Abstract

We present a theoretical analysis of the slow-light tunable optical buffers based on fiber Brillouin amplifiers (FBA). Its storage capacity was discussed for return-to-zero (RZ) and non-return-to-zero (NRZ) bit streams. Gain saturation and pulse broadening are two key factors which limit the buffer capacity. Gain saturation is an inherent characteristic of the FBA. Broadening of the amplified pulse always accumulates with increasing gain owing to the dispersion during stimulated Brillouin scattering (SBS) process. It is shown that the maximum buffer capacity varies with data bit rate and for continuous wave (CW) or quasi-CW pump it is 0.53 and 1.04 bit for RZ and NRZ respectively. Also, the optimum data bit rate to achieve the best storage capacity is obtained.

©2007 Optical Society of America

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References

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  1. K. Y. Song, M. G. Herraez, and L. Thevenaz, “Observation of pulse delaying and advancement in optical fibers using stimulated Brillouin scattering,” Opt. Express 13, 82–88 (2005).
    [Crossref] [PubMed]
  2. Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. M. 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]
  3. K. Y. Song, M. G. Herraez, and L. Thevenaz, “Long optically controlled delays in optical fibers,” Opt. Lett. 30, 1782–1784 (2005).
    [Crossref] [PubMed]
  4. M. G. Herraez, K. Y. Song, and L. Thevenaz, “Arbitrary-bandwidth Brillouin slow light in optical fibers,” Opt. Express 14, 1395–1400 (2006).
    [Crossref]
  5. Z. M. Zhu, M. C. Dawes, D. J. Gauthier, L. Zhang, and A. E. Willner, “12-GHz-Bandwidth SBS slow light in optical fibers,” in proceedings of OFC 2006, paper PDP1.
  6. K. Y. Song and K. Hotate, “25 GHz bandwidth Brillouin slow light in optical fibers,” Opt. Lett. 32, 217–219 (2007).
    [Crossref] [PubMed]
  7. 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]
  8. 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]
  9. L. L. Yi, L. Zhan, W. S. Hu, and Y. X. Xia, “Delay of broadband signals using slow light in stimulated Brillouin scattering With phase-modulated pump,” IEEE Photon. Technol. Lett. 19, 619–621 (2007).
    [Crossref]
  10. M. D. Stenner and M. A. Neifeld, “Distortion management in slow-light pulse delay,” Opt. Express 13, 9995–10002 (2005).
    [Crossref] [PubMed]
  11. T. Schneider, M. Junker, K. U. Lauterbach, and R. Henker, “Distortion reduction in cascaded slow light delays,” Electron. Lett. 42, 1110–1112 (2006).
    [Crossref]
  12. Z. W. Lu, Y. K. Dong, and Q. Li, “Slow light in multi-line Brillouin gain spectrum,” Opt. Express 15, 1871–1877 (2007).
    [Crossref] [PubMed]
  13. J. B. Khurgin, “Performance limits of delay lines based on optical amplifiers,” Opt. Lett. 31, 948–950 (2006).
    [Crossref] [PubMed]
  14. Z. M. Zhu and D. J. Gauthier, “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]
  15. V. P. Kalosha, L. Chen, and X. Bao, “Slow and fast light via SBS in optical fibers for short pulses and broadband pump,” Opt. Express 14, 12693–12703 (2006).
    [Crossref] [PubMed]
  16. E. Shumakher, N. Orbach, A. Nevet, D. Dahan, and G. Eisenstein, “On the balance between delay, bandwidth and signal distortion in slow light systems based on stimulated Brillouin scattering in optical fibers,” Opt. Express 14, 5877–5884 (2006).
    [Crossref] [PubMed]
  17. G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2005), Chap. 9.
  18. R. S. Tucker, P. C. Ku, and C. J. Chang-Hasnain, “Slow-light optical buffers: Capabilities and fundamental limitations,” J. Lightw. Technol. 23, 4046–4066 (2005).
    [Crossref]
  19. L. Zhang, T. Luo, W. Zhang, C. Yu, Y. Wang, and A. E. Willner, “Optimizing operating conditions to reduce data pattern dependence induced by slow light elements,” in proceedings of OFC 2006, paper OFP7.

2007 (3)

L. L. Yi, L. Zhan, W. S. Hu, and Y. X. Xia, “Delay of broadband signals using slow light in stimulated Brillouin scattering With phase-modulated pump,” IEEE Photon. Technol. Lett. 19, 619–621 (2007).
[Crossref]

K. Y. Song and K. Hotate, “25 GHz bandwidth Brillouin slow light in optical fibers,” Opt. Lett. 32, 217–219 (2007).
[Crossref] [PubMed]

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

2006 (7)

2005 (6)

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2005), Chap. 9.

Bao, X.

Bernini, R.

Bigelow, M. S.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. M. 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]

Boyd, R. W.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. M. 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]

Chang-Hasnain, C. J.

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

Chen, L.

Dahan, D.

Dawes, M. C.

