Based on the nonlinearity of the nonlinear optical coupler (NOC) and the amplifying capacity of the backward Raman fiber amplifier (PBRFA), a new optical system to compress the optical pulse (optical pulse self-compressor: OPSC) is proposed. Using the expressions describing relationship between output intensities from both output ports and input one of NOC and the expression describing the amplification of the PBRFA, the compressing process of the optical pulse propagating through OPSC is simulated. The results show that the peak of optical pulse will be enhanced and the duration of optical pulse will be reduced significantly, and the shape of input pulse is completely compressed with certain efficiency. It means the optical pulse is self-compressed without the pump pulse

Bien, Chu Van

Lanh, Chu Van

Luu, Mai Van

Quy, Ho Quang

Thanh, Thai Doan

Vietnam Academy of Science and Technology: Journals Online

Volume 22, Number 3 September 2012
Contents
Page
Nung Van Don, Cao Thi Bich, and Nguyen Ba An – New Deterministic Protocol for Joint Remote
Preparation of Two-qubit States
193
Shalini Dangwal, P. S. Bisht and O. P. S. Negi – Octonionic Extension of U(1)×SU(2) Gauge Analyticity
of Dyons
201
Tran Huu Phat, Nguyen Van Long, and Nguyen Van Thu – Neutrality Effects on the Phase Structure of
the Linear Sigma Model with the Non-standard Symmetry Breaking
213
Le Duc Anh and Hoang Anh Tuan – Mott Transitions in the 2-band Hubbard Model: A Coherent Potential
Approximation Study
223
Than Trong Huy, Nguyen Dinh Tung Luan, Truong Van Chuong, and Le Van Hong – Dielectric and
Relaxor Ferroelectric Properties in PZT-PMnN-PSbN Ceramics
229
Trinh Thi Loan, Nguyen Ngoc Long, and Le Hung Cuong – Synthesis and Photoluminescent Property
of MgO:Cr3+ Powders
239
Nguyen Thi Quynh Hoa, Luu Tien Hung, Nguyen Thi Minh, Le Thi Kieu Nga, and Nguyen
Hong Quang – Microstructure and Optical Properties of Transition Metal (Co, Ni)-Doped TiO2 Nanowires
Synthesized by Solvothermal Method
247
Ho Quang Quy, Chu Van Lanh, Mai Van Luu, Thai Doan Thanh, and Chu Van Bien – Optical Pulse
Self-compressor Combined the Nonlinear Coupler with Backward Raman Fiber Amplifier
254
L. X. Chung, P. Egelhof, S. Ilieva, B. Streicher, R. Borger, C. Rigollet, N. Kalantar-nayestanaki,
A. Najafi, T. Davinson, P. J. Woods, V. Eremin, M. Mutterer, M. Von Schmid, and N. T. Khai –
Prototyping of DSSDs for Particle Tracking and Spectroscopy within the EXL Project at Fair
263
Le Hong Khiem, Tran Dinh Trong, and Nguyen Van Thao – A Feasibility Study in Application of a
Gamma Scattering Technique for Inspecting Density Variation by Monte Carlo Method
275
Nguyen Ngoc Duy and Le Hong Khiem – Investigation of Gas Gain of Gem-foil Used in Low Energy
Radioactive Beam Experiment
283

