Abstract

In this article the theoretical investigation and the experimental verification of an almost distortion-free pulse delay are presented. The proposed Brillouin slow-light system provides very large fractional delay at very low distortion since the pulse shape and the pulse width are maintained during the delaying process. Beyond that, the method is compatible with any other conventional Brillouin based slow-light system to significantly increase its efficiency.

© 2010 Optical Society of America

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References

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  1. T. Asami and S. Namiki, “Energy consumption targets for network systems,” in 34th European Conference on Optical Communication (ECOC) (2008), paper Tu.4.A.3.
    [CrossRef]
  2. L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594-598 (1999).
    [CrossRef]
  3. Z. Zhu, D. J. Gauthier, and R. W. Boyd, “Stored light in an optical fiber via stimulated Brillouin scattering,” Science 318, 1748-1750 (2007).
    [CrossRef] [PubMed]
  4. 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]
  5. E. Mateo, F. Yaman, and G. Li, “Control of four-wave mixing phase-matching condition using the Brillouin slow-light effect in fibers,” Opt. Lett. 33, 488-490 (2008).
    [CrossRef] [PubMed]
  6. W. Xue, S. Sales, J. Capmany, and J. Mørk, “Microwave phase shifter with controllable power response based on slow- and fast-light effects in semiconductor optical amplifiers,” Opt. Lett. 34, 929-931 (2009).
    [CrossRef] [PubMed]
  7. K. Y. Song, M. González Herráez, and L. Thévenaz, “Observation of pulse delaying and advancement in optical fibers using stimulated Brillouin scattering,” Opt. Express 13, 82-88 (2005).
    [CrossRef] [PubMed]
  8. 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]
  9. M. González Herráez, K. Y. Song, and L. Thévenaz, “Arbitrary-bandwidth Brillouin slow light in optical fibers,” Opt. Express 14, 1395-1400 (2006).
    [CrossRef] [PubMed]
  10. S. Chin, M. G. Herráez, and L. Thévenaz, “Zero-gain slow and fast light propagation in an optical fiber,” Opt. Express 14, 10684-10692 (2006).
    [CrossRef] [PubMed]
  11. T. Schneider, M. Junker, and K.-U. Lauterbach, “Time delay enhancement in stimulated-Brillouin-scattering-based slow-light systems,” Opt. Lett. 32, 220-222 (2007).
    [CrossRef] [PubMed]
  12. 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]
  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. 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]
  15. 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]
  16. T. Schneider, R. Henker, K.-U. Lauterbach, and M. Junker, “Distortion reduction in slow light systems based on stimulated Brillouin scattering,” Opt. Express 16, 8280-8285 (2008).
    [CrossRef] [PubMed]
  17. T. Schneider, A. Wiatrek, and R. Henker, “Zero-broadening and pulse compression slow light in an optical fiber at high pulse delays,” Opt. Express 16, 15617-15622 (2008).
    [CrossRef] [PubMed]
  18. M. González Herráez and L. Thévenaz, “Physical limits to broadening compensation in a linear slow light system,” Opt. Express 17, 4732-4739 (2009).
    [CrossRef] [PubMed]
  19. A. Wiatrek, R. Henker, S. Preußler, M. J. Ammann, A. T. Schwarzbacher, and T. Schneider, “Zero-broadening measurement in Brillouin based slow-light delays,” Opt. Express 17, 797-802 (2009).
    [CrossRef] [PubMed]
  20. A. Wiatrek, R. Henker, S. Preußler, and T. Schneider, “Pulse broadening cancellation in cascaded slow-light delays,” Opt. Express 17, 7586-7591 (2009).
    [CrossRef] [PubMed]
  21. S. Chin, M. González-Herráez, 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]
  22. T. Schneider, “Time delay limits of stimulated-Brillouin-scattering-based slow light systems,” Opt. Lett. 33, 1398-1400 (2008).
    [CrossRef] [PubMed]
  23. T. Schneider, R. Henker, K.-U. Lauterbach, and M. Junker, “Comparison of delay enhancement mechanisms for SBS-based slow light systems,” Opt. Express 15, 9606-9613 (2007).
    [CrossRef] [PubMed]
  24. A. V. Oppenheim, R. W. Schafer, and J. R. Buck, Discrete-Time Signal Processing (Prentice-Hall, 1998).
  25. V. Lucarini, J. J. Saarinen, K.-E. Peiponen, and E. M. Vartianinen, Kramers-Kronig Relations in Optical Materials Research (Springer, 2005).
  26. G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2007).
  27. M. F. Ferreira, J. F. Rocha, and J. L. Pinto, “Analysis of the gain and noise characteristics of fibre Brillouin amplifiers,” Opt. Quantum Electron. 26, 35-44 (1994).
    [CrossRef]
  28. K. Y. Song, M. González Herráez, and L. Thévenaz, “Gain-assisted pulse advancement using single and double Brillouin gain peaks in optical fibers,” Opt. Express 13, 9758-9765 (2005).
    [CrossRef] [PubMed]
  29. C. L. Tang, “Saturation and spectral characteristics of the Stokes emission in the stimulated Brillouin process,” J. Appl. Phys. 37, 2945 (1966).
    [CrossRef]
  30. J. B. Khurgin, “Performance limits of delay lines based on optical amplifiers,” Opt. Lett. 31, 948-950 (2006).
    [CrossRef] [PubMed]

