Abstract

We use an information-theoretic method developed by Neifeld and Lee [J. Opt. Soc. Am. A 25, C31 (2008)] to analyze the performance of a slow-light system. Slow-light is realized in this system via stimulated Brillouin scattering in a 2km-long, room-temperature, highly nonlinear fiber pumped by a laser whose spectrum is tailored and broadened to 5GHz. We compute the information throughput (IT), which quantifies the fraction of information transferred from the source to the receiver and the information delay (ID), which quantifies the delay of a data stream at which the information transfer is largest, for a range of experimental parameters. We also measure the eye-opening (EO) and signal-to-noise ratio (SNR) of the transmitted data stream and find that they scale in a similar fashion to the information-theoretic method. Our experimental findings are compared to a model of the slow-light system that accounts for all pertinent noise sources in the system as well as data-pulse distortion due to the filtering effect of the SBS process. The agreement between our observations and the predictions of our model is very good. Furthermore, we compare measurements of the IT for an optimal flattop gain profile and for a Gaussian-shaped gain profile. For a given pump-beam power, we find that the optimal profile gives a 36% larger ID and somewhat higher IT compared to the Gaussian profile. Specifically, the optimal (Gaussian) profile produces a fractional slow-light ID of 0.94 (0.69) and an IT of 0.86 (0.86) at a pump-beam power of 450mW and a data rate of 2.5Gbps. Thus, the optimal profile better utilizes the available pump-beam power, which is often a valuable resource in a system design.

