Group velocity dispersion reduction in fibre-based slow-light systems via stimulated Brillouin scattering

Abstract

Presented are theoretical investigations and simulations of a reduction of the group velocity dispersion (GVD) in slow-light systems by an optimisation of the gain spectrum of the stimulated Brillouin scattering (SBS). A comparison between a natural Brillouin gain spectrum and a broadened Brillouin gain spectrum with and without two additional losses at its wings is demonstrated. The focus of the theoretical examination was set on the superposition of a gain and two losses with an equal magnitude. Therefore, a low GVD and a high group index change could be achieved and hence, a small pulse distortion and a high time delay can be expected.

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Dublin Institute of Technology
ARROW@DIT
Articles
School of Electronic and Communications
Engineering
2008-01-01
Group Velocity Dispersion Reduction in Fibre-
based Slow-light Systems via Stimulated Brillouin
Scattering
Ronny Henker
Deutsche Telekom Fachhochschule Leipzig
A. Wiatrek
Deutsche Telekom Fachhochschule Leipzig
K. U. Lauterbach
Deutsche Telekom Fachhochschule Leipzig
Max Ammann
Dublin Institute of Technology, max.ammann@dit.ie
Andreas Thomas Schwarzbacher
Dublin Institute of Technology
See next page for additional authors
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Recommended Citation
Henker, R., Wiatrek, A., Lauterbach, K., Ammann, M., Schwarzbacher, A., Schneider, T.: Group velocity dispersion reduction in fibre-
based slow-light systems via stimulated Brillouin scattering. Electronics Letters ,September 25, 2008, Vol.44, pp.1185-1186.

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Authors
Ronny Henker, A. Wiatrek, K. U. Lauterbach, Max Ammann, Andreas Thomas Schwarzbacher, and Thomas
Schneider
This article is available at ARROW@DIT:http://arrow.dit.ie/engscheceart/31

