Abstract

We demonstrate a 5-GHz-broadband tunable slow-light device based on stimulated Brillouin scattering in a standard highly-nonlinear optical fiber pumped by a noise-current-modulated laser beam. The noise-modulation waveform uses an optimized pseudo-random distribution of the laser drive voltage to obtain an optimal flat-topped gain profile, which minimizes the pulse distortion and maximizes pulse delay for a given pump power. In comparison with a previous slow-modulation method, eye-diagram and signal-to-noise ratio (SNR) analysis show that this broadband slow-light technique significantly increases the fidelity of a delayed data sequence, while maintaining the delay performance. A fractional delay of 0.81 with a SNR of 5.2 is achieved at the pump power of 350 mW using a 2-km-long highly nonlinear fiber with the fast noise-modulation method, demonstrating a 50% increase in eye-opening and a 36% increase in SNR in the comparison.

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    [Crossref] [PubMed]
  7. 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]
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    [Crossref] [PubMed]
  11. 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).
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    [Crossref] [PubMed]
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    [Crossref]

2010 (2)

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]

A. Kobyakov, M. Sauer, and D. Chowdhury, “Stimulated Brillouin scattering in optical fibers,” Adv. Opt. Photon. 2, 1–59 (2010).
[Crossref]

2009 (1)

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

2008 (5)

2007 (4)

2006 (2)

2005 (4)

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]

1986 (1)

N. A. Olsson and J. P. Van Der Ziel, “Fibre Brillouin amplifier with electronically controlled bandwidth,” Electron. Lett. 22,488–490 (1986).
[Crossref]

Andonovic, I.

A. Zadok, H. Shalom, M. Tur, W. D. Cornwell, and I. Andonovic, “Spectral shift and broadening of DFB lasers under direct modulation,” IEEE Photon. Technol. Lett.10, 1709 (1998).
[Crossref]

Bigo, S.

Bo, Z.

Z. Bo, L. S. Yan, J. Y. Yang, I. Fazal, and A. E. 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.

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

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, Nonlinear optics (Academic Press, San Diego, 2008), Ch. 9.

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]

Chang-Hasnain, C. J.

Chowdhury, D.

Cornwell, W. D.

A. Zadok, H. Shalom, M. Tur, W. D. Cornwell, and I. Andonovic, “Spectral shift and broadening of DFB lasers under direct modulation,” IEEE Photon. Technol. Lett.10, 1709 (1998).
[Crossref]

Dawes, A. M. C.

Eyal, A.

Fazal, I.

Z. Bo, L. S. Yan, J. Y. Yang, I. Fazal, and A. E. 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]

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]

Gauthier, D. J.

González Herráez, M.

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]

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

Hotate, K.

Hu, W.

Jaouen, Y.

Kobyakov, A.

Ku, P. C.

Kurashima, T.

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]

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.

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]

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 and J. P. Van Der Ziel, “Fibre Brillouin amplifier with electronically controlled bandwidth,” Electron. Lett. 22,488–490 (1986).
[Crossref]

Pant, R.

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.

Sauer, M.

Shalom, H.

A. Zadok, H. Shalom, M. Tur, W. D. Cornwell, and I. Andonovic, “Spectral shift and broadening of DFB lasers under direct modulation,” IEEE Photon. Technol. Lett.10, 1709 (1998).
[Crossref]

Sharping, J. E.

Shiraki, K.

Song, K. Y.

Stenner, M. D.

Su, Y.

Thévenaz, L.

L. Thévenaz, “Slow and fast light in optical fibres,” Nat. Photonics 2, 474–481 (2008).
[Crossref]

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]

M. González Herráez, K. Y. 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.

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]

A. Zadok, H. Shalom, M. Tur, W. D. Cornwell, and I. Andonovic, “Spectral shift and broadening of DFB lasers under direct modulation,” IEEE Photon. Technol. Lett.10, 1709 (1998).
[Crossref]

Van Der Ziel, J. P.

N. A. Olsson and J. P. Van Der Ziel, “Fibre Brillouin amplifier with electronically controlled bandwidth,” Electron. Lett. 22,488–490 (1986).
[Crossref]

Willner, A. E.

Yamamoto, T.

Yan, L

Yan, L. S.

Z. Bo, L. S. Yan, J. Y. Yang, I. Fazal, and A. E. 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. Y.

Z. Bo, L. S. Yan, J. Y. Yang, I. Fazal, and A. E. 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.

Zadok, A.

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]

A. Zadok, H. Shalom, M. Tur, W. D. Cornwell, and I. Andonovic, “Spectral shift and broadening of DFB lasers under direct modulation,” IEEE Photon. Technol. Lett.10, 1709 (1998).
[Crossref]

Zhang, B

Zhang, L

Zhang, L.

Zhu, 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]

Zhu, Z.

