245
(Invited Paper)
NEGATIVE GROUP VELOCITY SUPERLUMINAL
PROPAGATION IN OPTICAL FIBERS USING STIMULATED
BRILLOUIN SCATTERING
Li Zhan*, Liang Zhang, Jinmei Liu, Qishun Shen, Yuxing Xia
Department of Physics, State Key Lab of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong
University, Shanghai, 200240, China
*
[email protected]
Keywords: fast light, superluminal propagation, negative
group velocity, stimulated Brillouin scattering, slow light.
Abstract
We demonstrated the superluminal propagation at negative
group velocity using stimulated Brillouin scattering (SBS) in
optical fibers. In the scheme, the Stokes wave is circulated
back into the ring cavity for Brillouin lasing to enhance the
peak loss. The experiment demonstrated the superluminal
light propagation can be realized by increasing the input
signal power. The largest time advancement of 221.2ns has
been observed. Correspondingly, the negative group velocity
is -0.15c and the group index is -6.636.
1 Introduction
To control the group velocity of light propagation in different
materials have been attracted much interest recently [1-14]. It
is becoming an important role in the implementation of alloptical communication system, since it has an inviting
application prospects for developing fast-access memories
and optically-controlled delay lines. Otherwise, the light
superluminal propagation (where, the group velocity
 g exceed c) or even with a negative  g , have been studied
theoretically [15][16], and also observed experimentally
[17][18], e.g., in absorbing medium [19][20], atomic medium
[21][22], photonic crystals [23],active optical fibers[24-26],
fiber Bragg gratings,[27] corrugated waveguide [28], lefthanded materials [29], and saturated absorption medium
[30][31]. The consistency of such phenomena with causality
has also been verified experimentally [25].
The realization of slowing or advancing light in optical fibers
forwards a great step to the all-optical communication
systems. Several methods were proposed to control the group
velocity of light pulses in fibers based on the nonlinear effects
such as stimulated Brillouin scattering (SBS) [4], stimulated
Raman scattering (SRS) [5] and parametric amplification [6],
or using the group delay reflected from active fiber Bragg
gratings (FBG) [7] and the gap solitons in FBGs [8]. Fast or
slow light based on SBS in fibers has been proved to be an
efficient and flexible method to realize optical advancement
or delay, owing to its many advantages such as low pump
power level, longer delay, and operating at any wavelength.
In early SBS slow-light experiments, the delay is small and
the applicable bandwidth is limited to dozens of MHz [9-10].
Further experiments optimized the delay efficiency [11] and
extended the bandwidth [12][13]. However, the group
velocity can reach neither superluminal nor negative owing to
the saturation effect of Stokes wave.
In this paper, we observed the superluminal light propagation
at negative group velocity using SBS in a fiber ring lasing
cavity. The largest advancement of 221.2ns obtained and the
negative group was -0.15c and the group index was - 6.636.
2 Experimental setup and principles
The setup to demonstrate superluminal light in fiber ring is
shown in Fig. 1. A 10m single-mode optical fiber (SMF) is
used as the SBS medium. To generate the signal, we used a
tunable laser source (TLS) of 1550 nm, which is modulated
using an electro-optic modulator(EOM) to produce a
sinusoidally pulse signal of 1 MHz repetition rate. Adjusting
the DC bias of function generator applied to the EOM, we can
obtain the signal with a DC component which creates the
Stokes wave essentially.
Fig. 1. Setup to realize the SBS superluminal light.
EOM: electro-optic modulator, EDFA: Erbium-doped
fiber amplifier, SMF: single-mode optical fiber.
Then the signal is boosted using a erbium-doped fiber
amplifier (EDFA) before it's reached into the SMF. A fiber
ring lasing cavity constructed by a optical circulator and the
SMF is employed in order to circulate the Stokes light back
into the SBS medium for Brillouin lasing. 90% of the backpropagate stokes is served as pump light of SBS in turn. The
power of the signal wave and the Stokes wave are observed at
optical coupler's output port and the temporal traces of signal
light within the fiber is monitored successively by measuring
output waveform with the same photodetector and recorded
by a digital storage oscilloscope.
The phenomenon of fast light appears when the light
propagates in the anomalous dispersion medium. If the
dispersion is anomalous dn / d   0 , then the group velocity
 g of a light pulse can exceed the speed in a medium c / n or
The 9th International Conference on Optical Communications and Networks (ICOCN2010)
Nanjing, China, 24-27, October, 2010
246
even in a vacuum c. If dn/d  1 , a negative group
velocity is obtained. The delay time T is negative and a
light can propagate sooner than that had travelled the same
distance in a vacuum.
