Abstract

We develop a simple theory that relates the performance of an optical component to the variance of the amplitude of its phase ripple that has been weighted by the incoming signal spectrum. Comparisons of model predictions for chirped fiber gratings with 10-Gbit/s test-bed simulations and measurements agree.

© 2004 Optical Society of America

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References

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  1. D. Garthe, G. Milner, Y. Cai, “System performance of broadband dispersion compensation gratings,” Electron. Lett. 34, 582–583 (1998).
    [CrossRef]
  2. M. Eiselt, C. B. Clausen, R. W. Tkach, “Performance characterization of components with group delay fluctuations,” Photon. Technol. Lett. 15, 1076–1078 (2003).
    [CrossRef]
  3. G. P. Agrawal, Fiber-Optic Communication Systems, 2nd ed. (Wiley, New York, 1997).
  4. C. Sheerer, C. Glingener, G. Fischer, M. Bohn, W. Rosenkranz, “Influence of filter group delay ripples on system performance,” in Proceedings of European Conference on Optical Communication (Societe des Electriciens et des Electroniciens, Paris, 1999), pp. 410–411.
  5. B. J. Eggleton, A. Ahuja, P. S. Westbrook, J. A. Rogers, P. Kuo, T. N. Nielsen, B. Mikkelsen, “Integrated tunable fiber gratings for dispersion management in high-bit-rate systems,” J. Lightwave Technol. 18, 1418–1432 (2000).
    [CrossRef]
  6. H. Yoshimi, Y. Takushima, K. Kikuchi, “A simple method for estimating the eye-opening penalty caused by group-delay ripple of optical filters,” presented at the European Conference on Optical Communication, Copenhagen, Denmark, 8–12 Septemer 2002, paper 10.4.4.
  7. K. Ennser, M. Ibsen, M. Durkin, M. N. Zervas, R. I. Laming, “Influence of nonideal chirped fiber grating characteristics on dispersion cancellation,” Photon. Technol. Lett. 10, 1476–1478 (1998).
    [CrossRef]
  8. J. F. Brennan, M. R. Matthews, W. V. Dower, D. J. Treadwell, W. Wang, J. Porque, X. Fan, “Dispersion correction with a robust fiber grating over the full C-band at 10 Gbit/s rates with 0.3-dB power penalties,” Photon. Technol. Lett. 15, 1722–1724 (2003).
    [CrossRef]

2003

M. Eiselt, C. B. Clausen, R. W. Tkach, “Performance characterization of components with group delay fluctuations,” Photon. Technol. Lett. 15, 1076–1078 (2003).
[CrossRef]

J. F. Brennan, M. R. Matthews, W. V. Dower, D. J. Treadwell, W. Wang, J. Porque, X. Fan, “Dispersion correction with a robust fiber grating over the full C-band at 10 Gbit/s rates with 0.3-dB power penalties,” Photon. Technol. Lett. 15, 1722–1724 (2003).
[CrossRef]

2000

1998

K. Ennser, M. Ibsen, M. Durkin, M. N. Zervas, R. I. Laming, “Influence of nonideal chirped fiber grating characteristics on dispersion cancellation,” Photon. Technol. Lett. 10, 1476–1478 (1998).
[CrossRef]

D. Garthe, G. Milner, Y. Cai, “System performance of broadband dispersion compensation gratings,” Electron. Lett. 34, 582–583 (1998).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Fiber-Optic Communication Systems, 2nd ed. (Wiley, New York, 1997).

Ahuja, A.

Bohn, M.

C. Sheerer, C. Glingener, G. Fischer, M. Bohn, W. Rosenkranz, “Influence of filter group delay ripples on system performance,” in Proceedings of European Conference on Optical Communication (Societe des Electriciens et des Electroniciens, Paris, 1999), pp. 410–411.

Brennan, J. F.

J. F. Brennan, M. R. Matthews, W. V. Dower, D. J. Treadwell, W. Wang, J. Porque, X. Fan, “Dispersion correction with a robust fiber grating over the full C-band at 10 Gbit/s rates with 0.3-dB power penalties,” Photon. Technol. Lett. 15, 1722–1724 (2003).
[CrossRef]

Cai, Y.

D. Garthe, G. Milner, Y. Cai, “System performance of broadband dispersion compensation gratings,” Electron. Lett. 34, 582–583 (1998).
[CrossRef]

Clausen, C. B.

M. Eiselt, C. B. Clausen, R. W. Tkach, “Performance characterization of components with group delay fluctuations,” Photon. Technol. Lett. 15, 1076–1078 (2003).
[CrossRef]

Dower, W. V.

J. F. Brennan, M. R. Matthews, W. V. Dower, D. J. Treadwell, W. Wang, J. Porque, X. Fan, “Dispersion correction with a robust fiber grating over the full C-band at 10 Gbit/s rates with 0.3-dB power penalties,” Photon. Technol. Lett. 15, 1722–1724 (2003).
[CrossRef]

Durkin, M.