Adv. Opt. Photon. (1)

Appl. Phys. Lett. (1)

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

Electron. Lett. (1)

N. A. Olsson and J. P. Van Der Ziel, “Fibre Brillouin amplifier with electronically controlled bandwidth,” Electron. Lett. 22,488–490 (1986).
[Crossref]

IEEE Photon. Technol. Lett. (1)

Z. Bo, L. S. Yan, J. Y. Yang, I. Fazal, and A. E. 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. (3)

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. B (1)

Nat. Photonics (1)

L. Thévenaz, “Slow and fast light in optical fibres,” Nat. Photonics 2, 474–481 (2008).
[Crossref]

Opt. Express (7)

Opt. Lett. (1)

Phys. Rev. A (1)

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

A. Zadok, H. Shalom, M. Tur, W. D. Cornwell, and I. Andonovic, “Spectral shift and broadening of DFB lasers under direct modulation,” IEEE Photon. Technol. Lett.10, 1709 (1998).
[Crossref]

R. W. Boyd, Nonlinear optics (Academic Press, San Diego, 2008), Ch. 9.

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Figures (6)

Fig. 1
Fig. 1

Pump spectral distribution optimization procedure for the case of fast noise modulation. Modulation voltage waveform V (t) (left column), probability distribution P (bin size = 0.025 V) (middle column) and resultant pump beam spectrum p(ωp) (right column) are shown for flat-distributed white noise modulation V (t) = 2.5 V× f (t), where f (t) is a random variable that is approximate uniformly distributed between −0.5 and 0.5 (upper row), bi-peak symmetric noise modulation V (t) = 2.5 V×tanh[10 f (t)] (middle row) and optimal noise modulation V (t) = 2.5 V×tanh[10(f (t) + 0.06)] (bottom row). A Gaussian spectral profile resulted from a Gaussian noise modulation V (t) = 2.5 V×g(t), where g(t) is a random variable with standard normal distribution, is inserted into the Figs. c,f and i for comparison. The DC injection current is 110 mA.

Fig. 2
Fig. 2

Pump spectral distribution optimization procedure for the case of slow modulation. Modulation waveform V (t) (left column) and measured pump spectrum profile p(ωp) (right column) are shown for triangular modulation (upper row), with the addition of a small quadratic term (middle row), and for the optimum waveform (lower row). The DC injection current is 110 mA.

Fig. 3
Fig. 3

Experiment setup. Spectrally broadened pump and signal beams counter-propagate in the 2-km-long slow light medium (HNLF, OFS Inc.), where they interact via the SBS process. The SBS frequency shift in HNLF is 9.62 GHz. A fiber Bragg grating (FBG, bandwidth 0.1 nm) is used to filter out the Rayleigh backscattering of the pump beam from the amplified and delayed signal pulse sequence before detection. AWG: arbitrary function generator (Tektronix AFG3251), DFB1: 1550-nm DFB laser diode (Sumitomo Electric, STL4416), EDFA: erbium doped fiber amplifier (IPG Photonics EAD 1K), DFB2: 1550-n DFB laser diode (Fitel FOL15DCWC), MZM: Mach-Zehnder Modulator, PG: electronic signal pattern generator, PR: 12 GHz photo-receiver (New Focus 1544b), FPC: fiber polarization controllers, CIR: optical circulator.

Fig. 4
Fig. 4

(a) SBS gain profiles for fast (solid black line) and slow modulations (red dashed line) at Pp = 70 mW. (b) SBS gain saturation for fast and slow modulation methods. The black solid line shows the SBS gain G for the fast noise modulation, which grows linearly with pump power Pp until saturated. The red dashed line shows the SBS gain G for the slow modulation, which starts to saturate gradually at a much smaller Pp compared to the fast modulation method.

Fig. 5
Fig. 5

Slow light performance for fast (solid black line) and slow (dashed red line) modulation waveforms in HNLF, and slow modulation waveform in LEAF (dotted green line). (a) Slow light delay as a function of Pp. The theoretically predicted delay for a rectangular-like optimized gain profile (blue dash-dot line) and for a super-Gaussian gain profile (cyan dash-double dot line) in the HNLF fiber are also shown. SBS gain saturation is avoided using a signal data sequence with a small peak optical power Ps0 = 12 μW; (b) Averaged output signal profiles at Pp = 350 mW for the first single pulse in the data sequence, together with the undelayed pulse profile at Pp = 0 mW (blue dotted line) in HNLF. Both fast and slow modulation methods result in very similar pulse profile modification without significant broadening. The amplitude of the pulses is normalized as a percentage of the peak pulse height; Fidelity metrics are shown in (c) EO and (d) SNR as functions of Pp, demonstrating better performance for the fast modulation.

Fig. 6
Fig. 6

Eye diagrams of delayed and amplified data sequences for (a) slow and (b) fast modulation waveforms at Pp = 350 mW in HNLF. The arrows in the figure show the EO for each case.

Equations (3)

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ω p ( t ) = a 0 i ( t ) i ( t ) h ( t ) ,
V ( t ) = v max / 2 × { a t 2 + ( 4 / T a T / 4 ) t if t < T / 4 a t 2 ( 4 / T + a 3 T / 4 ) t + 2 + ( 2 a T 2 ) / 4 2 if T / 4 < t 3 T / 4 a t 2 + ( 4 / T a 9 T / 4 ) t + ( 5 a T 2 ) / 4 4 if 3 T / 4 < t T ,
G = ln ( P s / P s 0 ) .

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