Communications in Physics, Vol. 22, No. 3 (2012), pp. 254-262
OPTICAL PULSE SELF-COMPRESSOR COMBINED THE
NONLINEAR COUPLER WITH BACKWARD RAMAN FIBER
AMPLIFIER
HO QUANG QUY
Academy of Military Science and Technology
CHU VAN LANH AND MAI VAN LUU
Vinh University
THAI DOAN THANH
HCM City University of Food Industry
CHU VAN BIEN
Hong Duc University
Abstract. Based on the nonlinearity of the nonlinear optical coupler (NOC) and the amplifying
capacity of the backward Raman fiber amplifier (PBRFA), a new optical system to compress the
optical pulse (optical pulse self-compressor: OPSC) is proposed. Using the expressions describing
relationship between output intensities from both output ports and input one of NOC and the
expression describing the amplification of the PBRFA, the compressing process of the optical pulse
propagating through OPSC is simulated. The results show that the peak of optical pulse will
be enhanced and the duration of optical pulse will be reduced significantly, and the shape of input
pulse is completely compressed with certain efficiency. It means the optical pulse is self-compressed
without the external pump pulse.
I. INTRODUCTION
There are many techniques interested and used to compress the optical pulse as the
amplitude passive modulation, the mode-locking, the intra-cavity saturation absorption-
amplification [1, 2], the stimulated Raman backscattering in plasma [10–29], etc. The
operating principle of all mentioned techniques is based on the nonlinearity in the optical
medium under the interaction of the intense laser beam [2,9,10,15,19]. In the early 1970 s,
Stolen and Ippen [30] demonstrated Raman amplification in optical fibers. By the early
part of 2000 s, almost every long-haul (typically defined ∼300 km to 800 km) or ultralong-
haul (above 800 km) fiber-optic transmission system uses Raman amplification [13], and
there are many works interested in the stimulated Raman backscattering in fiber [6–8]. As
the operating principle of the pumped backward Raman amplification, the longer pulse
propagating along the opposite direction of the signal pulse is necessary. So, the classical
pulse compressing system always needs two optical pulses, one of them plays the role of
the pump source and second one plays the role of the signal.
In our previous work [3], the nonlinear optical coupler has been proposed and the
nonlinearity appeared in the transfer efficiency-input intensity characteristic. Due to the
H. Q. QUY, C. V. LANH, M. V. LUU, T. D. THANH, AND C. V. BIEN 255
nonlinearity of the nonlinear optical coupler, the output pulse selection at two ports is
found out, i.e. when the powerful signal is propagated through one port, meanwhile the
weak signal will propagate through second port in the conditional intensity density. The
intensity reducing at second port of NOC can be seen as the phenomenon appeared in the
saturation absorption medium. Thus, the combination of the nonlinear optical coupler
(NOC) with the pumped backward Raman fiber amplifier (PBRFA) will become a system
to compress the optical pulse.
In this paper, we propose the configuration of the optical pulse self-compressor
(OPSC) based on NOC and PBRFA. The simulated results will be presented to confirm
the pulse self-compression possibility of the proposed OPSC.
II. THEORETICAL BASICS
II.1. Intensity selection and pulse shortening of NOC
The NOC is consists of one linear optical fiber and Kerr fiber, which is illustrated
in Fig. 1 [3, 4]. The operating principle of NOC is similar to linear optical coupler except
the Kerr effect in nonlinear fiber [8]. Since the Kerr effect, the transfer coefficients at two
ports of NOC depend on input intensity, which are given as following [4]
ηlin =
[
C2
ω2ε2
0
n4
nl
I4
in
16
+C2
sin2
(
lcpl
√
ω2ε2
0
n4
nl
I4
in
16
+ C2
)]
(1− η)nonlin =
[
1− C
2
ω2ε2
0
n4
nl
I4
in
16
+C2
sin2
(
lcpl
√
ω2ε2
0
n4
nl
I4
in
16
+ C2
)] (1)
where, ω is the signal frequency, ε0 is electric permeability, Iin is the input intensity,
ηlin = Iout,in/Iin is transfer coefficient of linear fiber, (1 − η)nonlin = Iout,nonlin/Iin is
the transfer coefficient of nonlinear fiber (see Fig. 1), nnl is the nonlinear coefficient of
refractive index of nonlinear fiber, lcpl is the coupling length, and C is the linear coupling
coefficient, which depends on the radius of fiber, separation distance between two fibers,
refractive index, and signal wavelength [5].
Fig. 1. Nonlinear optical coupler.
256 OPTICAL PULSE SELF-COMPRESSOR COMBINED THE NONLINEAR COUPLER ...
Consider the parameters of the NOC are follows: C = 0.694/mm, nnl = 1.0× 10
−12
mm2/W, lcpl = 2.5 mm. The transmittance efficiency-input intensity characteristics at
two ports are simulated for optical beam with wavelength λ = 1.5µm, and illustrated in