SBS is a nonlinear process that caused by the interaction
between a light wave and an acoustic wave. When a pump
light with a frequency  p propagates through a fiber, a
3 Results and discussion
Figure 2 show the observed output signals waveform under
different Stokes powers. It is clearly observed that the larger
the Stokes power is, the faster the signal pulse propagates.
backward-scattered Stokes wave is generated with a
downshifted frequency at p   B (  B is the Stokes shift). If
the Stokes light is injected in a back-propagate direction to
the pump light, it is amplified in SBS process. Meanwhile, the
pump light experiences an absorption , which is the condition
of the fast light and superluminal. This narrowband (~30
MHz) gain and loss band of SBS is used to achieve strong
changes in the group index of light.
For a continuous wave (CW) or quasi-CW pump, The
group index ng  c  g via the SBS process is given by[13]
ng  n f 
where, n f
cg 0 I p 1  [2(  s ) /  B ]2
,
 B {1  [2(  s ) /  B ]2 }2
(1)
is the group index of fibers without any
nonlinearity effect, g0 is the SBS gain factor,  B is the SBS
linewidth, s   p   B is the peak frequency of SBS gain,
I p  Ppump Aeff is the pump intensity, Aeff is the effective
core area of fiber. Thus, the group index change
ng  ng  n fg via SBS process is proportional to the pump
power. Thus, the time delay by SBS
g 0 Pp L 1  [2(  s ) /  B ]
Td  L( n g  n f ) / c 
(2)
2 2
 B Aeff {1  [2(  s ) /  B ] }
When [2(  s ) /  B ]  1 , Eq. (2) can be expressed as
2
Td  L( n g  n f ) / c 
g 0 Pp L
 B Aeff
.
(3)
To control the speed of the signal, a pump light with the
precise frequency is required, pump  signal   B for slow
Fig. 2. Signal pulse after propagating through a 10m
SMF for different Stokes powers. Waveform heights
are normalized to facilitate comparison.
Figure 3 show the observed output signals under different
Stokes powers. There is no SBS effect when the input signal
power is below the SBS threshold power. Thus, the output
signal is delayed with time of 48.6ns which is signal light
propagating time through 10 m-long SMF.
As the input power is beyond threshold power, the output
signal is closer and closer to the input signal, and then
precedes it with a negative group velocity. In Figure 3, the
decrease in the pulse width is also observed since the width of
the back-propagate stokes light is approximately as small as
35MHz and the SBS effect has a strong frequency
dependence. The loss around the signal carrier frequency is
stronger than that at other frequency which causes the change
of the signal pulse spectrum.
delt2=221.2ns
light and pump  signal   B for fast light. Here, the Stokes
2648.6ns
delt1=48.6ns
2697.2ns
input signal
output signal
0.057mW
0.090mW
0.18 mW
1.08 mW
4.08 mW
9.08 mW
13.88mW
29.48mW
41.38mW
43.58mW
60.18mW
74.68mW
85.88mW
99.88mW
118.0mW
138.0mW
0.8
Norm. Ampl
wave generated by spontaneous Brillouin scattering at a
frequency downshifted B below the signal, in turn, serve as
a pump light. Above the SBS threshold, the signal power is
transferred to the Stokes wave and experiences absorption to
achieve the fast light and superluminal propapgation.
The group index change is proportional to the backward
Stokes power as Eq. (1), which increases as the input signal
power increases. In our experiment, the Stokes light is
circulated back into the SBS medium for Brillouin lasing by
employing a fiber ring lasing cavity which is constructed by a
optical circulator and the SMF. Thus, the power of the backpropagating Stokes light is enhanced. The group index change
is optimized and the advancement is enlarged. Controllable
superluminal light propagation at negative group velocity in
optical fibers will be realized by manipulating the input signal
power or the loss of fiber ring cavity.
2427.4ns
1.0
0.6
0.4
0.2
0.0
2000
2200
2400
2600
2800
3000
3200
Time / ns
Fig. 3. Input and output signal after propagation
through the 10-m length of SMF for different Stokes
powers.
The 9th International Conference on Optical Communications and Networks (ICOCN2010)
Nanjing, China, 24-27, October, 2010
247
Fig. 4 shows the group index change is proportional to the
Stokes power. In our experiment, the maximum measured
superluminal group velocity was 3.14c and the group index
was 0.318. With the stokes power of 12 mW, the minimum
negative group was -4.902c and the group index was -0.204.
The maximum negative group was -0.151 and the group index
was -6.636 with the stokes power of 124.2 mW.
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The 9th International Conference on Optical Communications and Networks (ICOCN2010)
Nanjing, China, 24-27, October, 2010