Z. M. Zhu, M. C. Dawes, D. J. Gauthier, L. Zhang, and A. E. Willner, “12-GHz-Bandwidth SBS slow light in optical fibers,” in proceedings of OFC 2006, paper PDP1.

Dong, Y. K.

Eisenstein, G.

Eyal, A.

Gaeta, A. L.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. M. 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]

Gauthier, D. J.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. M. 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. M. Zhu and D. J. Gauthier, “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]

Z. M. Zhu, M. C. Dawes, D. J. Gauthier, L. Zhang, and A. E. Willner, “12-GHz-Bandwidth SBS slow light in optical fibers,” in proceedings of OFC 2006, paper PDP1.

Henker, R.

T. Schneider, M. Junker, K. U. Lauterbach, and R. Henker, “Distortion reduction in cascaded slow light delays,” Electron. Lett. 42, 1110–1112 (2006).
[Crossref]

Herraez, M. G.

Hotate, K.

Hu, W. S.

L. L. Yi, L. Zhan, W. S. Hu, and Y. X. Xia, “Delay of broadband signals using slow light in stimulated Brillouin scattering With phase-modulated pump,” IEEE Photon. Technol. Lett. 19, 619–621 (2007).
[Crossref]

Junker, M.

T. Schneider, M. Junker, K. U. Lauterbach, and R. Henker, “Distortion reduction in cascaded slow light delays,” Electron. Lett. 42, 1110–1112 (2006).
[Crossref]

Kalosha, V. P.

Khurgin, J. B.

Ku, P. C.

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

Lauterbach, K. U.

T. Schneider, M. Junker, K. U. Lauterbach, and R. Henker, “Distortion reduction in cascaded slow light delays,” Electron. Lett. 42, 1110–1112 (2006).
[Crossref]

Li, Q.

Lu, Z. W.

Luo, T.

L. Zhang, T. Luo, W. Zhang, C. Yu, Y. Wang, and A. E. Willner, “Optimizing operating conditions to reduce data pattern dependence induced by slow light elements,” in proceedings of OFC 2006, paper OFP7.

Minardo, A.

Neifeld, M. A.

Nevet, A.

Okawachi, Y.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. M. 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]

Orbach, N.

Schneider, T.

T. Schneider, M. Junker, K. U. Lauterbach, and R. Henker, “Distortion reduction in cascaded slow light delays,” Electron. Lett. 42, 1110–1112 (2006).
[Crossref]

Schweinsberg, A.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. M. 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]

Sharping, J. E.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. M. 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]

Shumakher, E.

Song, K. Y.

Stenner, M. D.

Thevenaz, L.

Tucker, R. S.

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

Tur, M.

Wang, Y.

L. Zhang, T. Luo, W. Zhang, C. Yu, Y. Wang, and A. E. Willner, “Optimizing operating conditions to reduce data pattern dependence induced by slow light elements,” in proceedings of OFC 2006, paper OFP7.

Willner, A. E.

L. Zhang, T. Luo, W. Zhang, C. Yu, Y. Wang, and A. E. Willner, “Optimizing operating conditions to reduce data pattern dependence induced by slow light elements,” in proceedings of OFC 2006, paper OFP7.

Z. M. Zhu, M. C. Dawes, D. J. Gauthier, L. Zhang, and A. E. Willner, “12-GHz-Bandwidth SBS slow light in optical fibers,” in proceedings of OFC 2006, paper PDP1.

Xia, Y. X.

L. L. Yi, L. Zhan, W. S. Hu, and Y. X. Xia, “Delay of broadband signals using slow light in stimulated Brillouin scattering With phase-modulated pump,” IEEE Photon. Technol. Lett. 19, 619–621 (2007).
[Crossref]

Yi, L. L.

L. L. Yi, L. Zhan, W. S. Hu, and Y. X. Xia, “Delay of broadband signals using slow light in stimulated Brillouin scattering With phase-modulated pump,” IEEE Photon. Technol. Lett. 19, 619–621 (2007).
[Crossref]

Yu, C.

L. Zhang, T. Luo, W. Zhang, C. Yu, Y. Wang, and A. E. Willner, “Optimizing operating conditions to reduce data pattern dependence induced by slow light elements,” in proceedings of OFC 2006, paper OFP7.

Zadok, A.

Zeni, L.

Zhan, L.

L. L. Yi, L. Zhan, W. S. Hu, and Y. X. Xia, “Delay of broadband signals using slow light in stimulated Brillouin scattering With phase-modulated pump,” IEEE Photon. Technol. Lett. 19, 619–621 (2007).
[Crossref]

Zhang, L.

Z. M. Zhu, M. C. Dawes, D. J. Gauthier, L. Zhang, and A. E. Willner, “12-GHz-Bandwidth SBS slow light in optical fibers,” in proceedings of OFC 2006, paper PDP1.

L. Zhang, T. Luo, W. Zhang, C. Yu, Y. Wang, and A. E. Willner, “Optimizing operating conditions to reduce data pattern dependence induced by slow light elements,” in proceedings of OFC 2006, paper OFP7.

Zhang, W.

