Abstract

By gradually translating the peak frequency of guiding filters along its length, we create a fiber transmission line that is substantially opaque to noise while remaining transparent to solitons. This trick allows the use of stronger filters, and hence greater jitter reduction, without incurring the usual penalty of exponentially rising noise from the excess gain required to overcome filter loss.

© 1992 Optical Society of America

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References

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  1. J. P. Gordon, H. A. Haus, Opt. Lett. 11, 665 (1986).
  2. E. M. Dianov, A. V. Luchnikov, A. N. Pilipetskii, A. M. Prokhorov, Sov. Lightwave Commun. 1, 235 (1991).
  3. A. Mecozzi, J. D. Moores, H. A. Haus, Y. Lai, Opt. Lett. 16, 1841 (1991).
  4. Y. Kodama, A. Hasegawa, Opt. Lett. 17, 31 (1992).
  5. L. F. Mollenauer, E. Lichtman, G. T. Harvey, M. J. Neubelt, B. M. Nyman, Electron. Lett. 28, 792 (1992).
  6. Our solution [Eqs. (3) and (4)] to Eq. (2) is essentially the same as the one given earlier by P. A. Bélanger, L. Gagnon, C. Paré, Opt. Lett. 14, 943 (1989). (Different formulations tend to make the identification less than immediately obvious, however.)
  7. Unless otherwise indicated, all quantities here are in the Standard soliton units. See, for example, Eq. (1) and Appendix of L. F. Mollenauer, J. P. Gordon, M. N. Islam, IEEE J. Quantum Electron. QE-22, 157 (1986).
  8. J. P. Gordon, L. F. Mollenauer, IEEE J. Lightwave Technol. 9, 170 (1991).
  9. M. Nakazawa, E. Yamada, H. Kubota, K. Suzuki, Electron. Lett. 27, 1270 (1991).

1992 (2)

Y. Kodama, A. Hasegawa, Opt. Lett. 17, 31 (1992).

L. F. Mollenauer, E. Lichtman, G. T. Harvey, M. J. Neubelt, B. M. Nyman, Electron. Lett. 28, 792 (1992).

1991 (4)

E. M. Dianov, A. V. Luchnikov, A. N. Pilipetskii, A. M. Prokhorov, Sov. Lightwave Commun. 1, 235 (1991).

A. Mecozzi, J. D. Moores, H. A. Haus, Y. Lai, Opt. Lett. 16, 1841 (1991).

J. P. Gordon, L. F. Mollenauer, IEEE J. Lightwave Technol. 9, 170 (1991).

M. Nakazawa, E. Yamada, H. Kubota, K. Suzuki, Electron. Lett. 27, 1270 (1991).

1989 (1)

1986 (2)

Unless otherwise indicated, all quantities here are in the Standard soliton units. See, for example, Eq. (1) and Appendix of L. F. Mollenauer, J. P. Gordon, M. N. Islam, IEEE J. Quantum Electron. QE-22, 157 (1986).

J. P. Gordon, H. A. Haus, Opt. Lett. 11, 665 (1986).

Bélanger, P. A.

Dianov, E. M.

E. M. Dianov, A. V. Luchnikov, A. N. Pilipetskii, A. M. Prokhorov, Sov. Lightwave Commun. 1, 235 (1991).

Gagnon, L.

Gordon, J. P.

J. P. Gordon, L. F. Mollenauer, IEEE J. Lightwave Technol. 9, 170 (1991).

Unless otherwise indicated, all quantities here are in the Standard soliton units. See, for example, Eq. (1) and Appendix of L. F. Mollenauer, J. P. Gordon, M. N. Islam, IEEE J. Quantum Electron. QE-22, 157 (1986).

J. P. Gordon, H. A. Haus, Opt. Lett. 11, 665 (1986).

Harvey, G. T.

L. F. Mollenauer, E. Lichtman, G. T. Harvey, M. J. Neubelt, B. M. Nyman, Electron. Lett. 28, 792 (1992).

Hasegawa, A.

Haus, H. A.

Islam, M. N.

Unless otherwise indicated, all quantities here are in the Standard soliton units. See, for example, Eq. (1) and Appendix of L. F. Mollenauer, J. P. Gordon, M. N. Islam, IEEE J. Quantum Electron. QE-22, 157 (1986).

Kodama, Y.

Kubota, H.

M. Nakazawa, E. Yamada, H. Kubota, K. Suzuki, Electron. Lett. 27, 1270 (1991).

Lai, Y.

Lichtman, E.

L. F. Mollenauer, E. Lichtman, G. T. Harvey, M. J. Neubelt, B. M. Nyman, Electron. Lett. 28, 792 (1992).

Luchnikov, A. V.

E. M. Dianov, A. V. Luchnikov, A. N. Pilipetskii, A. M. Prokhorov, Sov. Lightwave Commun. 1, 235 (1991).

Mecozzi, A.

Mollenauer, L. F.

L. F. Mollenauer, E. Lichtman, G. T. Harvey, M. J. Neubelt, B. M. Nyman, Electron. Lett. 28, 792 (1992).

J. P. Gordon, L. F. Mollenauer, IEEE J. Lightwave Technol. 9, 170 (1991).

Unless otherwise indicated, all quantities here are in the Standard soliton units. See, for example, Eq. (1) and Appendix of L. F. Mollenauer, J. P. Gordon, M. N. Islam, IEEE J. Quantum Electron. QE-22, 157 (1986).

