Laser-induced non-linear light scattering in a suspension of black-body particles
Characteristics of non-linear scattering of powerful pulses of Q-switched YAG:Nd³⁺ laser in an aqueous suspension of submicron-sized black-body particles has been investigated. Proposed is a model describing the results of experiments. This model involves laser-induced overheating of suspended parti...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
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irk-123456789-1181732017-05-30T03:03:05Z Laser-induced non-linear light scattering in a suspension of black-body particles Zelensky, S.E. Characteristics of non-linear scattering of powerful pulses of Q-switched YAG:Nd³⁺ laser in an aqueous suspension of submicron-sized black-body particles has been investigated. Proposed is a model describing the results of experiments. This model involves laser-induced overheating of suspended particles and vaporization of surrounding water with subsequent rapid growth of vapor shells around the particles. 2004 Article Laser-induced non-linear light scattering in a suspension of black-body particles / S.E. Zelensky // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2004. — Т. 7, № 2. — С. 190-194. — Бібліогр.: 20 назв. — англ. 1560-8034 PACS: 42.65.-k http://dspace.nbuv.gov.ua/handle/123456789/118173 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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Characteristics of non-linear scattering of powerful pulses of Q-switched YAG:Nd³⁺ laser in an aqueous suspension of submicron-sized black-body particles has been investigated. Proposed is a model describing the results of experiments. This model involves laser-induced overheating of suspended particles and vaporization of surrounding water with subsequent rapid growth of vapor shells around the particles. |
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Zelensky, S.E. |
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Zelensky, S.E. Laser-induced non-linear light scattering in a suspension of black-body particles Semiconductor Physics Quantum Electronics & Optoelectronics |
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Zelensky, S.E. |
| author_sort |
Zelensky, S.E. |
| title |
Laser-induced non-linear light scattering in a suspension of black-body particles |
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Laser-induced non-linear light scattering in a suspension of black-body particles |
| title_full |
Laser-induced non-linear light scattering in a suspension of black-body particles |
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Laser-induced non-linear light scattering in a suspension of black-body particles |
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Laser-induced non-linear light scattering in a suspension of black-body particles |
| title_sort |
laser-induced non-linear light scattering in a suspension of black-body particles |
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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2004 |
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http://dspace.nbuv.gov.ua/handle/123456789/118173 |
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Laser-induced non-linear light scattering in a suspension of black-body particles / S.E. Zelensky // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2004. — Т. 7, № 2. — С. 190-194. — Бібліогр.: 20 назв. — англ. |
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Semiconductor Physics Quantum Electronics & Optoelectronics |
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AT zelenskyse laserinducednonlinearlightscatteringinasuspensionofblackbodyparticles |
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2025-07-08T13:30:41Z |
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| _version_ |
1837085692203630592 |
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Semiconductor Physics, Quantum Electronics & Optoelectronics. 2004. V. 7, N 2. P. 190-194.
© 2004, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine190
PACS: 42.65.-k
Laser-induced non-linear light scattering
in a suspension of black-body particles
S.E. Zelensky
Optics Division, Physics Department, Kyiv National Taras Shevchenko University,
6, prospect Glushkova, 03680 Kyiv, Ukraine, E-mail: zele@univ.kiev.ua, phone (044)266-2295
Abstract. Characteristics of non-linear scattering of powerful pulses of Q-switched YAG:Nd3+
laser in an aqueous suspension of submicron-sized black-body particles has been investi-
gated. Proposed is a model describing the results of experiments. This model involves laser-
induced overheating of suspended particles and vaporization of surrounding water with
subsequent rapid growth of vapor shells around the particles.
Keywords: laser-induced scattering, non-linear processes, black-body suspensions.
Paper received 03.03.04; accepted for publication 17.06.04.
1. Introduction
Interaction of powerful pulsed laser radiation with black-
body colloidal particles initiates a number of various non-
linear optical phenomena caused by laser-induced heat-
ing of particles. Primitive numerical estimations argue
that pulsed laser radiation of moderate surface power
density (5�50 MW cm�2) is capable to overheat a
submicron-sized black-body particle to a temperature of
thousands of Kelvins. The laser-induced incandescence
(LII) of micro-particles is observed experimentally both
in condensed matter and in gaseous phase [1�9]. The
behavior of LII is well described using the particle en-
ergy balance equation together with Planck�s formula
for black-body thermal emission.
The laser-induced incandescence is employed for
monitoring of soot particulate in flames and engine ex-
hausts [1�5]. When a powerful pulsed laser irradiates
microscopic black particles in a condensed matrix, acous-
tic waves are generated, which can be applied for detec-
tion of colloidal inclusions in ultra-pure liquids [10]. In
transparent luminescent condensed matter containing
suspended particles, LII can serve as a source of photo-
excitation of luminescence, which enables to measure the
luminescence quantum efficiency without the use of ref-
erence luminescent samples [8]. Non-linear reflection of
pulsed laser radiation at a dielectric-carbon suspension
interface can be exploited to produce optical switching
in nanosecond timescale [11,12].