2009

2008

2007

2006

2005

1999

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594-598 (1999).
[CrossRef]

1994

M. F. Ferreira, J. F. Rocha, and J. L. Pinto, “Analysis of the gain and noise characteristics of fibre Brillouin amplifiers,” Opt. Quantum Electron. 26, 35-44 (1994).
[CrossRef]

1966

C. L. Tang, “Saturation and spectral characteristics of the Stokes emission in the stimulated Brillouin process,” J. Appl. Phys. 37, 2945 (1966).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2007).

Ammann, M. J.

Asami, T.

T. Asami and S. Namiki, “Energy consumption targets for network systems,” in 34th European Conference on Optical Communication (ECOC) (2008), paper Tu.4.A.3.
[CrossRef]

Behroozi, C. H.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594-598 (1999).
[CrossRef]

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]

Boyd, R. W.

Z. Zhu, D. J. Gauthier, and R. W. Boyd, “Stored light in an optical fiber via stimulated Brillouin scattering,” Science 318, 1748-1750 (2007).
[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]

Buck, J. R.

A. V. Oppenheim, R. W. Schafer, and J. R. Buck, Discrete-Time Signal Processing (Prentice-Hall, 1998).

Capmany, J.

Chang-Hasnain, C. J.

Chin, S.

Dawes, A. M. C.

Dutton, Z.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594-598 (1999).
[CrossRef]

Eyal, A.

Ferreira, M. F.

M. F. Ferreira, J. F. Rocha, and J. L. Pinto, “Analysis of the gain and noise characteristics of fibre Brillouin amplifiers,” Opt. Quantum Electron. 26, 35-44 (1994).
[CrossRef]

Gaeta, A. L.

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]

Gauthier, D. J.

González Herráez, M.

González-Herráez, M.

Harris, S. E.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594-598 (1999).
[CrossRef]

Hau, L. V.

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594-598 (1999).
[CrossRef]

Henker, R.

Herráez, M. G.

Junker, M.

Khurgin, J. B.

Ku, P. -C.

Lauterbach, K. -U.

Li, G.

Lucarini, V.

V. Lucarini, J. J. Saarinen, K.-E. Peiponen, and E. M. Vartianinen, Kramers-Kronig Relations in Optical Materials Research (Springer, 2005).

Mateo, E.

Mørk, J.

Namiki, S.

T. Asami and S. Namiki, “Energy consumption targets for network systems,” in 34th European Conference on Optical Communication (ECOC) (2008), paper Tu.4.A.3.
[CrossRef]

Neifeld, M. A.

Okawachi, Y.

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]

Oppenheim, A. V.

A. V. Oppenheim, R. W. Schafer, and J. R. Buck, Discrete-Time Signal Processing (Prentice-Hall, 1998).

Pant, R.

Peiponen, K. -E.

