Abstract

A new method of tailoring stimulated Brillouin scattering (SBS) gain spectrum for slow light propagation is proposed by use of two Gaussian-shaped broadband pump beams with different powers and spectral widths. The central frequency interval between the two pump beams are carefully set to be two inherent Brillouin frequency shift, ensuring that the gain spectrum of one pump has the same central frequency with the loss spectrum of the other one. Different gain profiles are obtained and analyzed. Among them a special gain profile is found that ensures a zero-broadening of the signal pulse independent of the Brillouin gain. This is owing to the compensation between the positive gain-dependent broadening and the negative GVD (group velocity dispersion) dependent broadening. The relationship of two pump beams is also found for constructing such a gain profile. It provides us a new idea of managing the broadening of SBS-based slow pulse by artificially constructing and optimizing the profile of gain spectrum.

© 2008 Optical Society of America

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References

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  1. K. Y. Song, M. G. 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]
  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, Art. No. 153902 (2005).
    [CrossRef] [PubMed]
  3. D. Dahan and G. Eisenstien, "Tunable all optical delay via slow and fast light propagation in a Raman assisted fiber optical parametric amplifier: a route to all optical buffering," Opt. Express 13, 6234-6248 (2005).
    [CrossRef] [PubMed]
  4. D. J. Gauthier, "Slow light brings faster communications," Phys. World 18, 30-32 (2005).
  5. M. G. Herráez, K. Y. Song, and L. Thévenaz, "Optically controlled slow and fast light in optical fibers using stimulated Brillouin scattering," Appl. Phys. Lett. 87, Art. No. 081113 (2005).
  6. M. G. Herráez, K. Y. Song, and L. Thévenaz, "Arbitrary-bandwidth Brillouin slow light in optical fibers," Opt. Express 14, 1395-1400 (2006).
    [CrossRef]
  7. K. Y. Song, M. G. 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]
  8. M. D. Stenner, M. A. Neifeld, Z. M. Zhu, A. M. C. Dawes, and D. J. Gauthier, "Distortion management in slow-light pulse delay," Opt. Express 13, 9995-10002 (2005).
    [CrossRef] [PubMed]
  9. Z. M. Zhu, A. M. C. Dawes, D. J. Gauthier, L. Zhang, and A. E. Willner, "12-GHz-bandwidth SBS slow light in optical fibers," in Proc. of OFC 2006, paper PDP1 (2006).
  10. 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]
  11. 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]
  12. L. Y. Ren and Y. Tomita, "Reducing group-velocity-dispersion-dependent broadening of stimulated Brillouin scattering slow light in an optical fiber by use of a single pump laser," J. Opt. Soc. Am. B 25, 741-746 (2008).
    [CrossRef]
  13. 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]
  14. 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]
  15. Z. M. 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. K. Y. Song and K. Hotate, "25GHz bandwidth Brillouin slow light in optical fibers," Opt. Lett. 32, 217-219 (2007).
    [CrossRef] [PubMed]
  17. T. Schneider, M. Junker, and K. U. Lauterbach, "Potential ultra wide slow-light bandwidth enhancement," Opt. Express 14, 11082-11087 (2006).
    [CrossRef] [PubMed]
  18. 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]
  19. R. M. Camacho, M. V. Pack, and J. C. Howell, "Low-distortion slow light using two absorption resonances," Phys. Rev. A 73, Art. No. 063812 (2006).
    [CrossRef]
  20. B. Macke and B. Ségard, "Pulse normalization in slow-light media," Phys. Rev. A 73, Art. No. 043802 (2006).
    [CrossRef]

2008 (1)

2007 (3)

2006 (6)

2005 (5)

Bao, X.

Bernini, R.

Chen, L.

Dahan, D.

Dawes, A. M. C.

Eisenstein, G.

Eisenstien, G.

Eyal, A.

Gauthier, D. J.

Henker, R.

Herráez, M. G.

Hotate, K.

Junker, M.

Kalosha, V. P.

Lauterbach, K. U.

Minardo, A.

Neifeld, M. A.

Nevet, A.

Orbach, N.

Ren, L. Y.

Schneider, T.

Shumakher, E.

Song, K. Y.

Stenner, M. D.

Thévenaz, L.

Tomita, Y.

Tur, M.

Willner, A. E.

Zadok, A.

Zeni, L.

Zhang, L.

Zhu, Z. M.

J. Lightwave Technol. (1)

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

Opt. Express (11)

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]

K. Y. Song, M. G. 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]

D. Dahan and G. Eisenstien, "Tunable all optical delay via slow and fast light propagation in a Raman assisted fiber optical parametric amplifier: a route to all optical buffering," Opt. Express 13, 6234-6248 (2005).
[CrossRef] [PubMed]

K. Y. Song, M. G. 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. M. Zhu, A. M. C. Dawes, and D. J. Gauthier, "Distortion management in slow-light pulse delay," Opt. Express 13, 9995-10002 (2005).
[CrossRef] [PubMed]

M. G. Herráez, K. Y. Song, and L. Thévenaz, "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]

T. Schneider, M. Junker, and K. U. Lauterbach, "Potential ultra wide slow-light bandwidth enhancement," Opt. Express 14, 11082-11087 (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]

Opt. Lett. (1)

Phys. World (1)

D. J. Gauthier, "Slow light brings faster communications," Phys. World 18, 30-32 (2005).

Other (5)

M. G. Herráez, K. Y. Song, and L. Thévenaz, "Optically controlled slow and fast light in optical fibers using stimulated Brillouin scattering," Appl. Phys. Lett. 87, Art. No. 081113 (2005).