Fig. 2.
Fig. 2. The transfer efficiency through liner output port (solid) and nonlinear
output port (dot) of NOC with nnl = 1.0×10
−12 mm2/W , lcpl = 2.5 mm vs input
intensity density at λ = 1.5 µm.
From Fig. 2, we can see that, with given parameters of the NOC (i.e. with designed
NOC), a laser signal at wavelength of 1.5µm will be transmitted from linear output port
if its intensity density is more than about 20×1012 W/mm2, meanwhile transferred to
nonlinear output port if its intensity density less than 5×1012 W/mm2. It means that the
NOC has the property of intensity selection, which is presented in Fig. 3.
From Fig. 3, we can see that, the considered input pulse is Gaussian, i.e.
Iin(t) = Imax,in exp
(
− ln 2×
t2
τ2
)
(2)
with peak intensity density Imax,in = 4× 10
12W/mm2 and half-duration τ = 1× 10−9s, is
split into two parts, the intense pulse, Iout,lin, with slight changing of the peak intensity
density and duration, has gone out from linear output port, meanwhile the weak one,
Iout,nonlin, with big reduction of both peak and duration, from nonlinear output port. It
is important that the duration of weak pulse from nonlinear output port is reduced to
0.5×10−9 s. This property of the NOC give us an idea to set up pulse compression system
consists from NOC and PBRFA (i.e. OPSC). For this OPSC, the intense pulse can be
used as pumping pulse for PBRFA, and the weak shorten pulse will be amplified as the
signal pulse.
H. Q. QUY, C. V. LANH, M. V. LUU, T. D. THANH, AND C. V. BIEN 257
Fig. 3. Output pulses from two ports of NOC.
II.2. Operation of OPSC
Now, we propose an optical pulse compressor as shown in Fig. 4. Consider the input
Stokes long pulse injected into NOC through input port (1). After propagating through
NOC, the more intense pulse will go out from output port (3), which is injected into
PBRFA as the pump pulse, and guided to second output port (4) along the clock-hand
direction (assumed – z direction). Meanwhile, the weak and shorter pulse will go out from
output port (4), which is injected into PBRFA as the signal pulse, and guided to port
(3) along the opposite clock-hand direction (assumed +z direction). This pulse will be
amplified by stimulated Raman backscattering [33] and go out from port (2) with slight
changing.
II.3. Signal gain of PBRFA
Consider PBRFA is a single-mode fiber with length L. The signal pulse from port (4)
is injected at z = 0 and travels in the +z direction (along opposite clock-hand direction),
while the pump pulse from port (3) with peak power,Pmax,p[W], and duration, 2τ [s], is
injected at z = L and propagates along – z direction (along clock-hand direction). Let
α[dB/km] be the loss coefficient of the signal and let g [m/W] and A[m2] denote the Raman
gain constant and the effective Raman cross section, respectively.
258 OPTICAL PULSE SELF-COMPRESSOR COMBINED THE NONLINEAR COUPLER ...
Fig. 4. Set-up of OPSC.
In order to simplify the problem, we assume that pump energy depletion is negligi-
ble, and the duration of pump pulse (intense pulse) is long enough considerable as CW,
comparing to duration of signal pulse (weak pulse). Because the signal pulse travels along
opposite direction of the pump pulse, the interaction length is Lint = vgτ [m], which is
chosen to be the length of the PBRFA’s fiber, where vgis the group velocity of pulse. At
every point of this interval, zi = vgti (or ti) the pump amplitude is considered as
Pp(zi) = Pmax,p exp
(
− ln 2×
(zi − Lint)
2
L2int
)
exp [αp (zi − Lint)] (3)
Similar to that of work of Lin and Stolen [31], the signal gain obtained from the
pump pulse is given by
G(zi) = exp
[
gP (zi)zi
A
]
(4)
However, at every point the signal pulse has the propagation loss e−αszi . Hence the
net gain is given as
G(zi) = exp
[
gP (zi)zi
A
− αszi
]
(5)
As shown in Fig. 3, the pump pulse is more longer than the signal pulse, so in
distance increment, ∆z = vgτs, where τs is the duration of signal pulse, the gain coefficient
is considered to be constant, i.e. G (∆zi) ≈ G (zi), and the signal is enhanced by factor
G(zi), that means the output signal pulse after propagating through ∆zi can be expressed
as [32]
Pout.s(t,∆zi) ≈ G(zi)Pin,s(t) + n(zi) (6)
where, n (zi) is the quantum noise at point zi [21], Pin,s(t) is the input signal pulse injected
into the increment ∆zi.
H. Q. QUY, C. V. LANH, M. V. LUU, T. D. THANH, AND C. V. BIEN 259
We assume the loss and quantum noise are small negligible, using (5) and (6), we
have
Pamp(t, Lint) = Pin,s(t)
N∏
i=1
G(zi) = Pin,s(t)
N∏
i=1
exp
[
gP (zi)zi
A
]
(7)
where N = τp/τs ≈ τ/τs.
The signal pulse travels along the opposite direction of the pump pulse, the shape
of its can be expressed as
Pin,s(zi) = Pmax,s exp
(
- ln2×
(Lin,s − zi)
2
L2in,s
)
(8)
