# Using Nonuniform Fiber to Generate Slow Light via SBS

Authors: Wenhai Li; Xiaoyi Bao; V. P. Kalosha; Liang Chen; Ming-Jun Li
Journal: Research Letters in Optics
 (2008)

---

## Abstract

The data pulse delay based on slow light induced by stimulated Brillouin scattering (SBS) in a nonuniform dispersion decreasing fiber (DDF) is demonstrated experimentally, and the distortions of data pulses at different beat frequencies are studied. We found that a delay exceeding a pulse width can be achieved at particular beat frequency, and the DDF has larger delay versus gain slope coefficient with much better output pulse quality than single-mode fiber.


---

## Body

## 1. Introduction

Slow light via stimulated Brillouin scattering (SBS) in optical fiber has been an
active research area since 2005 [1–5]. The advantage
of achieving slow light in fiber using SBS is the low threshold power, robustness,
and simplicity of operation as it can be easily integrated with existing fiber
system for optical signal processing, data buffers, and optical equalizers. The
spectral bandwidth of the Brillouin scattering in a standard single-mode fiber
is about 30 MHz [1, 2], which is much narrower than the bandwidth of modern communication
systems, that are utilizing GBytes/sec data streams. In order to solve this
problem, various modulation schemes to broaden the Brillouin spectrum are
proposed for the pump source (to slow the light) or the probe source (to
advance the light) [3–6]. These schemes
all suffer from considerable signal distortion due to maximum Brillouin gain at
peak frequency of the pump wave because the beat frequency and phase-locking
condition are only satisfied for the peak frequency of pump and probe wave,
especially when the pulse trains are used, where intersymbol interference (ISI)
poses another limitation [3]. The maximum pulse delay is limited by saturation
of the pulse amplification via the Brillouin gain, which is a dispersion
process. When a large delay is required, either high pump power or long fiber
length is needed; hence the gain saturation at peak frequency is unavoidable.
In other words, the high pump power leads to the power increase to the probe
(data) which depletes the pump power. As a result, the Brillouin gain becomes
location and frequency dependent, so does the amplified data signal (pulse),
especially for pulse trains, where the rise and fall time could not be detected
correctly due to the SBS slow-light-induced distortion. Both saturation of the
probe (signal) and depletion of the pump prevent SBS slow light in optical
processing and as an optical buffer in fiber communications. Fortunately, both
impairments can be mitigated by the nonuniform fiber as an SBS slow light
generator based on distributed Brillouin frequency along the fiber length. Hence,
the effective length for each Brillouin frequency is much shorter than the
total fiber length in the pump modulation method [4–6], which creates
an effective modification of the Brillouin frequency bandwidth in the fiber with
fixed central frequency along the entire fiber length. With the use of a
nonuniform fiber, we obtained a variable Brillouin frequency along the fiber
length, allowing much higher pump power for each frequency components of the
pulse signal before the saturation appears; also the varied Brillouin peak
gives more uniform gain to each pulse spectral component than the pump
modulation scheme. As long as the fiber is designed with appropriate frequency
location, slope and varied Brillouin frequency covers the pulse spectrum. This
method is very different from any pump modulation scheme in which the frequency
resonance condition is the same over the entire fiber distance [4, 6], the same
principle applies to resonance and absorption scheme [7], in which the pump
source includes two frequencies at Stokes and anti-Stokes at ω0+ΩB and ω0−ΩB for the probe signal of ω0 to get zero gain through the
combination of an absorption and gain resonance. However, the energy exchange between the ω0+ΩB as a pump signal and the pulsed signal ω0 is not the same as the energy exchange between
the ω0 as a pulsed probe signal and the modulated
signal of ω0−ΩB,
as the pump energy is always much stronger than that of the probe signal.
Therefore, the unbalance of the absorption and gain will be created along the fiber
length and this process is nonunfiorm due to the higher depletion of the gain,
especially when the long fiber length or higher pump power are used to achieve
larger delay. While in nonuniform fiber the situation is different, because the
variable Brillouin frequency locates at different fiber locations, the pump
power is transferred to the different frequency components which are in
resonance of the Brillouin frequency for the probe beam (data pulse). Therefore,
the nonuniform fiber provides a solution of flexibility and simplicity for slow
light generation with CW pump and no need for the complicated modulation form.
This idea was first demonstrated theoretically in [8] with linear relation of
the Brillouin frequency versus the fiber location, and Brillouin gain is the
Lorentzian shape of 30 MHz. In this work, the Brillouin gain has double peaks
with broader bandwidth of 500 MHz, the peak Brillouin frequency varies along
the fiber within 500 MHz to cover 3 nanoseconds pulse spectrum. This process provides
higher power spectrum density over effectively short fiber length for
the specific pulse spectral component of the data pulses and avoids the
saturation of the peak gain of the Brillouin spectrum. This preserves high
fidelity of the input pulse shape and allows high gain and large delay over the
entire pulse spectrum and fiber length, thus the saturation impairment is
reduced significantly, which leads to minimum distortion for the output pulse.In the paper, we experimentally demonstrated long fractional
delay of nanosecond data pulse with low distortion based on SBS slow light by
using nonuniform dispersion decreasing fiber (DDF). With using a CW pump only, the
scheme achieves a delay exceeding a pulse width at particular beat frequency
and with larger delay versus gain slope coefficient and much better output
pulse quality than single-mode fiber.