K. Ennser, M. Ibsen, M. Durkin, M. N. Zervas, R. I. Laming, “Influence of nonideal chirped fiber grating characteristics on dispersion cancellation,” Photon. Technol. Lett. 10, 1476–1478 (1998).
[CrossRef]

Eggleton, B. J.

Eiselt, M.

M. Eiselt, C. B. Clausen, R. W. Tkach, “Performance characterization of components with group delay fluctuations,” Photon. Technol. Lett. 15, 1076–1078 (2003).
[CrossRef]

Ennser, K.

K. Ennser, M. Ibsen, M. Durkin, M. N. Zervas, R. I. Laming, “Influence of nonideal chirped fiber grating characteristics on dispersion cancellation,” Photon. Technol. Lett. 10, 1476–1478 (1998).
[CrossRef]

Fan, X.

J. F. Brennan, M. R. Matthews, W. V. Dower, D. J. Treadwell, W. Wang, J. Porque, X. Fan, “Dispersion correction with a robust fiber grating over the full C-band at 10 Gbit/s rates with 0.3-dB power penalties,” Photon. Technol. Lett. 15, 1722–1724 (2003).
[CrossRef]

Fischer, G.

C. Sheerer, C. Glingener, G. Fischer, M. Bohn, W. Rosenkranz, “Influence of filter group delay ripples on system performance,” in Proceedings of European Conference on Optical Communication (Societe des Electriciens et des Electroniciens, Paris, 1999), pp. 410–411.

Garthe, D.

D. Garthe, G. Milner, Y. Cai, “System performance of broadband dispersion compensation gratings,” Electron. Lett. 34, 582–583 (1998).
[CrossRef]

Glingener, C.

C. Sheerer, C. Glingener, G. Fischer, M. Bohn, W. Rosenkranz, “Influence of filter group delay ripples on system performance,” in Proceedings of European Conference on Optical Communication (Societe des Electriciens et des Electroniciens, Paris, 1999), pp. 410–411.

Ibsen, M.

K. Ennser, M. Ibsen, M. Durkin, M. N. Zervas, R. I. Laming, “Influence of nonideal chirped fiber grating characteristics on dispersion cancellation,” Photon. Technol. Lett. 10, 1476–1478 (1998).
[CrossRef]

Kikuchi, K.

H. Yoshimi, Y. Takushima, K. Kikuchi, “A simple method for estimating the eye-opening penalty caused by group-delay ripple of optical filters,” presented at the European Conference on Optical Communication, Copenhagen, Denmark, 8–12 Septemer 2002, paper 10.4.4.

Kuo, P.

Laming, R. I.

K. Ennser, M. Ibsen, M. Durkin, M. N. Zervas, R. I. Laming, “Influence of nonideal chirped fiber grating characteristics on dispersion cancellation,” Photon. Technol. Lett. 10, 1476–1478 (1998).
[CrossRef]

Matthews, M. R.

J. F. Brennan, M. R. Matthews, W. V. Dower, D. J. Treadwell, W. Wang, J. Porque, X. Fan, “Dispersion correction with a robust fiber grating over the full C-band at 10 Gbit/s rates with 0.3-dB power penalties,” Photon. Technol. Lett. 15, 1722–1724 (2003).
[CrossRef]

Mikkelsen, B.

Milner, G.

D. Garthe, G. Milner, Y. Cai, “System performance of broadband dispersion compensation gratings,” Electron. Lett. 34, 582–583 (1998).
[CrossRef]

Nielsen, T. N.

Porque, J.

J. F. Brennan, M. R. Matthews, W. V. Dower, D. J. Treadwell, W. Wang, J. Porque, X. Fan, “Dispersion correction with a robust fiber grating over the full C-band at 10 Gbit/s rates with 0.3-dB power penalties,” Photon. Technol. Lett. 15, 1722–1724 (2003).
[CrossRef]

Rogers, J. A.

Rosenkranz, W.

C. Sheerer, C. Glingener, G. Fischer, M. Bohn, W. Rosenkranz, “Influence of filter group delay ripples on system performance,” in Proceedings of European Conference on Optical Communication (Societe des Electriciens et des Electroniciens, Paris, 1999), pp. 410–411.

Sheerer, C.

C. Sheerer, C. Glingener, G. Fischer, M. Bohn, W. Rosenkranz, “Influence of filter group delay ripples on system performance,” in Proceedings of European Conference on Optical Communication (Societe des Electriciens et des Electroniciens, Paris, 1999), pp. 410–411.

Takushima, Y.

H. Yoshimi, Y. Takushima, K. Kikuchi, “A simple method for estimating the eye-opening penalty caused by group-delay ripple of optical filters,” presented at the European Conference on Optical Communication, Copenhagen, Denmark, 8–12 Septemer 2002, paper 10.4.4.

Tkach, R. W.

M. Eiselt, C. B. Clausen, R. W. Tkach, “Performance characterization of components with group delay fluctuations,” Photon. Technol. Lett. 15, 1076–1078 (2003).
[CrossRef]

Treadwell, D. J.