© 2011 Optical Society of America

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  1. R. W. Boyd and D. J. Gauthier, “Controlling the velocity of light pulses,” Science 326, 1074–1077 (2009).
    [CrossRef] [PubMed]
  2. R. S. Tucker, P. C. Ku, and C. J. Chang-Hasnain, “Slow-light optical buffers: capabilities and fundamental limitations,” J. Lightwave Technol. 23, 4046–4066 (2005).
    [CrossRef]
  3. Z. Bo, L. Yan, J. Yang, I. Fazal, and A. Willner, “A single slow-light element for independent delay control and synchronization on multiple Gb/s data channels,” IEEE Photon. Technol. Lett. 19, 1081–1083 (2007).
    [CrossRef]
  4. Z. Shi, R. W. Boyd, R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, “Slow-light Fourier transform interferometer,” Phys. Rev. Lett. 99, 240801 (2007).
    [CrossRef]
  5. Z. Shi and R. W. Boyd, “Slow-light interferometry: practical limitations to spectroscopic performance,” J. Opt. Soc. Am. B 25, C136–C143 (2008).
    [CrossRef]
  6. R. Zhang, Y. Zhu, J. Wang, and D. J. Gauthier, “Slow light with a swept-frequency source,” Opt. Express 18, 27263–27269(2010).
    [CrossRef]
  7. A. Schweinsberg, Z. Shi, J. E. Vornehm, and R. W. Boyd, “Demonstration of a slow-light laser radar,” Opt. Express 19, 15760–15769 (2011).
    [CrossRef] [PubMed]
  8. M. Gonzalez-Herraez, K. Song, and L. Thévenaz, “Optically controlled slow and fast light in optical fibers using stimulated Brillouin scattering,” Appl. Phys. Lett. 87, 081113 (2005).
    [CrossRef]
  9. Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902 (2005).
    [CrossRef] [PubMed]
  10. Z. Zhu, D. J. Gauthier, Y. Okawachi, J. E. Sharping, A. L. Gaeta, R. W. Boyd, and A. E. Willner, “Numerical study of all-optical slow-light delays via stimulated Brillouin scattering in an optical fiber,” J. Opt. Soc. Am. B 22, 2378–2384 (2005).
    [CrossRef]
  11. M. D. Stenner, M. A. Neifeld, Z. Zhu, A. M. C. Dawes, and D. J. Gauthier, “Distortion management in slow-light pulse delay,” Opt. Express 13, 9995–10002 (2005).
    [CrossRef] [PubMed]
  12. A. Minardo, R. Bernini, and L. Zeni, “Low distortion Brillouin slow light in optical fibers using AM modulation,” Opt. Express 14, 5866–5876 (2006).
    [CrossRef] [PubMed]
  13. A. Zadok, A. Eyal, and M. Tur, “Extended delay of broadband signals in stimulated Brillouin scattering slow light using synthesized pump chirp,” Opt. Express 14, 8498–8505 (2006).
    [CrossRef] [PubMed]
  14. T. Schneider, M. Junker, and K.-U. Lauterbach, “Potential ultra wide slow-light bandwidth enhancement,” Opt. Express 14, 11082–11087 (2006).
    [CrossRef] [PubMed]
  15. Z. Zhu, A. M. C. Dawes, D. J. Gauthier, L. Zhang, and A. E. Willner, “Broadband SBS Slow Light in an Optical Fiber,” J. Lightwave Technol. 25, 201–206 (2007).
    [CrossRef]
  16. Z. Shi, R. Pant, Z. Zhu, M. D. Stenner, M. A. Neifeld, D. J. Gauthier, and R. W. Boyd, “Design of a tunable time-delay element using multiple gain lines for large fractional delay with high data fidelity,” Opt. Lett. 32, 1986–1988 (2007).
    [CrossRef] [PubMed]
  17. L. Yi, Y. Jaouen, W. Hu, Y. Su, and S. Bigo, “Improved slow-light performance of 10 Gb/s NRZ, PSBT and DPSK signals in fiber broadband SBS,” Opt. Express 15, 16972–16979(2007).
    [CrossRef] [PubMed]
  18. Z. Lu, Y. Dong, and Q. Li, “Slow light in multi-line Brillouin gain spectrum,” Opt. Express 15, 1871–1877 (2007).
    [CrossRef] [PubMed]
  19. R. Pant, M. D. Stenner, M. A. Neifeld, and D. J. Gauthier, “Optimal pump profile designs for broadband SBS slow-light systems,” Opt. Express 16, 2764–2777 (2008).
    [CrossRef] [PubMed]
  20. E. Cabrera-Granado, O. G. Calderon, S. Melle, and D. J. Gauthier, “Observation of large 10 Gb/s SBS slow light delay with low distortion using an optimized gain profile,” Opt. Express 16, 16032–16042 (2008).
    [CrossRef] [PubMed]
  21. T. Sakamoto, T. Yamamoto, K. Shiraki, and T. Kurashima, “Low distortion slow light in flat Brillouin gain spectrum by using optical frequency comb,” Opt. Express 16, 8026–8032(2008).
    [CrossRef] [PubMed]
  22. Y. Dong, Z. Lu, Q. Li, and Y. Liu, “Broadband Brillouin slow light based on multifrequency phase modulation in optical fibers,” J. Opt. Soc. Am. B 25, C109–C115 (2008).
    [CrossRef]
  23. M. Lee, R. Pant, and M. A. Neifeld, “Improved delay performance of broadband stimulated Brillouin Scattering (SBS) slow-light system using fiber Bragg gratings,” Appl. Opt. 47, 6404–6415 (2008).
    [CrossRef] [PubMed]
  24. Z. Zhang, X. Zhou, R. Liang, and S. Shi, “Influence of third-order dispersion on delay performance in broadband Brillouin slow light,” J. Opt. Soc. Am. B 26, 2211–2217 (2009).
    [CrossRef]
  25. S. Chin, M. Gonzalez-Herraez, and L. Thévenaz, “Complete compensation of pulse broadening in an amplifier-based slow light system using a nonlinear regeneration element,” Opt. Express 17, 21910–21917 (2009).
    [CrossRef] [PubMed]
  26. Y. Zhu, M. Lee, M. A. Neifeld, and D. J. Gauthier, “High-fidelity broadband stimulated-Brillouin-scattering-based slow light using fast noise modulation,” Opt. Express 19, 687–697(2011).
    [CrossRef] [PubMed]
  27. R. W. Boyd, D. J. Gauthier, A. L. Gaeta, and A. E. Willner, “Erratum: Maximum time delay achievable on propagation through a slow-light medium,” Phys. Rev. A 72, 059903(2005).
    [CrossRef]
  28. J. B. Khurgin, “Performance limits of delay lines based on optical amplifiers,” Opt. Lett. 31, 948–950 (2006).
    [CrossRef] [PubMed]
  29. D. A. B. Miller, “Fundamental limit to linear one-dimensional slow light structures,” Phys. Rev. Lett. 99, 203903 (2007).
    [CrossRef]
  30. M. A. Neifeld and M. Lee, “Information theoretic framework for the analysis of a slow-light delay device,” J. Opt. Soc. Am. B 25, C31–C38 (2008).
    [CrossRef]
  31. C. E. Shannon, “A mathematical theory of communications,” Bell Syst. Tech. J. 27, 379–423 (1948).
  32. B. Zhang, L. Yan, I. Fazal, L. Zhang, A. E. Willner, Z. Zhu, and D. J. Gauthier, “Slow light on Gbit/s differential-phase-shift-keying signals,” Opt. Express 15, 1878–1883 (2007).
    [CrossRef] [PubMed]
  33. G. P. Agrawal, Fiber-Optic Communication Systems, 3rd ed. (Wiley, 2002).
    [CrossRef]
  34. Z. Zuqing, M. Funabashi, P. Zhong, X. Bo, L. Paraschis, and S. J. B. Yoo, “Jitter and amplitude noise accumulations in cascaded all-optical regenerators,” J. Lightwave Technol. 26, 1640–1652 (2008).
    [CrossRef]
  35. J. D. Fast, Entropy. The Significance of the Concept of Entropy and Its Applications in the Science and Technology (McGraw-Hill, 1962).
    [PubMed]
  36. S. Le Floch and P. Cambon, “Theoretical evaluation of the Brillouin threshold and the steady-state Brillouin equations in standard single-mode optical fibers,” J. Opt. Soc. Am. A 20, 1132–1137 (2003).
    [CrossRef]
  37. Y. Zhu, E. Cabrera-Granado, O. G. Calderon, S. Melle, Y. Okawachi, A. L. Gaeta, and D. J. Gauthier, “Competition between the Modulation Instability and Stimulated Brillouin Scattering in a Broadband Slow Light Device,” J. Opt. 12, 104019 (2010).
    [CrossRef]
  38. R. Holzlohner, H. N. Ereifej, V. S. Grigoryan, G. M. Carter, and C. R. Menyuk, “Experimental and theoretical characterization of a 40 Gb/s long-haul single-channel transmission system,” J. Lightwave Technol. 20, 1124–1131 (2002).
    [CrossRef]
  39. S. Norimatsu and M. Maruoka, “Accurate Q-factor estimation of optically amplified systems in the presence of waveform distortions,” J. Lightwave Technol. 20, 19–27 (2002).
    [CrossRef]
  40. R. W. Boyd, K. Rzaewski, and P. Narum, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A 42, 5514–5521(1990).
    [CrossRef] [PubMed]
  41. S. Sternklar, Y. Glick, and S. Jackel, “Noise limitations of Brillouin two-beam coupling: theory and experiment,” J. Opt. Soc. Am. B 9, 391–394 (1992).
    [CrossRef]
  42. N. A. Olsson, “Lightwave systems with optical amplifiers,” J. Lightwave Technol. 7, 1071–1082 (1989).
    [CrossRef]
  43. A. Ghosh, D. Venkitesh, and R. Vijaya, “Study of Brillouin amplifier characteristics toward optimized conditions for slow light generation,” Appl. Opt. 48, G48–G52 (2009).
    [CrossRef] [PubMed]
  44. F. Ravet, X. Bao, J. Snoddy, Y. Li, and L. Chen, “Characterization of Brillouin fiber generator and amplifier for optimized working condition of distributed sensors,” Opt. Fiber Technol. 15, 304–309 (2009).
    [CrossRef]

2011 (2)

2010 (2)

R. Zhang, Y. Zhu, J. Wang, and D. J. Gauthier, “Slow light with a swept-frequency source,” Opt. Express 18, 27263–27269(2010).
[CrossRef]

