Abstract

We describe a methodology to maximize slow-light pulse delay subject to a constraint on the allowable pulse distortion. We show that optimizing over a larger number of physical variables can increase the distortion-constrained delay. We demonstrate these concepts by comparing the optimum slow-light pulse delay achievable using a single Lorentzian gain line with that achievable using a pair of closely-spaced gain lines. We predict that distortion management using a gain doublet can provide approximately a factor of 2 increase in slow-light pulse delay as compared with the optimum single-line delay. Experimental results employing Bril-louin gain in optical fiber confirm our theoretical predictions.

© 2005 Optical Society of America

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References

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    [CrossRef]
  3. J. E. Heebner, R. W. Boyd, and Q. Park, "Slow light, induced dispersion, enhanced nonlinearity, and optical solitons in a resonator-array waveguide," Phys. Rev. E 65, 036619 (2002).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  7. H. Cao, A. Dogariu, and L. J. Wang, "Negative group delay and pulse compression in superluminal pulse propagation," IEEE J. Sel. Top. Quantum Electron. 9, 52-58 (2003).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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  18. M. Nikles, L. Thévenaz, and P. A. Robert, "Brillouin gain spectrum characterization in single-mode optical fibers," J. Lightwave Technol. 15, 1842-1851 (1997).
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    [CrossRef]
  20. Q. Sun, Y. V. Rostovtsev, J. P. Dowling, M. O. Scully, and M. S. Zhubairy, "Optically controlled delays for broadband pulses," Phys. Rev. A 72 031802(R) (2005).
    [CrossRef]

European Phys. J. D (1)

B. Macke and B. Ségard, "Propagation of light-pulses at a negative group-velocity," European Phys. J. D 23, 125-141 (2003).
[CrossRef]

IEEE J. Quantum Electron. (1)

G. Lenz, B. J. Eggleton, C. K. Madsen, and R. E. Slusher, "Optical delay lines based on optical filters," IEEE J. Quantum Electron. 37 525-532 (2001).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

H. Cao, A. Dogariu, and L. J. Wang, "Negative group delay and pulse compression in superluminal pulse propagation," IEEE J. Sel. Top. Quantum Electron. 9, 52-58 (2003).
[CrossRef]

J. Lightwave Technol. (1)

M. Nikles, L. Thévenaz, and P. A. Robert, "Brillouin gain spectrum characterization in single-mode optical fibers," J. Lightwave Technol. 15, 1842-1851 (1997).
[CrossRef]

J. Opt. Soc. Am. B (2)

J. E. Heebner, P. Chak, S. Pereira, J. E. Sipe, R. W. Boyd, "Distributed and localized feedback in microresonator sequences for linear and nonlinear optics," J. Opt. Soc. Am. B, 21 1818-1832 (2004).
[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," to appear in J. Opt. Soc. Am. B 22 (2005).

Opt. Express (1)

Opt. Lett. (3)

Phys. Rev. A (3)

Q. Sun, Y. V. Rostovtsev, J. P. Dowling, M. O. Scully, and M. S. Zhubairy, "Optically controlled delays for broadband pulses," Phys. Rev. A 72 031802(R) (2005).
[CrossRef]

R. W. Boyd, D. J. Gauthier, A. L. Gaeta, and A. E. Willner, "Maximum time delay achievable on propagation through a slow-light medium," Phys. Rev. A 71, 023801 (2005).
[CrossRef]

M. Bashkansky, G. Beadie, Z. Dutton, F. K. Fatemi, J. Reintjes, and M. Steiner, "Slow-light dynamics of largebandwidth pulses in warm rubidium vapor," Phys. Rev. A 72, 033819 (2005).
[CrossRef]

Phys. Rev. E (3)

Y. A. Vlasov, S. Petit, G. Klein, B. Hönerlage, and C. Hirlimann, "Femtosecond measurements of the time of flight of photons in a three-dimensional photonic crystal," Phys. Rev. E 60, 1030-1035 (1999).
[CrossRef]