L. Zhang, T. Luo, W. Zhang, C. Yu, Y. Wang, and A. E. Willner, “Optimizing operating conditions to reduce data pattern dependence induced by slow light elements,” in proceedings of OFC 2006, paper OFP7.

Zhu, Z. M.

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. M. 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. M. Zhu and D. J. Gauthier, “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]

Z. M. Zhu, M. C. Dawes, D. J. Gauthier, L. Zhang, and A. E. Willner, “12-GHz-Bandwidth SBS slow light in optical fibers,” in proceedings of OFC 2006, paper PDP1.

Electron. Lett. (1)

T. Schneider, M. Junker, K. U. Lauterbach, and R. Henker, “Distortion reduction in cascaded slow light delays,” Electron. Lett. 42, 1110–1112 (2006).
[Crossref]

IEEE Photon. Technol. Lett. (1)

L. L. Yi, L. Zhan, W. S. Hu, and Y. X. Xia, “Delay of broadband signals using slow light in stimulated Brillouin scattering With phase-modulated pump,” IEEE Photon. Technol. Lett. 19, 619–621 (2007).
[Crossref]

J. Lightw. Technol. (1)

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

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

Opt. Express (8)

M. D. Stenner and M. A. Neifeld, “Distortion management in slow-light pulse delay,” Opt. Express 13, 9995–10002 (2005).
[Crossref] [PubMed]

M. G. Herraez, K. Y. Song, and L. Thevenaz, “Arbitrary-bandwidth Brillouin slow light in optical fibers,” Opt. Express 14, 1395–1400 (2006).
[Crossref]

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]

E. Shumakher, N. Orbach, A. Nevet, D. Dahan, and G. Eisenstein, “On the balance between delay, bandwidth and signal distortion in slow light systems based on stimulated Brillouin scattering in optical fibers,” Opt. Express 14, 5877–5884 (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]

V. P. Kalosha, L. Chen, and X. Bao, “Slow and fast light via SBS in optical fibers for short pulses and broadband pump,” Opt. Express 14, 12693–12703 (2006).
[Crossref] [PubMed]

K. Y. Song, M. G. Herraez, and L. Thevenaz, “Observation of pulse delaying and advancement in optical fibers using stimulated Brillouin scattering,” Opt. Express 13, 82–88 (2005).
[Crossref] [PubMed]

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

Opt. Lett. (3)

Phys. Rev. Lett. (1)

Y. Okawachi, M. S. Bigelow, J. E. Sharping, Z. M. 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]

Other (3)

Z. M. Zhu, M. C. Dawes, D. J. Gauthier, L. Zhang, and A. E. Willner, “12-GHz-Bandwidth SBS slow light in optical fibers,” in proceedings of OFC 2006, paper PDP1.

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 2005), Chap. 9.

L. Zhang, T. Luo, W. Zhang, C. Yu, Y. Wang, and A. E. Willner, “Optimizing operating conditions to reduce data pattern dependence induced by slow light elements,” in proceedings of OFC 2006, paper OFP7.

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Figures (3)

Fig. 1.
Fig. 1. Characteristics of the SBS resonances (a) Gain and effective refractive index (b) Delay time

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Fig. 2.
Fig. 2. (a). The maximum of broadening-constrained gain parameter versus input pulse width (b) Relations between saturation gain and the peak power of the probe pulse (c) Comparison of Gsat and GB,max as a function of input pulse width for different peak powers for NRZ data when B=1.5. There is an available gain zone in red dot frame.

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Fig. 3.
Fig. 3. The maximum of storage bits versus bit rate (a) RZ pulses with different peak powers for B=2 (b) RZ pulses for different broadening factors for 10nw peak power (c) NRZ pulses with different peak powers for B=2 (d) NRZ pulses with different broadening factors for 10nw peak power

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Equations (8)

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g ( ω ) = g p I p ( Γ B ⁄ 2 ) 2 ( ω − ω 0 ) 2 + ( Γ B ⁄ 2 ) 2
n r − 1 = − c 2 π ω P ∫ − ∞ ∞ g ( s ) s − ω ds
n r = c g p I p ω ( ω − ω 0 ) ⁄ Γ B ( 1 + [ 2 ( ω − ω 0 ) ⁄ Γ B ] 2 ) + 1
T d ≈ g p I p L Γ B 1 − [ 2 ( ω − ω 0 ) ⁄ Γ B ] 2 ( 1 + [ 2 ( ω − ω 0 ) ⁄ Γ B ] 2 ) 2
N bit = T d B bit ≈ G B B bit ⁄ Γ B = { G B ⁄ ( 4 Γ B τ FWHM ) RZ G B ⁄ ( 2 Γ B τ FWHM ) NRZ
B = τ out ⁄ τ in = [ 1 + G B 16 ln 2 / ( τ in 2 τ B 2 ) ] 1 ⁄ 2
G B ≤ Γ B 2 τ in 2 ( B 2 − 1 ) ⁄ ( 16 ln 2 )
G sat = ln ( exp [ ( 1 − ξ ) G A ] − ξ 1 − ξ )

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