgin, J. N.

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

Gordon, J. P.

Haus, H. A.

J. P. Gordon and H. A. Haus, Opt. Lett. 11, 665 (1986).
[CrossRef] [PubMed]

H. A. Haus and J. A. Mullen, Phys. Rev. 128, 2407 (1962).
[CrossRef]

Kozlov, V. V.

Mullen, J. A.

H. A. Haus and J. A. Mullen, Phys. Rev. 128, 2407 (1962).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Phys. Lett. (1)

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

Phys. Rev. (1)

H. A. Haus and J. A. Mullen, Phys. Rev. 128, 2407 (1962).
[CrossRef]

Phys. Rev. D (1)

C. M. Caves, Phys. Rev. D 26, 1817 (1982).
[CrossRef]

Other (1)

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

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 (2)

Fig. 1
Fig. 1

Top, sketch of one segment of a transmission line with zero net loss/gain: (a) postamplification, (b) preamplification, (c) distributed losses and gain. Bottom, normalized added frequency and timing noise, σW2j-σW20/σWs2 and σX2j-σX20/σXs2, j=a,b,c.

Fig. 2
Fig. 2

(a) Sketch of pulse shapes and a fiber line with dispersion compensation and zero net loss/gain. (b) Mean photon number, n/n0; (c) frequency jitter in numbers of SFD, σW/σWs; (d) timing jitter in numbers of STD, σX/σXs, all versus distance. The parameters are z2=20 km, α=0.2 dB/km, k=1 ps2/km, τp=4 ps, σW0=σWs, and σX0=σXs. Curves labeled “quantum” are calculated as described in Ref. 4 for the fiber section and according to Eqs. (17) and (18) for the gain section. The curves labeled “conventional” are plotted as explained in the text and in Ref. 4.

Equations (24)

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

W^dωωϕ^ϕ^N^-1,
X^i2dωϕ^ωϕ^-ϕ^ϕ^ωN^-1,
N^-1dωϕ^N^+1-2ϕ^.
φ0=n0/π1/2ωp1/2 exp-ω2/2ωp2,
σW02=1n02dωω2φ02=ωp22n0,
σX02=1n02dωφ0ω2=ωp-22n0.
ϕ^z,ω=gωϕ^0,ω+gωf^,
f^ω,f^ω=g-1ω-1δω-ω.
N^z=GN^0+f^N+A^N,
W^z=GW^0N^0+A^P+f^PN^-1,
X^z=GX^0N^0+A^X+f^XN^-1.
N^-1GN^0-A^N-f^NGN^0-2.
W^z=W^0+f^PN^0-1+A^P-W^0A^N+f^NN^0-1,
X^z=X^0+f^XN^0-1+A^X-X^0A^N+f^NN^0-1.
af^ωf^ωa=1-g-1ωδω-ω.
σN2=G2σN02+G2-GσN02,
σW2=σW02+1-G-1σW02,
σX2=σX02+1-G-1σX02.
σWs2ωp2/2n¯,    σXs2ωp-2/2n¯,
σi2loss=σi20+eαL-1σis2,
σi2a=σi2loss+1-G-1eαLσis2,
σi2a=σi20+2G-1σis2,    i=W,X.
σi2b=σi20+21-G-1σis2,
σi2c=σi20+1-G-1σis2+eαL-1σis2,

Metrics