Y. Zhu, E. Cabrera-Granado, O. G. Calderon, S. Melle, Y. Okawachi, A. L. Gaeta, and D. J. Gauthier, “Competition between the Modulation Instability and Stimulated Brillouin Scattering in a Broadband Slow Light Device,” J. Opt. 12, 104019 (2010).
[CrossRef]

2009 (5)

2008 (8)

R. Pant, M. D. Stenner, M. A. Neifeld, and D. J. Gauthier, “Optimal pump profile designs for broadband SBS slow-light systems,” Opt. Express 16, 2764–2777 (2008).
[CrossRef] [PubMed]

T. Sakamoto, T. Yamamoto, K. Shiraki, and T. Kurashima, “Low distortion slow light in flat Brillouin gain spectrum by using optical frequency comb,” Opt. Express 16, 8026–8032(2008).
[CrossRef] [PubMed]

Z. Zuqing, M. Funabashi, P. Zhong, X. Bo, L. Paraschis, and S. J. B. Yoo, “Jitter and amplitude noise accumulations in cascaded all-optical regenerators,” J. Lightwave Technol. 26, 1640–1652 (2008).
[CrossRef]

M. A. Neifeld and M. Lee, “Information theoretic framework for the analysis of a slow-light delay device,” J. Opt. Soc. Am. B 25, C31–C38 (2008).
[CrossRef]

E. Cabrera-Granado, O. G. Calderon, S. Melle, and D. J. Gauthier, “Observation of large 10 Gb/s SBS slow light delay with low distortion using an optimized gain profile,” Opt. Express 16, 16032–16042 (2008).
[CrossRef] [PubMed]

Y. Dong, Z. Lu, Q. Li, and Y. Liu, “Broadband Brillouin slow light based on multifrequency phase modulation in optical fibers,” J. Opt. Soc. Am. B 25, C109–C115 (2008).
[CrossRef]

Z. Shi and R. W. Boyd, “Slow-light interferometry: practical limitations to spectroscopic performance,” J. Opt. Soc. Am. B 25, C136–C143 (2008).
[CrossRef]

M. Lee, R. Pant, and M. A. Neifeld, “Improved delay performance of broadband stimulated Brillouin Scattering (SBS) slow-light system using fiber Bragg gratings,” Appl. Opt. 47, 6404–6415 (2008).
[CrossRef] [PubMed]

2007 (8)

Z. Lu, Y. Dong, and Q. Li, “Slow light in multi-line Brillouin gain spectrum,” Opt. Express 15, 1871–1877 (2007).
[CrossRef] [PubMed]

B. Zhang, L. Yan, I. Fazal, L. Zhang, A. E. Willner, Z. Zhu, and D. J. Gauthier, “Slow light on Gbit/s differential-phase-shift-keying signals,” Opt. Express 15, 1878–1883 (2007).
[CrossRef] [PubMed]

Z. Zhu, A. M. C. Dawes, D. J. Gauthier, L. Zhang, and A. E. Willner, “Broadband SBS Slow Light in an Optical Fiber,” J. Lightwave Technol. 25, 201–206 (2007).
[CrossRef]

Z. Shi, R. Pant, Z. Zhu, M. D. Stenner, M. A. Neifeld, D. J. Gauthier, and R. W. Boyd, “Design of a tunable time-delay element using multiple gain lines for large fractional delay with high data fidelity,” Opt. Lett. 32, 1986–1988 (2007).
[CrossRef] [PubMed]

L. Yi, Y. Jaouen, W. Hu, Y. Su, and S. Bigo, “Improved slow-light performance of 10 Gb/s NRZ, PSBT and DPSK signals in fiber broadband SBS,” Opt. Express 15, 16972–16979(2007).
[CrossRef] [PubMed]

D. A. B. Miller, “Fundamental limit to linear one-dimensional slow light structures,” Phys. Rev. Lett. 99, 203903 (2007).
[CrossRef]

Z. Bo, L. Yan, J. Yang, I. Fazal, and A. Willner, “A single slow-light element for independent delay control and synchronization on multiple Gb/s data channels,” IEEE Photon. Technol. Lett. 19, 1081–1083 (2007).
[CrossRef]

Z. Shi, R. W. Boyd, R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, “Slow-light Fourier transform interferometer,” Phys. Rev. Lett. 99, 240801 (2007).
[CrossRef]

2006 (4)

2005 (6)

M. Gonzalez-Herraez, K. Song, and L. Thévenaz, “Optically controlled slow and fast light in optical fibers using stimulated Brillouin scattering,” Appl. Phys. Lett. 87, 081113 (2005).
[CrossRef]

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef] [PubMed]

R. W. Boyd, D. J. Gauthier, A. L. Gaeta, and A. E. Willner, “Erratum: Maximum time delay achievable on propagation through a slow-light medium,” Phys. Rev. A 72, 059903(2005).
[CrossRef]

Z. Zhu, D. J. Gauthier, Y. Okawachi, J. E. Sharping, A. L. Gaeta, R. W. Boyd, and A. E. Willner, “Numerical study of all-optical slow-light delays via stimulated Brillouin scattering in an optical fiber,” J. Opt. Soc. Am. B 22, 2378–2384 (2005).
[CrossRef]

M. D. Stenner, M. A. Neifeld, Z. Zhu, A. M. C. Dawes, and D. J. Gauthier, “Distortion management in slow-light pulse delay,” Opt. Express 13, 9995–10002 (2005).
[CrossRef] [PubMed]

R. S. Tucker, P. C. Ku, and C. J. Chang-Hasnain, “Slow-light optical buffers: capabilities and fundamental limitations,” J. Lightwave Technol. 23, 4046–4066 (2005).
[CrossRef]

2003 (1)

2002 (2)

1992 (1)

1990 (1)

R. W. Boyd, K. Rzaewski, and P. Narum, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A 42, 5514–5521(1990).
[CrossRef] [PubMed]

1989 (1)

N. A. Olsson, “Lightwave systems with optical amplifiers,” J. Lightwave Technol. 7, 1071–1082 (1989).
[CrossRef]

1948 (1)

C. E. Shannon, “A mathematical theory of communications,” Bell Syst. Tech. J. 27, 379–423 (1948).

Agrawal, G. P.