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Group velocity dispersion reduction in
fibre-based slow-light systems via
stimulated Brillouin scattering
R. Henker, A. Wiatrek, K.-U. Lauterbach, M.J. Ammann,
A.T. Schwarzbacher and T. Schneider
Presented are theoretical investigations and simulations of a reduction
of the group velocity dispersion (GVD) in slow-light systems by an
optimisation of the gain spectrum of the stimulated Brillouin scattering
(SBS). A comparison between a natural Brillouin gain spectrum and a
broadened Brillouin gain spectrum with and without two additional
losses at its wings is demonstrated. The focus of the theoretical exam-
ination was set on the superposition of a gain and two losses with an
equal magnitude. Therefore, a low GVD and a high group index
change could be achieved and hence, a small pulse distortion and a
high time delay can be expected.
Introduction: Different slow-light systems have been discussed and
developed as a powerful tool to reduce the group velocity of optical
signals during the last years. This area has enjoyed much recent interest
because of the potential practical applications in optical telecommunica-
tion and information systems like optical buffers, synchronisers or
equalisers.
In particular, the nonlinear effect of stimulated Brillouin scattering
(SBS) has become important for fibre-based slow-light systems [1, 2],
because it offers several advantages compared to other methods. But,
it also has two disadvantages. First, the maximum time delay is
limited owing to the saturation of the Brillouin amplification process
and, secondly, the delay of the pulses is accompanied by pulse distor-
tions (pulse shape broadening) owing to the group velocity dispersion
(GVD) and the spectral narrowing by the SBS gain. Therefore, different
mechanisms for tailoring the shape of the Brillouin spectrum have been
investigated. By a broadening of the Brillouin gain pump source via
multiple pump lines [3] or a direct modulation with a noise source
[4, 5], a uniform spectrum over a broad bandwidth can be produced.
Hence, the pulse distortions can be reduced [6] and higher delayable
data rates are possible. However, this decreases the time delay signifi-
cantly. An enhancement of the maximum time delay can be achieved
by a superposition of Brillouin gain and loss spectra, which decouples
the time delay from the amplifier gain [7]. In [8] we have already pre-
sented a mechanism to increase the maximum time delay drastically
to four times the initial pulse width. In contrast to the studied techniques
with multiple gain lines in [3] it is based on a superposition of one
Brillouin gain spectrum with two additional Brillouin loss spectra at
its wings.
In this Letter, we present the theory and simulations that this method
has also the potential to reduce the GVD and the pulse distortions
drastically.
Theory: The propagation of a pulse in a medium as a function of the
frequency v can be described by the complex wave number [9]:
kðvÞ ¼P
1
i¼0
kiðv ? v0Þi
i!
with ki¼
dik
dvi
??
v¼v0
ð1Þ
The first derivative k1¼ dk/dv corresponds to the reciprocal group vel-
ocity whereas the second derivative k2¼ d2k/dv2is the GVD. For a
Brillouin gain with a Lorentzian shape the complex wave number can
be written as [9]:
?
where z is the length of the medium, c is the speed of light in vacuum, n0
is the refractive index, v0is the line centre of the gain distribution, g1is
the half FWHM-bandwidth of the SBS gain as angular frequency and
g1¼ gPLeff/Aeffisthe line centre gain with g asthe Brillouin coefficient,
P as input pump power, and Leffand Aeffas the effective length and area
of the fibre. The imaginary part of (2) leads to an amplification of the
pulses and the real part to a phase change. Furthermore, the derivation
of the real part leads to the group index change, which causes the
slow-light time delay. In the line centre it is Dt ¼ g1/g1. This delay is
accompanied with a broadening of the output pulse due to the
GVD and higher-order terms of (1). The pulse broadening factor B
as the relation between the output tout and input pulse width tin
kðvÞ ¼n0
cv þg1
z
g1
ðv ? v0Þ þ jg1
?
ð2Þ
can be described by [6]:
B ¼tout
tin
¼
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
t2
1 þ16 ln2
ing2
1
g1
s
ð3Þ
As can be seen from (3) the broadening factor decreases for high gain
bandwidths. Hence, the pulse distortions can be reduced by a gain
broadening. If the Brillouin gain spectrum is broadened it becomes
Gaussian shaped and the complex wave number changes to [5]:
kðvÞ ¼n0
cv þg1
jz
e
?
v?v0
gG
??2
erfc ?jv ? v0
gG
??
0
@
1
A
ð4Þ
with gGas the 1/e-bandwidth and erfc() as the complementary error
function. Then, the time delay is decreased and can be written as
Dt ¼ 2 g1/(gGpp). But, if the value of the Brillouin gain broadening
is comparable with the Brillouin shift, the influence of the Brillouin
loss leads to an enhancement of the time delay at the centre of the
Stokes resonance [5], which is not further investigated here. However,
by adding two narrow Lorentzian shaped Brillouin loss spectra g2,
