True time reversal via dynamic Brillouin gratings in
polarization maintaining fibers
Sanghoon Chin, Nikolay Primerov, Kwang Yong Song, Luc Th
´
evenaz
Ecole Polytechnique F
´
ed
´
erale de Lausanne, STI-GR-SCI Station 11, CH-1015 Lausanne, Switzerland
luc.thevenaz@epfl.ch
Marco Santagiustina, Leonora Ursini
CNIT-Department of Information Engineering, University of Padova, via Gradenigo 6b, 35131, Padova, Italy
marco.santagiustina@unipd.it
Abstract: A novel technique to realize true time reversal of an optical signal, using dynamic
Brillouin gratings in high-birefringence fibers, is proposed. A data sequence of optical pulses with
2-ns duration was efficiently time-reversed.
c
2010 Optical Society of America
OCIS codes: (060.4370) Nonlinear optics, fibers; (290.5900) Scattering, stimulated Brillouin; (070.4340) Nonlinear optical
signal processing
In acoustics and electromagnetics, low frequency time reversal has been successfully realized, showing many po-
tential applications in communications, medicine and material analysis [1, 2, 3]. Experimental demonstration of
ultrafast optical waveform time reversal has been also made, using various physical phenomena such as spectrally
decomposed-wave mixing [4, 5], photon echo [6] and spectral hole-burning holography [7]. In this paper, we pro-
pose and experimentally demonstrate a novel technique to perform true time reversal (TTR) of optical signals in an
all-fiber configuration making use of dynamic Brillouin gratings (DBG) in high birefringence optical fibers [8]. The
proposed setup is simpler with respect to the fiber optic time-lens proposed in [9], and so very attractive for appli-
cations in optical communications and microwave-photonics [10]. Light storage and retrieval in optical fibers has
been succesfully demonstrated [11, 12] by exploiting the stimulated Brillouin scattering (SBS) occurring between two
counter-propagating optical pulses. The acoustic wave, generated by the interaction, retains the characteristics of the
colliding pulses and actually modulates the fiber refractive index, thus creating a DBG (Bragg-like). A new light beam
can be scattered on to the DBG, thus enabling the original optical waveform to be retrieved [11, 12]. In polarization
maintaining (PM) fibers, the storage/retrieval processes can be realized on the two orthogonal states of polarization
aligned to the birefringence axis [8, 13] thus enabling a practical method to decouple the read and write channels. In
fact, the acoustic wave equally scatters all light polarizations owing to its longitudinal nature. In Fig. 1, the process to
achieve TTR is sketched. The linearly polarized input data sequence, A
in
d
, and the counter-propagating (write) pulse,
A
w
, are launched along the slow axis of a PM fiber. The signals interact through SBS if their frequencies satisfy the
Brillouin condition ν
in
d
− ν
w
= ν
B
. The interaction generates an acoustic wave, Q, in which the data sequence A
in
d
is
spatially stored. The reading pulse, A
r
, linearly polarized along the fast axis is launched just after the data sequence,
thus interacting with the stored acoustic wave and generating a counter-propagating output waveform, A
out
d
, polarized
along the fast axis and at frequency ν
out
d
= ν
r
− ν
B
. The part of the input sequence which is stored last is the first to
be retrieved and so TTR is realized. The write/input data and read/output data pulses also satisfy SBS phase matching
conditions from which one obtains ν
r
= (1 + ∆n/n
s
)ν
in
d
, where ∆n = n
s
− n
f
is the fiber birefringence [8, 13].
The process is governed by the following equations:
∂
z
A
in
d
+ β
1s
∂
t
A
in
d
= −η
1
g
B
QA
w
+ jη
2
γ(|A
in
d
|
2
)A
in
d
, −∂
z
A
w
+ β
1s
∂
t
A
w
= η
1
g
B
Q
∗
A
in
d
+ jη
2
γ(|A
w
|
2
)A
w
, (1)
∂
z
A
r
+ β
1 f
∂
t
A
r
= −η
1
g
B
QA
out
d
+ jη
2
γ(|A
r
|
2
)A
r
, −∂
z
A
out
d
+ β
1 f
∂
t
A
out
d
= η
1
g
B
Q
∗
A
r
+ jη
2
γ(|A
out
d
|
2
)A
out
d
, (2)
2τ
B
∂
t
Q + Q = A
d
A
∗
w
+ (A
out
d
)
∗
A
r
. (3)
Fig. 1: Process for the realization of TTR in PM fibers via DBG.
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Fig. 2: Input data sequence, composed by 6
bits of duration 2 ns.
Fig. 3: Comparison of experimentally (green
curve) and numerically (black curve) reversed
sequence with ideally reversed input sequence
(blue curve). Write/read pulses of 2ns dura-
tion.
Fig. 4: Comparison of simulation results
without (black curve) and with (red curve) the
exponential post-correction (write/read pulses
of 0.25ns duration) with ideally reversed input
sequence (blue curve).
The main difference with eqs. of ref. [13] is that the self phase modulation is taken into account because of the high
peak power (>100 W) of the write/read pulses. The parameters of the simulations and experiments implementing
the scheme of Fig. 1 are: fiber length L = 20 m, input data central wavelength λ
d
= 1535 nm, fiber birefringence
∆n = 5·10
−4
, SBS shift ν
B
= 10.93 GHz, SBS gain g
B
= 5 ·10
−11
m/W , acoustic wave lifetime τ
B
= 4 ns, nonlinearity
coefficient γ = 2.6·10
−3
m
−1
W
−1
. η
1
= 2·10
−3
Ω
−1
and η
2
= 8·10
−14
Ω
−1
m
2
are normalization factors. Peak powers
are: P
in
d
= 500 mW , P
w
= 160 W , P
r
= 100 W respectively for the data, the write and read pulses. Fig. 2 shows the input
data sequence of 6 bits with duration 2 ns each. The write and read pulses in the experiments have the same duration.
In Fig. 3, TTR is experimentally demonstrated (green curve); the agreement with the numerical results (black curve)
obtained integrating the governing eqs. with the input sequence of Fig. 2 is good. However, output pulses are broader
and weaker of those of an ideally reversed sequence (blue curve). The differences in the peak levels are mainly due
to the fact that the acoustic wave decays exponentially (exp[−t/(2τ
B
)]) during storage. So, the first bit to be stored,
i.e. the last to be retrieved, is affected by a larger decay. The broadening, instead, is due to the inherent spectral
filtering effect during write/read process that realizes a convolution of the optical pulses, as can be demonstrated by
direct integration of eq. 3. The explanations of the observed experimental distortions are confirmed in Fig. 4, where
we show the results of the numerical integration of eqs. (1, 2, 3) with the input sequence of Fig. 2 but by numerically
post-compensating the exponential decay and by using shorter write/read pulses (0.25ns) (black curve).
In conclusion, a novel method for true time reversal has been proposed by exploiting DBG in PM fibers. A data se-
quence of 2 ns optical pulses has been experimentally time reversed. The numerical analysis is in good agreement with
experiments and demonstrates that high-fidelity reversal can be achieved. Possible applications in electromagnetics
[2] and MWP [10] can be envisaged.
This research has been carried out within the FP7, FET-Open, Project GOSPEL, n. 219299.
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