G. P. Agrawal, Fiber-Optic Communication Systems, 3rd ed. (Wiley, 2002).
[CrossRef]

Bao, X.

F. Ravet, X. Bao, J. Snoddy, Y. Li, and L. Chen, “Characterization of Brillouin fiber generator and amplifier for optimized working condition of distributed sensors,” Opt. Fiber Technol. 15, 304–309 (2009).
[CrossRef]

Bernini, R.

Bigelow, M. S.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef] [PubMed]

Bigo, S.

Bo, X.

Bo, Z.

Z. Bo, L. Yan, J. Yang, I. Fazal, and A. Willner, “A single slow-light element for independent delay control and synchronization on multiple Gb/s data channels,” IEEE Photon. Technol. Lett. 19, 1081–1083 (2007).
[CrossRef]

Boyd, R. W.

A. Schweinsberg, Z. Shi, J. E. Vornehm, and R. W. Boyd, “Demonstration of a slow-light laser radar,” Opt. Express 19, 15760–15769 (2011).
[CrossRef] [PubMed]

R. W. Boyd and D. J. Gauthier, “Controlling the velocity of light pulses,” Science 326, 1074–1077 (2009).
[CrossRef] [PubMed]

Z. Shi and R. W. Boyd, “Slow-light interferometry: practical limitations to spectroscopic performance,” J. Opt. Soc. Am. B 25, C136–C143 (2008).
[CrossRef]

Z. Shi, R. Pant, Z. Zhu, M. D. Stenner, M. A. Neifeld, D. J. Gauthier, and R. W. Boyd, “Design of a tunable time-delay element using multiple gain lines for large fractional delay with high data fidelity,” Opt. Lett. 32, 1986–1988 (2007).
[CrossRef] [PubMed]

Z. Shi, R. W. Boyd, R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, “Slow-light Fourier transform interferometer,” Phys. Rev. Lett. 99, 240801 (2007).
[CrossRef]

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef] [PubMed]

R. W. Boyd, D. J. Gauthier, A. L. Gaeta, and A. E. Willner, “Erratum: Maximum time delay achievable on propagation through a slow-light medium,” Phys. Rev. A 72, 059903(2005).
[CrossRef]

Z. Zhu, D. J. Gauthier, Y. Okawachi, J. E. Sharping, A. L. Gaeta, R. W. Boyd, and A. E. Willner, “Numerical study of all-optical slow-light delays via stimulated Brillouin scattering in an optical fiber,” J. Opt. Soc. Am. B 22, 2378–2384 (2005).
[CrossRef]

R. W. Boyd, K. Rzaewski, and P. Narum, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A 42, 5514–5521(1990).
[CrossRef] [PubMed]

Cabrera-Granado, E.

Y. Zhu, E. Cabrera-Granado, O. G. Calderon, S. Melle, Y. Okawachi, A. L. Gaeta, and D. J. Gauthier, “Competition between the Modulation Instability and Stimulated Brillouin Scattering in a Broadband Slow Light Device,” J. Opt. 12, 104019 (2010).
[CrossRef]

E. Cabrera-Granado, O. G. Calderon, S. Melle, and D. J. Gauthier, “Observation of large 10 Gb/s SBS slow light delay with low distortion using an optimized gain profile,” Opt. Express 16, 16032–16042 (2008).
[CrossRef] [PubMed]

Calderon, O. G.

Y. Zhu, E. Cabrera-Granado, O. G. Calderon, S. Melle, Y. Okawachi, A. L. Gaeta, and D. J. Gauthier, “Competition between the Modulation Instability and Stimulated Brillouin Scattering in a Broadband Slow Light Device,” J. Opt. 12, 104019 (2010).
[CrossRef]

E. Cabrera-Granado, O. G. Calderon, S. Melle, and D. J. Gauthier, “Observation of large 10 Gb/s SBS slow light delay with low distortion using an optimized gain profile,” Opt. Express 16, 16032–16042 (2008).
[CrossRef] [PubMed]

Camacho, R. M.

Z. Shi, R. W. Boyd, R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, “Slow-light Fourier transform interferometer,” Phys. Rev. Lett. 99, 240801 (2007).
[CrossRef]

Cambon, P.

Carter, G. M.

Chang-Hasnain, C. J.

Chen, L.

F. Ravet, X. Bao, J. Snoddy, Y. Li, and L. Chen, “Characterization of Brillouin fiber generator and amplifier for optimized working condition of distributed sensors,” Opt. Fiber Technol. 15, 304–309 (2009).
[CrossRef]

Chin, S.

Dawes, A. M. C.

Dong, Y.

Ereifej, H. N.

Eyal, A.

Fast, J. D.

J. D. Fast, Entropy. The Significance of the Concept of Entropy and Its Applications in the Science and Technology (McGraw-Hill, 1962).
[PubMed]

Fazal, I.

Z. Bo, L. Yan, J. Yang, I. Fazal, and A. Willner, “A single slow-light element for independent delay control and synchronization on multiple Gb/s data channels,” IEEE Photon. Technol. Lett. 19, 1081–1083 (2007).
[CrossRef]

B. Zhang, L. Yan, I. Fazal, L. Zhang, A. E. Willner, Z. Zhu, and D. J. Gauthier, “Slow light on Gbit/s differential-phase-shift-keying signals,” Opt. Express 15, 1878–1883 (2007).
[CrossRef] [PubMed]

Funabashi, M.

Gaeta, A. L.

Y. Zhu, E. Cabrera-Granado, O. G. Calderon, S. Melle, Y. Okawachi, A. L. Gaeta, and D. J. Gauthier, “Competition between the Modulation Instability and Stimulated Brillouin Scattering in a Broadband Slow Light Device,” J. Opt. 12, 104019 (2010).
[CrossRef]

Z. Zhu, D. J. Gauthier, Y. Okawachi, J. E. Sharping, A. L. Gaeta, R. W. Boyd, and A. E. Willner, “Numerical study of all-optical slow-light delays via stimulated Brillouin scattering in an optical fiber,” J. Opt. Soc. Am. B 22, 2378–2384 (2005).
[CrossRef]

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef] [PubMed]

R. W. Boyd, D. J. Gauthier, A. L. Gaeta, and A. E. Willner, “Erratum: Maximum time delay achievable on propagation through a slow-light medium,” Phys. Rev. A 72, 059903(2005).
[CrossRef]

Gauthier, D. J.