## 2. Experiment, Results, and Discussion

The experimental configuration for observing slow light via
SBS is similar to the setup in [9] for
the pump and probe interaction in the Brillouin medium of DDF [10]. The
wavelength of the probe and pump light is ~1319 nm. The probe light νS is modulated by a pulse generator through an
electro-optic modulator (EOM) to become a data pulse with 3 nanosecond pulse
width and coupled into DDF from its high-dispersion side. The pump light νP is launched into the fiber from its
low-dispersion side. The peak power of the data pulse is 2.3 mW and the pump
power varies from 0 to 17 mW through an optical attenuator. By tuning the
wavelength of the probe light, we can finely tune and lock the beat frequency
(measured by frequency counter) between the pump and probe (νB=νS−νP) within Hz using a phase-locked feedback
circuit within frequency counter.By measuring the depleted CW pump
beam from the output of the circulator and scanning the beat frequency of the
two lasers, a Brillouin loss spectrum of DDF from 11.6 to 12.4 GHz is obtained as
shown in Figure1. DDF has decreasing core refractive indices along the fiber
and a dispersion parameter of 7.7 (high-dispersion side) and −0.3 ps/nm/km
(low-dispersion side) at wavelength of 1550 nm. The mode field
diameter is about 5.0–7.0 μm and the fiber loss is 0.45 dB/km. The length
of DDF is 5.4 km. The overall Brillouin gain spectrum of the DDF was also measured using
the same method, as shown in Figure 2.Figure 1
DDF Brillouin gain spectra along fiber length.Figure 2
Brillouin gain spectrum of DDF.As can be seen, there are two peak frequencies in the gain spectrum profile: one
is located at 11.85 GHz, which is the Brillouin frequency around the midsection
of the fiber as shown in Figure1, and the other is at 12.15 GHz. This gain
profile was designed to have varied chromatic dispersion to suppress the
Brillouin threshold, which brings advantage of the smaller pulse fall time.We measure the delay and data pulse distortion by analyzing oscilloscope
records. The Brillouin gainG is calculated
by the ratio of the delayed data pulse intensity with nonzero pump power to the
one without pump power. The delay τ is measured by the time difference between the
peak time moments of the delayed pulses with and without pump power. Obviously,
the larger values of these ratios indicate larger broadening and smoothing due
to SBS, and hence the larger distortion of the data pulse. As the pump power
changes from 0 to 17 mW for the fixed data pulse of 2.3 mW, the Brillouin gain G increases from 0 to 25 dB, giving
maximum delay τ=3.17 nanseconds and relative delay τ/w = 1.1 bit. The normalized pulse width (w'/w), rise time (tr'/tr), and fall time (tf'/tf) is 1.0, 1.27, and 0.75, respectively, while
the normalized pulse width remains around 1 as shown in Figure 3 (solid), when
the beat frequency is locked at 12.15 GHz and the gain is 25 dB. Here, w', tr', and tf' denote the pulse width, rise, and fall time of
delayed data pulse, and w, tr, and tf denote the pulse width, rise, and fall time of
the data pulse, when the optical power of pump laser is zero. The SMF28 results
of CW pumping of 30 nanosecond (for 30 MHz bandwidth) pulse is shown in dotted
line of the same figure as comparison.Figure 3
Normalized pulse width, rise, and fall times versus gain for DDF (w=3 nanoseconds), comparing those for SMF (w=30 nanoseconds).The compensation effect of DDF can
