Limits to dispersion compensation in a linear Brillouin
slow-light system employing SBS slow- and fast-light
propagation in cascaded optical fibers
Zhiyao Zhang,* Xiaojun Zhou, Lan Lan, and Yong Liu
State Key Laboratory of Electronic Thin Films and Integrated Devices, School of Optoelectronic Information,
University of Electronic Science and Technology of China, Chengdu 610054, China
*Corresponding author: zhangzhiyao@uestc.edu.cn
Received October 20, 2011; revised December 6, 2011; accepted January 5, 2012;
posted January 6, 2012 (Doc. ID 156884); published March 21, 2012
A theoretical model for quantifying the pulse distortion introduced by the stimulated-Brillouin-scattering (SBS)-
induced (equivalent) dispersion in a linear Brillouin slow-light system is presented. Based on this model, a linear
Brillouin slow-light system employing fast-light propagation for dispersion compensation is analyzed. The results
show that the elimination of gain-nonuniformity-induced equivalent group-velocity dispersion can be achieved
with the sacrifice of introducing much larger high-order (equivalent) dispersion effects. It is also shown that the
simultaneous cancellation of gain-nonuniformity-induced equivalent group-velocity dispersion and third-order
dispersion as presented in a recent article is impossible. © 2012 Optical Society of America
OCIS codes: 290.5900, 230.1150, 060.2330.
1. INTRODUCTION
Recently, slow and fast light have attracted intensive attention
due to their potential applications in the fields of optical signal
processing, nonlinear optics, and microwave photonics [
1–3].
Various mechanisms, such as electromagnetically induced
transparency, coherent population oscillation, optical para-
metric amplification and stimulated scattering processes,
have been exploited to control the group velocity of a light
pulse, but all of them inevitably introduce extra dispersion
to the delayed or advanced pulse, which is detrimental or even
destructive in practical applications [
4]. Among these above-
mentioned mechanisms, slow light via stimulated Brillouin
scattering (SBS) in an optical fiber, which was first demon-
strated in 2005 [
5,6] and widely researched in the following
years [
7], has an outstanding advantage; i.e., its dispersion
property can be controlled through simply tailoring the pump
spectrum (equally, the gain spectrum) [
8,9]. Thus, substantial
effort has been carried out during these years to diminish the
pulse distortion (especially the pulse broadening) in the Bril-
louin slow light through engineering the SBS gain spectrum in
a single amplifier-based linear system [
10–17]. Besides, effort
has also been made to ease the pulse broadening through in-
troducing a fast-light stage after a slow-light one to reshape
the delayed pulse [
18], utilizing the gain-saturation-related
fast-light effect to reshape the delayed pulse in a single-stage
system [
19] or in a cascaded one [20], and employing a non-
linear optical fiber loop mirror to compress the delayed pulse
outputting from an amplifier-based slow-light system [
21]. Fol-
lowing the same research direction, a recent work [
22] has
reported the cancellation of both gain-nonuniformity-induced
equivalent group-velocity dispersion (GVD) and third-order
dispersion (TOD) in a linear Brillouin slow-light system with
a two-stage configuration like that presented in [
18,20], but
employing the pumping scheme proposed by an independent
research team [
17]. However, the authors in [22] made a mis-
take in deducing Eq. (
10) as presented in [22] (its correct ex-
pression is given in Appendix
A). This mistake makes the
conclusion given in [
22] excessively optimistic, as will be pro-
ven in detail in the following part of this paper.
In this paper, we first present a theoretical model for anal-
yzing the pulse distortion introduced by the SBS-induced
(equivalent) dispersion in a linear Brillouin slow-light system.
Then, we use this model to verify that the simultaneous can-
cellation of gain-nonuniformity-induced equivalent GVD and
TOD as presented in [
22] is impossible. Meanwhile, we will
show that the elimination of gain-nonuniformity-induced
equivalent GVD in the linear Brillouin slow-light system utiliz-
ing the pumping scheme shown in [
22] can bring much larger
high-order (equivalent) dispersion effects.
2. DISPERSION THEORY OF BRILLOUIN
SLOW LIGHT
SBS can be described as an amplification process in which a
strong pump light produces a gain (loss) spectrum around the
frequency downshifted (upshifted) from its central frequency
by a Brillouin frequency shift (e.g., ∼10 GHz in a silica fiber).
The profile of the gain (loss) spectrum is determined by the
convolution of the intrinsic Brillouin gain (loss) spectrum with
a Lorentzian shape and the pump spectrum with arbitrary
profile [
8]. Therefore, in the pump-undepletion (or pump-
unamplified) region (namely the linear Brillouin slow- or
fast-light region), the complex amplitude transfer function
of the probe light in the frequency domain can be written as
Hωexp
−
αL
2
gωipω
; (1)
where
Zhang et al. Vol. 29, No. 4 / April 2012 / J. Opt. Soc. Am. B 753
0740-3224/12/040753-05$15.00/0 © 2012 Optical Society of America