Y. Zhu, M. Lee, M. A. Neifeld, and D. J. Gauthier, “High-fidelity broadband stimulated-Brillouin-scattering-based slow light using fast noise modulation,” Opt. Express 19, 687–697(2011).
[CrossRef] [PubMed]

R. Zhang, Y. Zhu, J. Wang, and D. J. Gauthier, “Slow light with a swept-frequency source,” Opt. Express 18, 27263–27269(2010).
[CrossRef]

Y. Zhu, E. Cabrera-Granado, O. G. Calderon, S. Melle, Y. Okawachi, A. L. Gaeta, and D. J. Gauthier, “Competition between the Modulation Instability and Stimulated Brillouin Scattering in a Broadband Slow Light Device,” J. Opt. 12, 104019 (2010).
[CrossRef]

R. W. Boyd and D. J. Gauthier, “Controlling the velocity of light pulses,” Science 326, 1074–1077 (2009).
[CrossRef] [PubMed]

R. Pant, M. D. Stenner, M. A. Neifeld, and D. J. Gauthier, “Optimal pump profile designs for broadband SBS slow-light systems,” Opt. Express 16, 2764–2777 (2008).
[CrossRef] [PubMed]

E. Cabrera-Granado, O. G. Calderon, S. Melle, and D. J. Gauthier, “Observation of large 10 Gb/s SBS slow light delay with low distortion using an optimized gain profile,” Opt. Express 16, 16032–16042 (2008).
[CrossRef] [PubMed]

Z. Zhu, A. M. C. Dawes, D. J. Gauthier, L. Zhang, and A. E. Willner, “Broadband SBS Slow Light in an Optical Fiber,” J. Lightwave Technol. 25, 201–206 (2007).
[CrossRef]

B. Zhang, L. Yan, I. Fazal, L. Zhang, A. E. Willner, Z. Zhu, and D. J. Gauthier, “Slow light on Gbit/s differential-phase-shift-keying signals,” Opt. Express 15, 1878–1883 (2007).
[CrossRef] [PubMed]

Z. Shi, R. Pant, Z. Zhu, M. D. Stenner, M. A. Neifeld, D. J. Gauthier, and R. W. Boyd, “Design of a tunable time-delay element using multiple gain lines for large fractional delay with high data fidelity,” Opt. Lett. 32, 1986–1988 (2007).
[CrossRef] [PubMed]

R. W. Boyd, D. J. Gauthier, A. L. Gaeta, and A. E. Willner, “Erratum: Maximum time delay achievable on propagation through a slow-light medium,” Phys. Rev. A 72, 059903(2005).
[CrossRef]

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef] [PubMed]

M. D. Stenner, M. A. Neifeld, Z. Zhu, A. M. C. Dawes, and D. J. Gauthier, “Distortion management in slow-light pulse delay,” Opt. Express 13, 9995–10002 (2005).
[CrossRef] [PubMed]

Z. Zhu, D. J. Gauthier, Y. Okawachi, J. E. Sharping, A. L. Gaeta, R. W. Boyd, and A. E. Willner, “Numerical study of all-optical slow-light delays via stimulated Brillouin scattering in an optical fiber,” J. Opt. Soc. Am. B 22, 2378–2384 (2005).
[CrossRef]

Ghosh, A.

Glick, Y.

Gonzalez-Herraez, M.

S. Chin, M. Gonzalez-Herraez, and L. Thévenaz, “Complete compensation of pulse broadening in an amplifier-based slow light system using a nonlinear regeneration element,” Opt. Express 17, 21910–21917 (2009).
[CrossRef] [PubMed]

M. Gonzalez-Herraez, K. Song, and L. Thévenaz, “Optically controlled slow and fast light in optical fibers using stimulated Brillouin scattering,” Appl. Phys. Lett. 87, 081113 (2005).
[CrossRef]

Grigoryan, V. S.

Holzlohner, R.

Howell, J. C.

Z. Shi, R. W. Boyd, R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, “Slow-light Fourier transform interferometer,” Phys. Rev. Lett. 99, 240801 (2007).
[CrossRef]

Hu, W.

Jackel, S.

Jaouen, Y.

Junker, M.

Khurgin, J. B.

Ku, P. C.

Kurashima, T.

Lauterbach, K.-U.

Le Floch, S.

Lee, M.

Li, Q.

Li, Y.

F. Ravet, X. Bao, J. Snoddy, Y. Li, and L. Chen, “Characterization of Brillouin fiber generator and amplifier for optimized working condition of distributed sensors,” Opt. Fiber Technol. 15, 304–309 (2009).
[CrossRef]

Liang, R.

Liu, Y.

Lu, Z.

Maruoka, M.

Melle, S.

Y. Zhu, E. Cabrera-Granado, O. G. Calderon, S. Melle, Y. Okawachi, A. L. Gaeta, and D. J. Gauthier, “Competition between the Modulation Instability and Stimulated Brillouin Scattering in a Broadband Slow Light Device,” J. Opt. 12, 104019 (2010).
[CrossRef]

E. Cabrera-Granado, O. G. Calderon, S. Melle, and D. J. Gauthier, “Observation of large 10 Gb/s SBS slow light delay with low distortion using an optimized gain profile,” Opt. Express 16, 16032–16042 (2008).
[CrossRef] [PubMed]

Menyuk, C. R.

Miller, D. A. B.

D. A. B. Miller, “Fundamental limit to linear one-dimensional slow light structures,” Phys. Rev. Lett. 99, 203903 (2007).
[CrossRef]

Minardo, A.

Narum, P.

R. W. Boyd, K. Rzaewski, and P. Narum, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A 42, 5514–5521(1990).
[CrossRef] [PubMed]

Neifeld, M. A.

Norimatsu, S.

Okawachi, Y.