where Lin,s = vgτs.
After replacing the length argument zi by the time argumentt, and substituting (3),
(8) into (7), we have
Pamp,s(t) = Pmax,s exp
(
− ln 2×
(τs − t)
2
τ2s
)
N∏
i=1
exp
[
gvgtiPmax,p
A
exp
(
− ln 2×
(ti − τ)
2
τ2
)]
(9)
which describes the shape of the amplified pulse propagated through PBRFA only.
To have the shape of the output amplified pulse from port (2) of the NOC, we must
combine (1) with (9). Firstly, resolving (1) to find out Pmax,s, τs and Pmax,p; secondly,
substituting them into (9) to find out Pamp,s(t); finally, using (1) again to find out the
output amplified pulse. In the simulating process, we can replace the intensity P by the
intensity density: W = P/A [W/m2], then (9) can be rewritten as follows
Wamp,s(t) =Wmax,s exp
(
− ln 2×
(τs − t)
2
τ2s
)
N∏
i=1
exp
[
gvgtiWmax,p exp
(
− ln 2×
(ti − τ)
2
τ2
)]
(10)
II.4. Simulation of self-compression process
All NOC’s parameters are given as that in Section II.1. The input signal pulse
parameters are as follows:Wmax,in = 1.0 × 10
12W/m2, τ = 1 × 10−6 s. The PBRFA
parameters are as follows:g = 1.0 × 10−13 m/W, vg = 2 × 10
8 m/s [34], and Lt = vg.τ =
200 m.
For given above parameters, the shorten pulse is simulated (Fig. 5), and compared
with the input pulse (Fig. 6). From Fig. 5 can see that, the duration of optical pulse
is shorten to about2 × 10−8s, i.e. about 102times shorter, meanwhile, its peak intensity
density is enhanced to 1.3× 1013W/m2.
Let E =
+∞∫
−∞
W (t)dt = τWmax
√
pi
ln 2
be the energy density and the ratio of input pulse
to amplified pulse, ηenerg = Ein/Eamp be energy transfer efficiency. Let F =Wmax/2τ be
defined as the pulse “force” and ηcomp = Famp/Fin as the compression efficiency.
Then, from Fig. 5 we can see that although the energy transfer efficiency reaches
13% only, which means the energy density of pump pulse is not changed in good agreement
260 OPTICAL PULSE SELF-COMPRESSOR COMBINED THE NONLINEAR COUPLER ...
In
te
n
si
ty
d
en
si
ty
[w
/m
]
2
t [s]
In
te
n
si
ty
d
en
si
ty
[w
/m
]
2
t [s]
Fig. 5. Shorten pulse. Fig. 6. Comparison of input pulse with
shorten pulse.
with our approximation, but the duration of the amplified pulse is significantly reduced,
about 10−2 times shorter. Additionally, the force, Famp, of the amplified pulse increases
up to 0.65 × 1021, more bigger than that, Fin, of input pulse, 0.5 × 10
18. It means, the
self-compressing efficiency for our model, ηcomp, is very high about 1.3×10
3 (see Table 1.).
Table 1. Parameters of compressed pulses vs Raman gian.
g [m/W] 0.2× 10−13 0.3× 10−13 0.4× 10−13 0.5× 10−13 1.0× 10−13
Wmax [W/m
2] 4.6× 109 2.8× 1012 4.2× 1012 5.6× 1012 1.3× 1013
τ [s] 1× 10−7 0.5× 10−7 0.35× 10−7 0.12× 10−7 0.1× 10−7
F [W/m2.s] 2.3× 1016 2.8× 1019 6× 1019 4.35× 1020 0.65× 1021
ηcomp[*] 4.6× 10
−2 5.6× 101 1.2× 102 8.7× 102 1.3× 103
*Fin = 0.5× 10
18.
However, the shorten pulse’s shape, i.e. its peak power and duration as well as
compressing efficiency depend on design parameters, for example, their shape depend on
the Raman gain in Fig. 7. If the Raman gain constant increases, the peak power of
amplified pulses increases, meanwhile, their duration decreases.
H. Q. QUY, C. V. LANH, M. V. LUU, T. D. THANH, AND C. V. BIEN 261

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Fig. 7. Self-compressed pulses for different Raman gain: a) 0.5× 10−13 m/W; b)
0.4× 10−13 m/W; c) 0.3× 10−13 m/W; d) 0.2× 10−13 m/W.
III. CONCLUSION
Basing on the nonlinear optical coupler and the pump backward Raman fiber am-
plifier, the optical pulse self-compressor was newly proposed. The pulse selection at two
ports of NOC is shown out by the simulation. This property is a main reason to choose
output pulses from NOC as the pump and signal pulses for PBRFA. With proposed con-
figuration of the self-compressor, the expression for the amplified pulse was introduced by
some approximations. The simulated results have shown that by this configuration, the
optical pulse should be self-compressed with certain efficiency, which can be enhanced by
the matching conditions. However, the quality of the OPSC, especially, the compression
efficiency, depends on principle parameters as the nonlinear coefficient of the refractive
index, coupling length, radius of fiber core, peak intensity density and duration of input
pulse, etc. Those questions will be investigated in detail in the next articles.
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Received 28 November 2011.



Optical pulse Self-compressor combined the Nonlinear coupler with Backward Raman fiber amplifier

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Optical pulse Self-compressor combined the Nonlinear coupler with Backward Raman fiber amplifier

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