V. Lucarini, J. J. Saarinen, K.-E. Peiponen, and E. M. Vartianinen, Kramers-Kronig Relations in Optical Materials Research (Springer, 2005).

Pinto, J. L.

M. F. Ferreira, J. F. Rocha, and J. L. Pinto, “Analysis of the gain and noise characteristics of fibre Brillouin amplifiers,” Opt. Quantum Electron. 26, 35-44 (1994).
[CrossRef]

Preußler, S.

Rocha, J. F.

M. F. Ferreira, J. F. Rocha, and J. L. Pinto, “Analysis of the gain and noise characteristics of fibre Brillouin amplifiers,” Opt. Quantum Electron. 26, 35-44 (1994).
[CrossRef]

Saarinen, J. J.

V. Lucarini, J. J. Saarinen, K.-E. Peiponen, and E. M. Vartianinen, Kramers-Kronig Relations in Optical Materials Research (Springer, 2005).

Sales, S.

Schafer, R. W.

A. V. Oppenheim, R. W. Schafer, and J. R. Buck, Discrete-Time Signal Processing (Prentice-Hall, 1998).

Schneider, T.

Schwarzbacher, A. T.

Schweinsberg, A.

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]

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]

Song, K. Y.

Stenner, M. D.

Tang, C. L.

C. L. Tang, “Saturation and spectral characteristics of the Stokes emission in the stimulated Brillouin process,” J. Appl. Phys. 37, 2945 (1966).
[CrossRef]

Thévenaz, L.

Tucker, R. S.

Tur, M.

Vartianinen, E. M.

V. Lucarini, J. J. Saarinen, K.-E. Peiponen, and E. M. Vartianinen, Kramers-Kronig Relations in Optical Materials Research (Springer, 2005).

Wiatrek, A.

Willner, A. E.

Xue, W.

Yaman, F.

Zadok, A.

Zhang, L.

Zhu, Z.

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. Zhu, D. J. Gauthier, and R. W. Boyd, “Stored light in an optical fiber via stimulated Brillouin scattering,” Science 318, 1748-1750 (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]

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]

J. Appl. Phys.

C. L. Tang, “Saturation and spectral characteristics of the Stokes emission in the stimulated Brillouin process,” J. Appl. Phys. 37, 2945 (1966).
[CrossRef]

J. Lightwave Technol.

Nature

L. V. Hau, S. E. Harris, Z. Dutton, and C. H. Behroozi, “Light speed reduction to 17 metres per second in an ultracold atomic gas,” Nature 397, 594-598 (1999).
[CrossRef]

Opt. Express

M. González Herráez, K. Y. Song, and L. Thévenaz, “Arbitrary-bandwidth Brillouin slow light in optical fibers,” Opt. Express 14, 1395-1400 (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]

S. Chin, M. G. Herráez, and L. Thévenaz, “Zero-gain slow and fast light propagation in an optical fiber,” Opt. Express 14, 10684-10692 (2006).
[CrossRef] [PubMed]

K. Y. Song, M. González Herráez, and L. Thévenaz, “Observation of pulse delaying and advancement in optical fibers using stimulated Brillouin scattering,” Opt. Express 13, 82-88 (2005).
[CrossRef] [PubMed]

K. Y. Song, M. González Herráez, and L. Thévenaz, “Gain-assisted pulse advancement using single and double Brillouin gain peaks in optical fibers,” Opt. Express 13, 9758-9765 (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]

T. Schneider, R. Henker, K.-U. Lauterbach, and M. Junker, “Comparison of delay enhancement mechanisms for SBS-based slow light systems,” Opt. Express 15, 9606-9613 (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. Schneider, A. Wiatrek, and R. Henker, “Zero-broadening and pulse compression slow light in an optical fiber at high pulse delays,” Opt. Express 16, 15617-15622 (2008).
[CrossRef] [PubMed]

A. Wiatrek, R. Henker, S. Preußler, M. J. Ammann, A. T. Schwarzbacher, and T. Schneider, “Zero-broadening measurement in Brillouin based slow-light delays,” Opt. Express 17, 797-802 (2009).
[CrossRef] [PubMed]

M. González Herráez and L. Thévenaz, “Physical limits to broadening compensation in a linear slow light system,” Opt. Express 17, 4732-4739 (2009).
[CrossRef] [PubMed]

