February 10, 2008 / Vol. 6, No. 2 / CHINESE OPTICS LETTERS 137
Nonlinear optical properties of stimulated Brillouin
scattering process in submerged object detection
Yuelan L¨u (
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), Lihua Wu (
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uuu
), and Xueqing Chong (
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)
College of Science, Harbin Engineering University, Harbin 150001
Received March 9, 2007
Nonlinear optical properties of stimulated Brillouin scattering (SBS) to signal detection in water are
analyzed. With the threshold characteristics, SBS only occurs when the high power laser is focused in the
SBS cell. When there is an object present in front of the focus, it leads to lower incident intensity and then
SBS does not occur. The backward SBS signal depends on the focusing location. The nonlinear optical
properties of SBS process in the focusing regime are analyzed theoretically. With the object coming near
to the focusing center, the backward Stokes signal rises up from zero to a maximum, and then grows to
saturation. The delay time of the echo signal to pump signal can give the object location. In experiment,
the peak position of varying rate of energy can give object location.
OCIS codes: 010.3640, 190.5890, 140.3580, 140.7300.
People have made embedded studies on light dispersion
technology as a method o f ocean detection since the mid-
1960s
[1]
. In this area, measurements have been per-
formed for parameters such as veloc ity of sound, tem-
perature, salinity, and c oefficient of viscosity of the sea-
water mainly using Brillouin scattering
[2−7]
. Using in-
jected mode-locked pulse laser and high accuracy scan-
ning Fabry-Perot (F-P) interferometer, Fry et al. ob-
tained Brillouin scattering spectrum that almost reached
the theoretical limit
[6]
. On the basis of spontaneous Bril-
louin scattering in water, Gong et al.
[8,9]
put forward the
submerged o bject detection technology based on spon-
taneous B rillouin scattering, whose basic idea is to de-
termine the location of the object by the disappearance
of the spontaneo us Brillouin scattering signal in the wa-
ter. However, because the spontaneous Brillouin scat-
tering signal is very weak, the detection distance is not
very lo ng, and the system of the edge technique used
is complicated
[10]
. This method has some difficulties in
practical applications.
The feasibility of submerged object detection by fo-
cusing center in stimulated Brillouin scattering (SBS)
process is prop osed in this paper . The inflexion rate
of Stokes signal is used to determine the location o f the
submerged object. In this way, we can get stronger echo
signal and longer measurable distance.
The theoretical models a re set up to describe the
pulse propagation by the numerical solution of the three-
dimensional (3D) coupling equations, including Maxwell
wave equations and medium’s energy transport equa-
tions. Under the condition of slowly varying envelope ap-
proximation, the 3D transient SBS equations can be sim-
plified by three one-dimensional (1D) equations
[11−14]
.
In a SBS medium, the nonlinear SB S process resonantly
couples through electric-stra in which produces an acous-
tic field in the medium. Thus a back-scattering Stokes
field A
s
(z, t) is built from the excited acoustic field
f(z, t), which is a theoretical model including the sponta-
neous nature of the initiation of SBS
[8]
. Energ y is trans-
ported by the acoustic wave. Neglecting the acoustic
propagation and the optical Kerr effect, we can obtain
the slowly varying envelope approximation for the com-
plex amplitudes. T he e quations are used to simulate SBS
process a s follows:
n
c
∂
∂t
+
∂
∂z
A
l
= −αA
l
+ ikρA
s
, (1)
n
c
∂
∂t
+
∂
∂z
A
s
= αA
s
− ikρ
∗
A
l
, (2)
∂ρ
∂t
+
Γ
2
ρ = iΛA
l
A
∗
s
+ f, (3)
where n is the effective refraction index, c is the velocity
of light, ρ(z, t) is the density of medium, Γ is the damping
rate of acoustic field, k, Λ are SBS coupled coefficients,
A
l
is the amplitude of pump laser.
A SBS process is suggested to be initiated by thermal
noise f (z, t), which exists in the end of water and can
be amplified to build Stokes field. Based on the theo-
retical model of SBS initiated by one end noise thermal
field, we introduced the initiated condition of the Gaus-
sian random process as a n equal distribution of noise
field all through water. The coupled equations (1) − (3)
can be solved by using an implicit finite difference in
time and a backward differential scheme in space, which
greatly reduces the computer’s calculating time with
separating time and space domain. In order to gain
this procedure, the pulse is divided into small time in-
terva ls with the time increment assumed constant, and
then the difference forms of coupled wave equations are
established
[15]
. By an efficient numerical algorithm, a
quasi-transient numerical simulation is formed. SBS pro-
cess is built up in which dynamic properties of backward
reflected SBS can be shown. In the above simulation,
SBS parameters of water are adopted as fo llows. The
absorption coefficient α = 0.05 cm
−1
, the effective re-
fraction index n = 1.324, density ρ = 0.997 g/cm
3
,
gain g = 3.8 cm/GW, lifetime τ = 1.87 ns, k =
γ
e
ω
L
4cnρ
0
,
Λ =
γ
e
K
2
16πω
, γ
e
is the electrostriction coefficient, ρ
0
is the
average density of SBS media, K is the temperatur e , ω
L
is the laser frequency, and ω is the Stokes frequency. The
initial laser field (laser pulses are input at z = L, the end
1671-7694/2008/020137-04
c
2008 Chinese Optics Letters
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