J. E. Heebner, R. W. Boyd, and Q. Park, "Slow light, induced dispersion, enhanced nonlinearity, and optical solitons in a resonator-array waveguide," Phys. Rev. E 65, 036619 (2002).
[CrossRef]

Y. Xu, R. K. Lee, and A. Yariv, "Scattering theory analysis of waveguide-resonator coupling," Phys. Rev. E 62, 7389-7404 (2000).
[CrossRef]

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]

Progress in Optics (1)

R. W. Boyd and D. J. Gauthier, "'Slow' and 'Fast' Light," in Progress in Optics, Vol. 43, E. Wolf, ed. (Elsevier, Amsterdam, 2002), pp. 497-530.
[CrossRef]

SPIE (1)

Z. Dutton, M. Bashkansky, M. Steiner, and J. Reintjes, "Channelization architecture for wide-band slow light in atomic vapors," SPIE 5735, 115-129 (2005).
[CrossRef]

Other (1)

A. V. Oppenheim and A. S. Willsky, Signals and Systems, 2nd Ed. (Prentice Hall, Upper Saddle River, 1997).

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Figures (3)

Fig. 1.
Fig. 1.

Gain and dispersion for a single Lorentzian line (solid) and a doublet with separation δ = δ/√3 (dashed). Also shown are the two constituent lines (dotted) that make up the doublet. (a) The gain exponent has a broad flat top (a result of setting k 2 = 0), although it is larger for the same value of the individual gain coefficients. (b) The central region of approximately linear dispersion is very similar for both systems near the center of the lines, but extends farther for the gain-doublet case.

Fig. 2.
Fig. 2.

Simulation and experimental results for both the single Lorentzian line (solid lines for simulation, circles for experimental results) and the doublet (dashed lines for simulation, squares for experimental results). (a) Relative delay. (b) Lorentzian line-center amplitude gain coefficients g 01 and g 02. Also shown is the center-frequency gain coefficient for the doublet g 2((ω 0) (dot-dashed). (c) Line separation for the doublet. The horizontal line indicates the value of δ/γ that leads to k 2 = 0

Fig. 3.
Fig. 3.

Experiment setup based on a fiber Brillouin amplifier. TL1, TL2: tunable lasers; IS1, IS2: isolators; FPC1, FPC2, FPC3: fiber polarization controllers; MZM1, MZM2: Mach-Zehnder modulators; FG1, FG2: function generators; EDFA: Erbium-doped fiber amplifier; C1, C2: circulators; SMF-28e: 500-m-long SMF-28e fiber (the SBS amplifier); PM: power meter.

Equations (12)

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A ω z = A ω 0 e ik ( ω ) z ,
k ( ω ) = k 0 + k 1 ( ω ω c ) ,
k ( ω ) = ω c n 0 + g 0 z ( γ ω ( ω 0 δ ) + + γ ω ( ω 0 + δ ) + ) ,
k 2 = 4 i g 0 γ 2 z 3 δ 2 γ 2 ( δ 2 + γ 2 ) 3 .
t g = z ( k 1 1 c ) = z c ( n 0 1 ) + 3 4 g 0 γ ,
t g = z c ( n 0 1 ) + g 0 γ .
D a = H max H min H max + H min ,
D p = 1 2 π max [ H ( ω ) ( t p ω + ϕ 0 ) ] ω 0 Δ b ω 0 + Δ b ,
H 1 ( ω ) = exp ( iz n 0 ω c ) × exp ( g 1 ( ω ) )
= exp ( iz n 0 ω c + g 01 ( ω ω 0 ) + ) .
H 2 ( ω ) = exp ( iz n 0 ω c ) × exp ( g 2 ( ω ) )
= exp ( iz n 0 ω c + g 02 ( ω ω 0 δ ) + + g 02 ( ω ω 0 δ ) + ) .

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