be explained as follows. When the beat frequency is locked at 12.15 GHz, the
central frequency of the data pulse is located at the gain peak wavelength,
while the lower-frequency components relative to peak frequency in the pulse
spectrum are in the region with low gain, as shown in Figure2. The high gains
of side frequency components of DDF broaden the bandwidth of the data pulse and
compensate the pulse broadening, thus reduce the distortion. The smaller fall
time in DDF is caused by the chromatic
dispersion introduced by the dispersion decreasing fiber, as this fiber has a
dispersion parameter of 7.7 (high-dispersion side) and −0.3 ps/nm/km
(low-dispersion side). The probe pulse is launched at the high-dispersion end,
and the SBS slow-light generation also creates the dispersion, this slow-light
generated additional dispersion has been overcorrected by the fiber chromatic
dispersion, therefore the fall time has been reduced.Next, we tune and lock the beat frequency between probe and pump to
11.85, 11.95, 12.05, and 12.15 GHz, respectively. We have found that at beat
frequency of 12.15 GHz, the minimum pulse distortion can be achieved, as shown
in Figure3. The linear delay is due to the relative lower Brillouin gain of
the second Brillouin peak in Figure 2. The maximum delay is found at 11.95 GHz
and the nonlinear relation is accounted from double peak Brillouin spectrum in
Figure 2 in which 11.95 GHz corresponds to center of Brillouin gain spectrum
between two Brillouin peaks. Figure 4 shows the normalized delays versus gain
for DDF when the beat frequency is locked at 11.95 and 12.15 GHz, respectively,
as compared to those for single-mode fiber. One can see from the figure, when
the gain is 28 dB and the beat frequency is 11.95 GHz, a maximum of 1.1 bit
delay can be achieved for DDF. We also find that at different beat frequency,
the normalized delay τ/w increases with different slope coefficients α as the gain increases (Table 1). It is notable
that the coefficient for DDF at 12.15 GHz is 0.036 bit/dB and larger than the
coefficient for single-mode fiber of 0.026 bit/dB.Table 1
The slope coefficients of normalized
delay versus gain (α in bit/dB) at different beat frequencies νB.
νB11.8511.9512.0512.1512.8 (SMF)α0.0260.0340.0180.0360.026Figure 4
Normalized peak delays versus gain for DDF when the beat frequency is locked
at 11.95 and 12.15 GHz, comparing to those for single-mode fiber at 12.8 GHz.


## 3. Conclusions

In summary, we have found that a maximum of 1.1 bit relative delay can be
achieved for 500 MHz bandwidth nonuniform fiber and 3-nanosecond pulse with delay
gain ratio of 0.036 bit/dB. The smallest pulse distortion can be achieved when
the beat frequency is locked at 12.15 GHz, which has a frequency offset to the
center of the Brillouin spectrum profile, and the slope coefficient of the
relative delay versus gain is larger than that of single-mode fiber. The
current work has provided a guideline for making nonunfiorm fiber as slow light
generator, the better designed fiber can be made to increase the range of the
variable Brillouin frequency and to cover the 10 Gbps signal and in the same
time to incorporate the chromatic dispersion compensation via variable
chromatic dispersion along the fiber. This can generate ultimate simple
solution for generation of the slow light via SBS using nonuniform fiber.



---

*Source: 253634-2008-04-23.xml*