Y. Zhu, E. Cabrera-Granado, O. G. Calderon, S. Melle, Y. Okawachi, A. L. Gaeta, and D. J. Gauthier, “Competition between the Modulation Instability and Stimulated Brillouin Scattering in a Broadband Slow Light Device,” J. Opt. 12, 104019 (2010).
[CrossRef]

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef] [PubMed]

Z. Zhu, D. J. Gauthier, Y. Okawachi, J. E. Sharping, A. L. Gaeta, R. W. Boyd, and A. E. Willner, “Numerical study of all-optical slow-light delays via stimulated Brillouin scattering in an optical fiber,” J. Opt. Soc. Am. B 22, 2378–2384 (2005).
[CrossRef]

Olsson, N. A.

N. A. Olsson, “Lightwave systems with optical amplifiers,” J. Lightwave Technol. 7, 1071–1082 (1989).
[CrossRef]

Pant, R.

Paraschis, L.

Ravet, F.

F. Ravet, X. Bao, J. Snoddy, Y. Li, and L. Chen, “Characterization of Brillouin fiber generator and amplifier for optimized working condition of distributed sensors,” Opt. Fiber Technol. 15, 304–309 (2009).
[CrossRef]

Rzaewski, K.

R. W. Boyd, K. Rzaewski, and P. Narum, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A 42, 5514–5521(1990).
[CrossRef] [PubMed]

Sakamoto, T.

Schneider, T.

Schweinsberg, A.

A. Schweinsberg, Z. Shi, J. E. Vornehm, and R. W. Boyd, “Demonstration of a slow-light laser radar,” Opt. Express 19, 15760–15769 (2011).
[CrossRef] [PubMed]

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef] [PubMed]

Shannon, C. E.

C. E. Shannon, “A mathematical theory of communications,” Bell Syst. Tech. J. 27, 379–423 (1948).

Sharping, J. E.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef] [PubMed]

Z. Zhu, D. J. Gauthier, Y. Okawachi, J. E. Sharping, A. L. Gaeta, R. W. Boyd, and A. E. Willner, “Numerical study of all-optical slow-light delays via stimulated Brillouin scattering in an optical fiber,” J. Opt. Soc. Am. B 22, 2378–2384 (2005).
[CrossRef]

Shi, S.

Shi, Z.

Shiraki, K.

Snoddy, J.

F. Ravet, X. Bao, J. Snoddy, Y. Li, and L. Chen, “Characterization of Brillouin fiber generator and amplifier for optimized working condition of distributed sensors,” Opt. Fiber Technol. 15, 304–309 (2009).
[CrossRef]

Song, K.

M. Gonzalez-Herraez, K. Song, and L. Thévenaz, “Optically controlled slow and fast light in optical fibers using stimulated Brillouin scattering,” Appl. Phys. Lett. 87, 081113 (2005).
[CrossRef]

Stenner, M. D.

Sternklar, S.

Su, Y.

Thévenaz, L.

S. Chin, M. Gonzalez-Herraez, and L. Thévenaz, “Complete compensation of pulse broadening in an amplifier-based slow light system using a nonlinear regeneration element,” Opt. Express 17, 21910–21917 (2009).
[CrossRef] [PubMed]

M. Gonzalez-Herraez, K. Song, and L. Thévenaz, “Optically controlled slow and fast light in optical fibers using stimulated Brillouin scattering,” Appl. Phys. Lett. 87, 081113 (2005).
[CrossRef]

Tucker, R. S.

Tur, M.

Venkitesh, D.

Vijaya, R.

Vornehm, J. E.

Vudyasetu, P. K.

Z. Shi, R. W. Boyd, R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, “Slow-light Fourier transform interferometer,” Phys. Rev. Lett. 99, 240801 (2007).
[CrossRef]

Wang, J.

Willner, A.

Z. Bo, L. Yan, J. Yang, I. Fazal, and A. Willner, “A single slow-light element for independent delay control and synchronization on multiple Gb/s data channels,” IEEE Photon. Technol. Lett. 19, 1081–1083 (2007).
[CrossRef]

Willner, A. E.

Yamamoto, T.

Yan, L.

B. Zhang, L. Yan, I. Fazal, L. Zhang, A. E. Willner, Z. Zhu, and D. J. Gauthier, “Slow light on Gbit/s differential-phase-shift-keying signals,” Opt. Express 15, 1878–1883 (2007).
[CrossRef] [PubMed]

Z. Bo, L. Yan, J. Yang, I. Fazal, and A. Willner, “A single slow-light element for independent delay control and synchronization on multiple Gb/s data channels,” IEEE Photon. Technol. Lett. 19, 1081–1083 (2007).
[CrossRef]

Yang, J.

Z. Bo, L. Yan, J. Yang, I. Fazal, and A. Willner, “A single slow-light element for independent delay control and synchronization on multiple Gb/s data channels,” IEEE Photon. Technol. Lett. 19, 1081–1083 (2007).
[CrossRef]

Yi, L.

Yoo, S. J. B.

Zadok, A.

Zeni, L.

Zhang, B.

Zhang, L.

Zhang, R.

Zhang, Z.

Zhong, P.

Zhou, X.

Zhu, Y.

Y. Zhu, M. Lee, M. A. Neifeld, and D. J. Gauthier, “High-fidelity broadband stimulated-Brillouin-scattering-based slow light using fast noise modulation,” Opt. Express 19, 687–697(2011).
[CrossRef] [PubMed]

R. Zhang, Y. Zhu, J. Wang, and D. J. Gauthier, “Slow light with a swept-frequency source,” Opt. Express 18, 27263–27269(2010).
[CrossRef]

Y. Zhu, E. Cabrera-Granado, O. G. Calderon, S. Melle, Y. Okawachi, A. L. Gaeta, and D. J. Gauthier, “Competition between the Modulation Instability and Stimulated Brillouin Scattering in a Broadband Slow Light Device,” J. Opt. 12, 104019 (2010).
[CrossRef]

Zhu, Z.

Zuqing, Z.