J. F. Brennan, M. R. Matthews, W. V. Dower, D. J. Treadwell, W. Wang, J. Porque, X. Fan, “Dispersion correction with a robust fiber grating over the full C-band at 10 Gbit/s rates with 0.3-dB power penalties,” Photon. Technol. Lett. 15, 1722–1724 (2003).
[CrossRef]

Wang, W.

J. F. Brennan, M. R. Matthews, W. V. Dower, D. J. Treadwell, W. Wang, J. Porque, X. Fan, “Dispersion correction with a robust fiber grating over the full C-band at 10 Gbit/s rates with 0.3-dB power penalties,” Photon. Technol. Lett. 15, 1722–1724 (2003).
[CrossRef]

Westbrook, P. S.

Yoshimi, H.

H. Yoshimi, Y. Takushima, K. Kikuchi, “A simple method for estimating the eye-opening penalty caused by group-delay ripple of optical filters,” presented at the European Conference on Optical Communication, Copenhagen, Denmark, 8–12 Septemer 2002, paper 10.4.4.

Zervas, M. N.

K. Ennser, M. Ibsen, M. Durkin, M. N. Zervas, R. I. Laming, “Influence of nonideal chirped fiber grating characteristics on dispersion cancellation,” Photon. Technol. Lett. 10, 1476–1478 (1998).
[CrossRef]

Electron. Lett.

D. Garthe, G. Milner, Y. Cai, “System performance of broadband dispersion compensation gratings,” Electron. Lett. 34, 582–583 (1998).
[CrossRef]

J. Lightwave Technol.

Photon. Technol. Lett.

K. Ennser, M. Ibsen, M. Durkin, M. N. Zervas, R. I. Laming, “Influence of nonideal chirped fiber grating characteristics on dispersion cancellation,” Photon. Technol. Lett. 10, 1476–1478 (1998).
[CrossRef]

J. F. Brennan, M. R. Matthews, W. V. Dower, D. J. Treadwell, W. Wang, J. Porque, X. Fan, “Dispersion correction with a robust fiber grating over the full C-band at 10 Gbit/s rates with 0.3-dB power penalties,” Photon. Technol. Lett. 15, 1722–1724 (2003).
[CrossRef]

M. Eiselt, C. B. Clausen, R. W. Tkach, “Performance characterization of components with group delay fluctuations,” Photon. Technol. Lett. 15, 1076–1078 (2003).
[CrossRef]

Other

G. P. Agrawal, Fiber-Optic Communication Systems, 2nd ed. (Wiley, New York, 1997).

C. Sheerer, C. Glingener, G. Fischer, M. Bohn, W. Rosenkranz, “Influence of filter group delay ripples on system performance,” in Proceedings of European Conference on Optical Communication (Societe des Electriciens et des Electroniciens, Paris, 1999), pp. 410–411.

H. Yoshimi, Y. Takushima, K. Kikuchi, “A simple method for estimating the eye-opening penalty caused by group-delay ripple of optical filters,” presented at the European Conference on Optical Communication, Copenhagen, Denmark, 8–12 Septemer 2002, paper 10.4.4.

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Figures (4)

Fig. 1
Fig. 1

Phase ripple with an actual fiber grating: dashed curves, phase ripples within a 20-GHz spectral window at four different center wavelengths; solid curves, phase ripples weighted by a sinc function [dotted curve in (a)].

Fig. 2
Fig. 2

Eye diagrams simulated with a 29-1 PRBS at the wavelength positions in Fig. 1.

Fig. 3
Fig. 3

(a) Eye closure power penalty obtained from the eye diagrams in Fig. 2 with the decision point optimized, ■, for each wavelength position and □, for the back-to-back case; (b) normalized total energy loss calculated with, ■, weighted and, ▼, unweighted phase ripples; (c) different high-bit duration lengths at two wavelengths given in Fig. 1 after taking into account the occurrence of the bit length in the NRZ format. One unit of high-bit duration length is 100 ps for a 10-Gbit/s system.

Fig. 4
Fig. 4

(a) Grating group-delay ripples, GDR; (b) ■, 10-Gbit/s NRZ system measurements and the power penalty obtained from weighted phase ripples with the first nine shortest high-bit duration lengths used; (c) power penalty obtained with the weighted phase ripple with only the shortest high-bit duration length used; (d) 29-1 bit 10-Gbit/s NRZ simulation with only phase ripples considered. Step size: 10 pm for the test-bed measurement and 1 pm for the rest.

Equations (6)

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ϕω=k>0 Ak cosωtk+θk,
Hω=expjϕω=k>0n=-+ JnAkjn expjntkω+θk.
ΔE= |SiωHω-1|2dω |Siωϕω|2dω |ϕwω|2dω,
power penaltydB  -10 log101-ΔE-ε2ΔE1/2,
power penaltydB  -10 log101-ΔEK σw2,
σw2¯=i=1 Piσwi2,

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