with a separation 2d and a half FWHM-bandwidth g2, at the wings of
the gain the time delay can be enhanced to Dt ¼ 2 g1/(gGpp) þ
(d22 g2
[8]:
2)/(d2þ g2
2)2and (2) and (4) have to be expanded by the term
... ?g2
z
g2
ðv ? ðv0+ dÞÞ þ jg2
??
ð5Þ
The inset of Fig. 1 shows the superposition of a Brillouin gain spectrum
with two losses at its wings. The gain bandwidth, the time delay and the
GVD can be adjusted and controlled by the separation of the losses 2d.
1.0
0.8
0.6
0.4
0.2
0.0
–0.2
–0.4
–0.6
–0.8
normalised group index
normalised gain
–12
–8–4
0
(w–w0)/g2
w–w0
48 12
–1.0
–1.2
1.0
0.8
0.6
0.4
0.2
0.0
–0.2
–0.4
–0.6
–0.8
–1.0
gain
losses
overall gain
–10–505 10
Fig. 1 Normalised group index for natural gain (solid) and three times
broadened gain (dashed) with losses at d ¼ +1.7g2 (dotted) and d ¼
+4g2(dashed–dotted)
Inset shows the superposition (solid) of Brillouin gain (dashed) with two losses
(dotted) at its wings
Simulation results: The simulation results for equal gain and losses
g1¼ g2are shown in Figs. 1 and 2. The group index was normalised
to the maximum value of the natural gain case. As can be seen, a
high group index and hence a high time delay in the line centre is
achieved with a normal gain (solid line). But, the GVD is also very
high for this case and the pulses will experience a huge distortion. A
much higher group index could be achieved by adding two loss
spectra at the wings of the normal gain [8], which is not examined
here because there is no improvement of the GVD. But, if the gain is
broadened (here gG¼ 3g2, dashed line), the GVD is reduced drastically
and it runs linearly with a small slope in the middle of the Brillouin
profile. However, the group index in the line centre of the distribution
is decreased as well and it is barely 38%, as for the normal gain.
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(w–w0)/g2
1.5
1.0
0.5
0.0
–0.5
group velocity dispersion, a.u.
–1.0
–1.5
–12–8–4048 12
Fig. 2 Group velocity dispersion for natural gain (solid) and three
times broadened gain (dashed) with losses at d ¼ +1.7g2(dotted) and
d ¼ +4g2(dashed–dotted)
With the additional losses at the wings of the broadened gain the time
delay can be enhanced. Thereby, the separation of the two losses influ-
ences the height of the group index and the slope of the GVD directly. If
the losses are far away from the line centre their impact is negligible.
But, with a smaller separation the gain bandwidth is constrained
again. By varying d we determined two optimal operating points for
the separation. At d ¼ +4g2(dashed–dotted line) the maximum band-
width is achieved. In this case, the group index in the line centre is nearly
50%, as for a normal gain, whereas the GVD shows the same progress as
for the broadened gain without losses. Hence, the pulse distortions
should be at the minimum.
The highest group index for this case can be achieved by a loss sep-
aration of d ¼ +1.7g2(dotted line). Then, the group index is actually
63%. But, this is at the expense of the GVD, which runs with an even
steeper slope in the middle of the Brillouin profile. However, the
slope is still smoother than for the normal gain case.
With a very broad and flat Brillouin spectrum the GVD could even be
reduced to zero within the flat gain region around the line centre. If the
spectral components of the pulse do not exceed this region it would not
experience distortions due to the GVD. However, the time delay would
be very low and there is still a large change of the GVD at the edges of
the Brillouin spectrum, which leads to distortions of the pulse with an
increased bandwidth. On the other hand this can be used to achieve
zero-pulse-broadening by a compression of the pulse, which compen-
sates for the broadening owing to the spectral narrowing by the SBS
gain.
Conclusions: We have shown that a superposition of a Brillouin gain
with two losses at its wings has the potential to reduce the GVD drasti-
cally in fibre-based slow-light systems. As an example the gain was
broadened by a factor of three and the separation of the losses was
adjusted to achieve the maximum bandwidth or the maximum time
delay. Hence, the pulse distortions can be decreased in addition to an
enhancement of the time delay. However, this needs further
investigations.
Acknowledgments: We gratefully acknowledge the technical help of
M. Junker and J. Klinger from HfT Leipzig. K.-U. Lauterbach and
R. Henker acknowledge the financial support from Deutsche Telekom.
# The Institution of Engineering and Technology 2008
10 July 2008
Electronics Letters online no: 20082007
doi: 10.1049/el:20082007
R. Henker, A. Wiatrek, K.-U. Lauterbach and T. Schneider (Hochschule
fu ¨r Telekommunikation Leipzig (FH), Gustav-Freytag-Str. 43-45,
Leipzig 04277, Germany)
E-mail: ronny.henker@hft-leipzig.de
R. Henker, A. Wiatrek, K.-U. Lauterbach, M.J. Ammann and
A.T. Schwarzbacher(School of
Engineering, Dublin Institute of Technology, Kevin Street, Dublin 8,
Ireland)
Electronic& Communications
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