Abstract

We derive an analytical expression for the broadening of a Gaussian input pulse in an arbitrary linear slow light medium. The expression consists of two terms, one corresponding to amplitude broadening (low-pass filtering of the pulse bandwidth) and another corresponding to phase broadening (phase dispersion around the resonance). It is shown that for a Lorentzian gain profile, the amplitude broadening is dominant at small fractional delays. However, for large fractional delays, phase broadening is inevitably dominate.

© 2012 Optical Society of America

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References

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2011 (1)

M. González-Herráez and L. Thévenaz, Proc. SPIE 7949, 79491B (2011).
[CrossRef]

2010 (1)

2009 (1)

2008 (1)

2007 (1)

D. A. B. Miller, Phys. Rev. Lett. 99, 203903 (2007).
[CrossRef]

2006 (5)

2005 (3)

Boyd, R. W.

R. W. Boyd and D. J. Gauthier, in Progress in Optics, E. Wolf, ed. (Elsevier, 2002), Vol. 43, p. 497.

Cohen, L.

L. Cohen, Time-Frequency Analysis (Prentice Hall, 1995).

Dawes, A. M. C.

Eggleton, B. J.

J. T. Mok, C. M. Sterke, I. C. M. Littler, and B. J. Eggleton, Nat. Phys. 2, 775 (2006).
[CrossRef]

Eyal, A.

Fan, S.

Gauthier, D. J.

Gonzalez-Herraez, M.

González-Herráez, M.

M. González-Herráez and L. Thévenaz, Proc. SPIE 7949, 79491B (2011).
[CrossRef]

Herraez, M. G.

Herráez, M. G.

Khurgin, J. B.

Littler, I. C. M.

J. T. Mok, C. M. Sterke, I. C. M. Littler, and B. J. Eggleton, Nat. Phys. 2, 775 (2006).
[CrossRef]

Miller, D. A. B.

D. A. B. Miller, Phys. Rev. Lett. 99, 203903 (2007).
[CrossRef]

Mok, J. T.

J. T. Mok, C. M. Sterke, I. C. M. Littler, and B. J. Eggleton, Nat. Phys. 2, 775 (2006).
[CrossRef]

Neifeld, M. A.

Pant, R.

Povinelli, M. L.

Sandhu, S.

Song, K. Y.

Stenner, M. D.

Sterke, C. M.

J. T. Mok, C. M. Sterke, I. C. M. Littler, and B. J. Eggleton, Nat. Phys. 2, 775 (2006).
[CrossRef]

Thevenaz, L.

Thévenaz, L.

Tur, M.

Yanik, M. F.

Zadok, A.

Zhu, Z.

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Figures (1)

Fig. 1.
Fig. 1.

Amplitude (σX) and phase (σφ) broadenings accumulated in a Gaussian pulse as a function of the input pulse width σin normalized by the inverse bandwidth of the slow light system 2π/Δ. Computation has been done using the exact expression for the Lorentzian gain and Eq. (6). Experimentally obtained points have been added for comparison (taken from [13] and [15]). Inset shows the same broadening data plotted versus fractional delay.

Equations (9)

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g=g0+g2ω2+g4ω4+,
Φ=Φ1ω+Φ3ω3+Φ5ω5+,
σt2=1E+t2|A(t)|2dt,
E=+|A(t)|2dt
σt2=1Eω+|dA˜dω|2dω,
σt2=1Eω[+|dXdω|2dω++|X(ω)|2|dφdω|2dω]=σX2+σφ2,
G=exp(g0)[1+g2ω2+(g4+g222)ω4+],
σX2=σin21g21σin2(9g4+g22)21σin4+1+g21σin2+3(g4+g22)21σin4+
σφ2=27ϕ322σin41+5g21σin2+35(g4+g22)21σin41+g21σin2+3(g4+g22)21σin4++,

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