T. Schneider, R. Henker, K.-U. Lauterbach, and M. Junker, “Distortion reduction in slow light systems based on stimulated Brillouin scattering,” Opt. Express 16, 8280-8285 (2008).
[CrossRef] [PubMed]

A. Wiatrek, R. Henker, S. Preußler, and T. Schneider, “Pulse broadening cancellation in cascaded slow-light delays,” Opt. Express 17, 7586-7591 (2009).
[CrossRef] [PubMed]

S. Chin, M. González-Herráez, 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]

Opt. Lett.

Opt. Quantum Electron.

M. F. Ferreira, J. F. Rocha, and J. L. Pinto, “Analysis of the gain and noise characteristics of fibre Brillouin amplifiers,” Opt. Quantum Electron. 26, 35-44 (1994).
[CrossRef]

Phys. Rev. Lett.

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

Z. Zhu, D. J. Gauthier, and R. W. Boyd, “Stored light in an optical fiber via stimulated Brillouin scattering,” Science 318, 1748-1750 (2007).
[CrossRef] [PubMed]

Other

T. Asami and S. Namiki, “Energy consumption targets for network systems,” in 34th European Conference on Optical Communication (ECOC) (2008), paper Tu.4.A.3.
[CrossRef]

A. V. Oppenheim, R. W. Schafer, and J. R. Buck, Discrete-Time Signal Processing (Prentice-Hall, 1998).

V. Lucarini, J. J. Saarinen, K.-E. Peiponen, and E. M. Vartianinen, Kramers-Kronig Relations in Optical Materials Research (Springer, 2005).

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2007).

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Figures (7)

Fig. 1
Fig. 1

Experimental setup: MZM, Mach–Zehnder modulator; SSMF, standard single mode fiber; C, circulator; EDFA, erbium doped fiber amplifier; VOA, variable optical attenuator; PD, photodiode; OSA, optical spectrum analyzer; Osci, oscilloscope.

Fig. 2
Fig. 2

Amplification of the input signal spectrum (dashed gray line) in the linear regime (solid black line) and in the saturated regime (dashed black line), where the larger spectral components of the signal output power are limited by approaching the pump power spectrum (solid gray line).

Fig. 3
Fig. 3

Linear gain, saturated gain, saturated gain exponent (ln is natural logarithm), and its Hilbert transform versus frequency offset.

Fig. 4
Fig. 4

Spectral gain distribution of the single stages (gray) and the whole system on input conditions given in the text.

Fig. 5
Fig. 5

Phase responses of the single stages (gray) and the whole system on input conditions given in the text. The inset shows the simulated pulses in comparison to the reference pulse for the first stage and both stages working.

Fig. 6
Fig. 6

System output pulses for the first stage (Stage 1) and both stages (Stage 2) in comparison to the reference pulse.

Fig. 7
Fig. 7

Fractional pulse width, time delay, and RMS broadening as functions of the attenuation between the slow-light stages. The given parameters at the measurement graphs are the fractional values of the first stage.

Equations (8)

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

P In = P C   exp [ ln ( 2 ) ( ω Δ ω ) 2 ] ,
E Out   I E In   I = G ̱ I ( ω ) = exp [ g I ( ω ) + j φ I ( ω ) ] .
E Out = E In   exp { [ g I ( ω ) D + g ̃ II ( D , ω ) ] + j [ φ I ( ω ) + φ ̃ II ( D , ω ) ] } ,
E S z = ( g B 2 A eff Δ k e R P P α 2 ) E S + j ( g B 2 A eff Δ k e I P P + γ P S ) E S ,
E P z = ( g B 2 A eff Δ k e R P S + α 2 ) E P ,
Δ k e R = exp [ ln ( 2 ) ( ω ω 0 Γ ) 2 ] ,
Δ k e I = j   exp [ ln ( 2 ) ( ω ω 0 Γ ) 2 ] erf [ j ln ( 2 ) ω ω 0 Γ ] ,
σ t 2 = + t 2 | A ( t ) | 2 d t + | A ( t ) | 2 d t ,

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