Appl. Opt. (2)

Appl. Phys. Lett. (1)

M. Gonzalez-Herraez, K. Song, and L. Thévenaz, “Optically controlled slow and fast light in optical fibers using stimulated Brillouin scattering,” Appl. Phys. Lett. 87, 081113 (2005).
[CrossRef]

Bell Syst. Tech. J. (1)

C. E. Shannon, “A mathematical theory of communications,” Bell Syst. Tech. J. 27, 379–423 (1948).

IEEE Photon. Technol. Lett. (1)

Z. Bo, L. Yan, J. Yang, I. Fazal, and A. Willner, “A single slow-light element for independent delay control and synchronization on multiple Gb/s data channels,” IEEE Photon. Technol. Lett. 19, 1081–1083 (2007).
[CrossRef]

J. Lightwave Technol. (6)

J. Opt. (1)

Y. Zhu, E. Cabrera-Granado, O. G. Calderon, S. Melle, Y. Okawachi, A. L. Gaeta, and D. J. Gauthier, “Competition between the Modulation Instability and Stimulated Brillouin Scattering in a Broadband Slow Light Device,” J. Opt. 12, 104019 (2010).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (6)

Opt. Express (14)

S. Chin, M. Gonzalez-Herraez, and L. Thévenaz, “Complete compensation of pulse broadening in an amplifier-based slow light system using a nonlinear regeneration element,” Opt. Express 17, 21910–21917 (2009).
[CrossRef] [PubMed]

R. Zhang, Y. Zhu, J. Wang, and D. J. Gauthier, “Slow light with a swept-frequency source,” Opt. Express 18, 27263–27269(2010).
[CrossRef]

Y. Zhu, M. Lee, M. A. Neifeld, and D. J. Gauthier, “High-fidelity broadband stimulated-Brillouin-scattering-based slow light using fast noise modulation,” Opt. Express 19, 687–697(2011).
[CrossRef] [PubMed]

A. Schweinsberg, Z. Shi, J. E. Vornehm, and R. W. Boyd, “Demonstration of a slow-light laser radar,” Opt. Express 19, 15760–15769 (2011).
[CrossRef] [PubMed]

E. Cabrera-Granado, O. G. Calderon, S. Melle, and D. J. Gauthier, “Observation of large 10 Gb/s SBS slow light delay with low distortion using an optimized gain profile,” Opt. Express 16, 16032–16042 (2008).
[CrossRef] [PubMed]

L. Yi, Y. Jaouen, W. Hu, Y. Su, and S. Bigo, “Improved slow-light performance of 10 Gb/s NRZ, PSBT and DPSK signals in fiber broadband SBS,” Opt. Express 15, 16972–16979(2007).
[CrossRef] [PubMed]

R. Pant, M. D. Stenner, M. A. Neifeld, and D. J. Gauthier, “Optimal pump profile designs for broadband SBS slow-light systems,” Opt. Express 16, 2764–2777 (2008).
[CrossRef] [PubMed]

T. Sakamoto, T. Yamamoto, K. Shiraki, and T. Kurashima, “Low distortion slow light in flat Brillouin gain spectrum by using optical frequency comb,” Opt. Express 16, 8026–8032(2008).
[CrossRef] [PubMed]

A. Minardo, R. Bernini, and L. Zeni, “Low distortion Brillouin slow light in optical fibers using AM modulation,” Opt. Express 14, 5866–5876 (2006).
[CrossRef] [PubMed]

A. Zadok, A. Eyal, and M. Tur, “Extended delay of broadband signals in stimulated Brillouin scattering slow light using synthesized pump chirp,” Opt. Express 14, 8498–8505 (2006).
[CrossRef] [PubMed]

T. Schneider, M. Junker, and K.-U. Lauterbach, “Potential ultra wide slow-light bandwidth enhancement,” Opt. Express 14, 11082–11087 (2006).
[CrossRef] [PubMed]

Z. Lu, Y. Dong, and Q. Li, “Slow light in multi-line Brillouin gain spectrum,” Opt. Express 15, 1871–1877 (2007).
[CrossRef] [PubMed]

B. Zhang, L. Yan, I. Fazal, L. Zhang, A. E. Willner, Z. Zhu, and D. J. Gauthier, “Slow light on Gbit/s differential-phase-shift-keying signals,” Opt. Express 15, 1878–1883 (2007).
[CrossRef] [PubMed]

M. D. Stenner, M. A. Neifeld, Z. Zhu, A. M. C. Dawes, and D. J. Gauthier, “Distortion management in slow-light pulse delay,” Opt. Express 13, 9995–10002 (2005).
[CrossRef] [PubMed]

Opt. Fiber Technol. (1)

F. Ravet, X. Bao, J. Snoddy, Y. Li, and L. Chen, “Characterization of Brillouin fiber generator and amplifier for optimized working condition of distributed sensors,” Opt. Fiber Technol. 15, 304–309 (2009).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. A (2)

R. W. Boyd, K. Rzaewski, and P. Narum, “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A 42, 5514–5521(1990).
[CrossRef] [PubMed]

R. W. Boyd, D. J. Gauthier, A. L. Gaeta, and A. E. Willner, “Erratum: Maximum time delay achievable on propagation through a slow-light medium,” Phys. Rev. A 72, 059903(2005).
[CrossRef]

Phys. Rev. Lett. (3)

D. A. B. Miller, “Fundamental limit to linear one-dimensional slow light structures,” Phys. Rev. Lett. 99, 203903 (2007).
[CrossRef]

Z. Shi, R. W. Boyd, R. M. Camacho, P. K. Vudyasetu, and J. C. Howell, “Slow-light Fourier transform interferometer,” Phys. Rev. Lett. 99, 240801 (2007).
[CrossRef]

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. Zhu, A. Schweinsberg, D. J. Gauthier, R. W. Boyd, and A. L. Gaeta, “Tunable all-optical delays via Brillouin slow light in an optical fiber,” Phys. Rev. Lett. 94, 153902 (2005).
[CrossRef] [PubMed]

Science (1)

R. W. Boyd and D. J. Gauthier, “Controlling the velocity of light pulses,” Science 326, 1074–1077 (2009).
[CrossRef] [PubMed]

Other (2)

