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Distortion management in slow-light pulse delay

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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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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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