Z. M. Zhu, A. M. C. Dawes, D. J. Gauthier, L. Zhang, and A. E. Willner, "12-GHz-bandwidth SBS slow light in optical fibers," in Proc. of OFC 2006, paper PDP1 (2006).

R. M. Camacho, M. V. Pack, and J. C. Howell, "Low-distortion slow light using two absorption resonances," Phys. Rev. A 73, Art. No. 063812 (2006).
[CrossRef]

B. Macke and B. Ségard, "Pulse normalization in slow-light media," Phys. Rev. A 73, Art. No. 043802 (2006).
[CrossRef]

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, Art. No. 153902 (2005).
[CrossRef] [PubMed]

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Figures (7)

Fig. 1.
Fig. 1.

Spectral configuration of double broadband pump beams and the corresponding Brillouin gain as well as loss spectra of them. The total gain profile is constructed by overlapping the Stokes gain spectrum (gain1) of pump1 and the anti-Stokes loss one (loss2) of pump2, where the gain1 and the power spectrum of pump1 are normalized to unity, respectively. Here Δωp2=Δωp1/(2)1/3, Ip1/Ip2=2 and Δωp1=0.5ΩB.

Fig. 2.
Fig. 2.

Dependences of the time delay and the width of the flat-top on parameter b. Here Δωp1=0.5ωB, Pp1=0.2 W and Ip1/Ip2=Δωp1 3/Δωp2 3=b.

Fig. 3.
Fig. 3.

Spectral dependences of (a) the gain exponent and (b) the time delay for different values of a. Here Δωp1=0.5ΩB, Pp1=0.2 W and Δωp2=Δωp1/(2)1/3.

Fig. 4.
Fig. 4.

Dependences of Bgain, BGVD and B on parameter a. Here Δωp1=0.5ωB, Pp1=0.2 W and Δωp2=Δωp1/(2)1/3.

Fig. 5.
Fig. 5.

Spectral dependences of Brillouin gain and signal pulse intensity when a=2.073 for B=1. (a) Real and imaginary parts of gain; (b) Intensities of input and output pulses as well as the exponential gain. The 1/e full bandwidths for both the input and output pulses are shown in Fig. 5(b). Here Δωp1=0.5ΩB, Pp1=0.2 W and Δωp2=Δωp1/(2)1/3.

Fig. 6.
Fig. 6.

Dependences of a for B=1 on the spectral width (Δωp1) and the laser power (Pp1) of pump1 in our double pump scheme. (a) on Δωp1, where Pp1 is fixed at 0.2 W; and (b) on Pp1, where Δωp1 is fixed at 0.5ωB. The insert of Fig. 6(a) shows the allowable signal pulse-width δin calculated by Eq. (10) for different Δωp1. Here Δωp2=Δωp1/(2)1/3.

Fig. 7.
Fig. 7.

Dependences of the time delay and the pulse broadening on the laser power of pump1 under both the single pump scheme and the double pump scheme we proposed. (a) for time delay and (b) for pulse broadening factors Bgain, BGVD and B. Here δin=52 ps, a=2.085, Δωp1=0.5ΩB and Δωp2=Δωp1/(2)1/3.

Equations (11)

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g ( ω ) = g 0 ( ω ) I p ( ω ) = + g 0 ( ω ω p ) I p ( ω p ) d ω p ,
g 0 ( ω ω p ) = ± g B [ i γ ( ω ω p ± Ω B ) + i γ ] ,
I p ( ω p ) = I p 1 π Δ ω p 1 exp [ ( ω p ω p 01 Δ ω p 1 ) 2 ] + I p 2 π Δ ω p 2 exp [ ( ω p ω p 02 Δ ω p 2 ) 2 ] ,
g ( ω ) = g B π γ [ I p 1 Δ ω p 1 e ξ 1 2 erfc ( i ξ 1 ) I p 2 Δ ω p 2 e ξ 2 2 erfc ( i ξ 2 ) ] ,
Re [ g ( ω ) ] = g B π γ [ I p 1 Δ ω p 1 e ξ 1 2 I p 2 Δ ω p 2 e ξ 2 2 ] ,
Im [ g ( ω ) ] = 2 g B γ [ I p 1 Δ ω p 1 e ξ 1 2 0 ξ 1 e t 2 dt I p 2 Δ ω p 2 e ξ 2 2 0 ξ 2 e t 2 d t ] .
Δ T d ( ω ) = d Im [ g ( ω ) z 2 ] d ω ω
= g B z γ [ I p 1 Δ ω p 1 2 ( 1 2 ξ 1 e ξ 1 2 0 ξ 1 e t 2 d t ) I p 2 Δ ω p 2 2 ( 1 2 ξ 2 e ξ 2 2 0 ξ 2 e t 2 d t ) ] ,
Δ T d ( ω 0 ) = g B z γ [ I p 1 Δ ω p 1 2 I p 2 Δ ω p 2 2 ] = g B z γ I p 1 Δ ω p 1 2 ( 1 1 b 3 ) .
W flat top = 2 Δ ω p 2 = 2 Δ ω p 1 b 3 .
1 δ in = W flat top 2 = 2 Δ ω p 2 2 = 2 Δ ω p 1 2 b 3 .

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