G. P. Agrawal, Fiber-Optic Communication Systems, 3rd ed. (Wiley, 2002).
[CrossRef]

J. D. Fast, Entropy. The Significance of the Concept of Entropy and Its Applications in the Science and Technology (McGraw-Hill, 1962).
[PubMed]

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Figures (11)

Fig. 1
Fig. 1

(a) Experiment setup. HNLF: slow-light medium (HNLF, OFS, Inc.) FPC: fiber polarization controller, EDFA: erbium-doped fiber amplifier, CIR: circulator, MZM: Mach–Zehnder modulator, PD: photodiode, FBG: fiber Bragg grating, AWG: arbitrary waveform generator (Tektronix AFG3251), DFB: distributed feedback laser, VOA: variable optical attenuator, OS: oscilloscope and PG: pattern generator (Agilent 70843B). (b) Example of eye diagram measured by an oscilloscope. The vertical box indicates the region of the eye diagram used to measure the standard deviation of “1’s” and “0’s” at the eye-center.

Fig. 2
Fig. 2

Application of the IT analysis to an ideal delay device. (a) Example signals at the output of the slow-light medium in the absence (solid blue line) and presence (dashed red line) of the slow-light effect. (b) Mutual information as a function of output window. The vertical dashed line indicates the middle of the region of high mutual information, which determines the information delay.

Fig. 3
Fig. 3

Geometry of the SBS interaction. Complex field amplitudes for the signal, pump and Rayleigh back scattered waves, are denoted by E s , E p , and E Rayleigh , respectively, and the Langevin noise source is denoted by f.

Fig. 4
Fig. 4

Theoretically predicted power spectral density for the input signal P ˜ s ( L , Δ ω ) , amplified signal P ˜ s ( 0 , Δ ω ) , ASE signal P ˜ ase ( 0 , Δ ω ) , and total signal P ˜ tot ( 0 , Δ ω ) for the case when P p = 300 mW , P s , in = 1 P in , Δ ω G = 5 GHz , and BR = 2 Gbps . The other parameters are: Γ B = 2 π ( 30 MHz ), Ω B = 2 π ( 9.6 GHz ), α = 1 dB / km , A = 15 μm 2 , g 0 = 1.65 × 10 11 m / W , and L eff 1.6 km , which are appropriate for the HNLF used in the experiment (see Fig. 1).

Fig. 5
Fig. 5

Theoretically predicted amplified signal and noise contributions from the various sources as a function of pump power for P s , in = 1 P in , Δ ω G = 5 GHz , and BR = 2 Gbps . We account for the 7 dB attenuation due to the variable optical attenuator (VOA) used in the experimental setup.

Fig. 6
Fig. 6

(a) Flattop SBS gain spectrum with a width (FWHM) equal to 5 GHz for P p = 70 mW . (b) Gain and (c) pulse-peak-to-pulse-peak fractional slow delay experienced by a single super-Gaussian pulse of duration (FWHM) T p = 200 ps as a function of the pump power. The straight lines in (b) and (c) are a guide to the eye and consistent with the linear scaling expected for the slow-light system.

Fig. 7
Fig. 7

Input and output eye diagrams for several different pump powers, P s , in = 1 P in and BR = 2 Gbps . (a) Experimental results measured by an oscilloscope and (b) numerical simulations.

Fig. 8
Fig. 8

Delay and data fidelity metrics as a function of input signal power for BR = 2 Gbps . (a) Fractional information delays are denoted by the symbols. The dashed straight line is a guide to the eye and consistent with the linear scaling expected for a slow-light system. (b) Eye opening, (c) SNR, and (d) IT as a function of P p .

Fig. 9
Fig. 9

Delay and data fidelity metrics as a function of data rate for P s , in = 0.5 P in . (a) Fractional information delays are denoted by the symbols. The dashed straight lines are a guide to the eye. (b) Eye opening, (c) SNR, and (d) IT as a function of P p .

Fig. 10
Fig. 10

(a) Gain and (b) fractional delay for the optimal flattop and Gaussian gain profiles of width (FWHM) of 5 GHz . The measurements are made when propagating a single weak super-Gaussian pulse with T p = 200 ps through the slow-light medium. The solid and dashed straight lines are guides to the eye.

Fig. 11
Fig. 11

Delay and data fidelity metrics for the flattop and Gaussian gain profiles for BR = 2.5 Gbps and P s , in = 1 P in . (a) Fractional information delay is denoted by the symbols. The dashed straight lines are a guide to the eye. (b) Eye opening, (c) SNR, and (d) IT as a function of P p .

Equations (12)

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

SNR exp = u 1 u 0 σ 1 2 + σ 0 2 .
I ( X ; Y ) = m + i = 1 M p ( x i ) p ( Y | x i ) log 2 p ( x i ) p ( Y | x i ) i = 1 M p ( x j ) p ( Y | x j ) d Y ,
p ( Y | x i ) 1 ( 2 π σ 2 ) m N exp ( 1 2 σ 2 | Y x i | 2 ) ,
P s ˜ ( 0 , Δ ω ) = P s ˜ ( L , Δ ω ) H SBS ,
H SBS = exp ( α L ) exp [ G B B ( Δ ω ) L eff ] .
B ( Δ ω ) = 1 π [ tan 1 ( Δ ω + Δ ω G / 2 Γ B / 2 ) tan 1 ( Δ ω Δ ω G / 2 Γ B / 2 ) ]
σ aj 2 = R 2 ( P s , out σ j 1 / u j 1 ) 2 ,
P ˜ ase ( 0 , Δ ω ) = K ASE [ H SBS ( exp ( α L ) + α G B B ( Δ ω ) ) ( 1 + α G B B ( Δ ω ) ) ] ,
σ s s p 2 = 4 R 2 P s , out P ase ( 0 , Δ ω = 0 ) Δ ν e .
σ s p s p 2 = 4 R 2 P ase ( 0 , Δ ω = 0 ) 2 Δ ν e Δ ν o ,
σ sh 2 = 2 q ( R P s , out + i d ) Δ ν e ,
σ th 2 = 4 k B T Δ ν e R L .

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