Moores, J. D.

Nakazawa, M.

M. Nakazawa, E. Yamada, H. Kubota, K. Suzuki, Electron. Lett. 27, 1270 (1991).

Neubelt, M. J.

L. F. Mollenauer, E. Lichtman, G. T. Harvey, M. J. Neubelt, B. M. Nyman, Electron. Lett. 28, 792 (1992).

Nyman, B. M.

L. F. Mollenauer, E. Lichtman, G. T. Harvey, M. J. Neubelt, B. M. Nyman, Electron. Lett. 28, 792 (1992).

Paré, C.

Pilipetskii, A. N.

E. M. Dianov, A. V. Luchnikov, A. N. Pilipetskii, A. M. Prokhorov, Sov. Lightwave Commun. 1, 235 (1991).

Prokhorov, A. M.

E. M. Dianov, A. V. Luchnikov, A. N. Pilipetskii, A. M. Prokhorov, Sov. Lightwave Commun. 1, 235 (1991).

Suzuki, K.

M. Nakazawa, E. Yamada, H. Kubota, K. Suzuki, Electron. Lett. 27, 1270 (1991).

Yamada, E.

M. Nakazawa, E. Yamada, H. Kubota, K. Suzuki, Electron. Lett. 27, 1270 (1991).

Electron. Lett. (2)

L. F. Mollenauer, E. Lichtman, G. T. Harvey, M. J. Neubelt, B. M. Nyman, Electron. Lett. 28, 792 (1992).

M. Nakazawa, E. Yamada, H. Kubota, K. Suzuki, Electron. Lett. 27, 1270 (1991).

IEEE J. Lightwave Technol. (1)

J. P. Gordon, L. F. Mollenauer, IEEE J. Lightwave Technol. 9, 170 (1991).

IEEE J. Quantum Electron. (1)

Unless otherwise indicated, all quantities here are in the Standard soliton units. See, for example, Eq. (1) and Appendix of L. F. Mollenauer, J. P. Gordon, M. N. Islam, IEEE J. Quantum Electron. QE-22, 157 (1986).

Opt. Lett. (4)

Sov. Lightwave Commun. (1)

E. M. Dianov, A. V. Luchnikov, A. N. Pilipetskii, A. M. Prokhorov, Sov. Lightwave Commun. 1, 235 (1991).

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Figures (3)

Fig. 1
Fig. 1

Noise spectral density versus frequency, at various distances along a transmission line with sliding filters, normalized to that density obtained at 10 Mm with no filtering, for solitons of τ = 20 ps with D = 0.4 ps/(nm km) and zc = 250 km. Filtering, excess gain, and sliding rates (all per zc) are η = 0.6, α = 0.205, and ω f = 0.1 (= −5.6 GHz/Mm), respectively.

Fig. 2
Fig. 2

Standard deviations of the soliton energy (ones) and of the noise in empty bit periods (zeros) versus distance, both normalized to the soliton energy itself for the sliding filter scheme of Fig. 1 (dotted curves) and with no filtering at all, save for a single filter at z passing only eight noise modes (solid curves). The assumed fiber loss rate and effective core area are 0.21 dB/km and 50 μm2, respectively; amplifier spacing and excess spontaneous emission factor are 28 km and 1.4, respectively.

Fig. 3
Fig. 3

Standard deviations in soliton arrival times versus distance, with sliding filters (dotted curves) and with no filtering at all (solid curves). Jitter from the acoustic effect, which depends on the bit rate (in gigabits per second as indicated next to each curve), is included. Inset: histogram (points) of relative arrival times at 10 Mm of 150 pulses from numerical simulation of transmission with noise and sliding filters; the best-fit Gaussian (solid curve) has a standard deviation of 1.76 ps. All assumed parameters are the same as in Figs. 1 and 2.

Equations (14)

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ln F ( ω ω f ) = i ζ 1 ( ω ω f ) ζ 2 ( ω ω f ) 2 i ζ 3 ( ω ω f ) 3 + ,
u z = i ( 1 2 2 u t 2 + u * u 2 ) + 1 2 [ α η ( i t ω f ) 2 ] u ,
u = P sech ( t ) exp ( i ϕ ) , ϕ = K z ν ln cosh ( t ) ,
ν = 3 2 η [ ( 1 + 8 η 2 9 ) 1 / 2 1 ] = 2 3 η 4 27 η 3 + ,
α = ( η / 3 ) ( 1 + ν 2 ) ,
P = ( 1 + η 2 ) ( 1 ν 2 / 2 ) ,
K = ( 1 / 2 ) ( 1 ν 2 ) + ( ν 2 / 3 ) ( 2 ν 2 ) .
1 A d A d z = α η [ ( Ω ω f ) 2 + 1 3 A 2 ] ,
d Ω d z = 2 3 η ( Ω ω f ) A 2 .
Δ Ω = 3 2 η ω f .
γ 1 = 2 3 η ( 1 + 6 Δ Ω ) , γ 2 = 2 3 η ( 1 6 Δ Ω ) ,
δ E s 2 E s 2 N γ E E s ,
f ( γ t , z ) 3 ( γ t z ) 2 ,
N ( ω , z ) = 1 L 0 z exp { α x η [ ( ω ω f z ) 2 x + ( ω ω f z ) ω f x 2 + ω f 2 x 3 / 3 ] } d x .

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