When a suspension of black-body particles is irradi-
ated with a powerful pulsed laser, the phenomenon of
optical power limiting is observed, which consists in non-
linear dependence of the cell transmittance on the inci-
dent laser fluence. With the increase of input laser power
the cell transmittance decreases significantly, hence the
output becomes clamped, which is useful for protection
of optical devices against laser damage. Broadband op-
tical limiting (from the visible to the infrared region) is
observed in aqueous and other suspensions of black-body
particles (for example, carbon black suspensions)
[13,14], carbon nanotubes [15�17], fullerene solutions
[14], etc.
The primary cause of optical limiting in suspensions
of absorbing particles is self-induced scattering of pulsed
laser radiation. There are two basic mechanisms of la-
ser-induced scattering. (i) The laser-induced heating of
suspended particles is followed by the overheating and
quick vaporization of the surrounding liquid; hence vapor
bubbles (vapor shells) grow around the particles and the
light scattering increases significantly. (ii) Thermionic
emission from overheated particles leads to avalanche
ionization in the laser field, and the resulting microplasma
expands and strongly scatters laser light.
Concerning the relative contribution of the mentioned
two mechanisms of non-linear laser-induced light scat-
tering, the authors [13,14] have drawn a conclusion that
laser-induced formation of vapor bubbles becomes ac-
tual at relatively high intensities of laser radiation. On
S.E. Zelensky: Laser-induced non-linear light scattering in a suspension of �
191SQO, 7(2), 2004
the other hand, the authors [18,19] have performed an
extensive time-resolved investigation of degenerate four-
wave mixing in an absorbing colloidal suspension and
concluded that the main mechanism of optical non-lin-
earity at the laser surface power density of approximately
1.5 MW cm�2 is the rapid growth of vapor bubbles at the
surfaces of the laser-heated particles. In [9], on the basis
of the vapor-bubble mechanism of optical limiting, the
authors have proposed a simple model for calculation of
the parameters measured experimentally and obtained
good agreement of the results of experiments and calcu-
lations.
In this paper, we examine the non-linear properties of
laser-induced light scattering in an aqueous suspension
of submicron-sized black-body particles.
2. Experimental details
The measurements were performed with an aqueous sus-
pension of absorbing particles, which was prepared by
diluting and filtering black gouache paint. In contradis-
tinction to dye solutions, paints are suspensions of in-
soluble pigment particles in transparent liquids. Pigments
of black paints are typically made of carbon or some
other chemicals. The chemical composition of the pig-
ment used in this work is unknown. However, chemical
composition of the pigment particles seems to be a sec-
ondary factor for the experiments on laser-induced scat-
tering. For example, experiments show, that LII and la-
ser-induced scattering (optical limiting) are observed with
various paints and even with turbid natural water.
Concerning the size of particles, typical paints con-
tain particles of various shapes and sizes within the range
of 0.01�5 µm. For the suspensions investigated in this
paper, nephelometric measurements have indicated the
average particle radius of approximately 0.1 µm.
In this paper, optical measurements were performed
with the use of a computer-controlled spectrometer with
Q-switched YAG:Nd3+ laser (wavelength 1064 nm, pulse
duration 25 ns FWHM, repetition rate approximately
1 s�1). The laser was equipped with a diaphragm inside
the resonator, which provided a smooth bell-shaped cross-
beam distribution of laser power. The photodetectors
operated in the integrating mode, i.e. they detected the
energy of each single optical pulse. The averaging pro-
cedure was implemented in the software.
All the measurements were performed at room tem-
perature. The investigated suspension was pumped
through the optical cell with a flow rate of approximately
0.5 l min�1, so that each laser pulse interacted with a
�fresh� portion of the suspension.
3. Results and discussion
Consider the interaction of a powerful laser pulse of na-
nosecond duration with an aqueous suspension of black-
body particles. For the calculation of power of scattered
laser light, PS, as a function of incident laser surface
power density, F0, the model [9] can be used. This model
implies the following processes. Within the laser pulse
duration, microscopic particles are heated by laser ra-
diation and transfer a portion of the obtained energy to
the vaporization of surrounding water. The process can
be conceived as a nucleation and growth of vapor shells
around the particles. Denote G the ratio of the particle
energy transferred to the vaporization of surrounding
water to the particle energy obtained from the laser beam,
namely G = Λdm(Fσ0dt)�1, where Λ is the latent heat of
vaporization of water, Λdm is the mass of water vapor-
ized during the time interval dt, σ0 is the particle absorp-
tion cross-section at the laser wavelength, F is the laser
surface power density. As a first approximation, the pa-
rameter G can be treated as a constant. According to [9],
the value of G is estimated approximately as 0.01�0.5 %
for aqueous suspensions of submicron particles. The
model implies that the vapor shells grow during the laser
pulse with the speed largely dominated by inertia-con-
trolled processes. The radius of the core-shell particle
can be estimated with the use of the particle energy bal-
ance equation together with the equation of ideal gas state.
So, the volume of water vapor, V, increases with time in
direct proportion to the integral of laser power density,
∫
∞−
′′
t
tdfFtV )(~)( . For particles with the radius of r0 ≈
≈ 0.1 µm, calculations show that the radius, r, of a core-
shell particle at the end of the laser pulse can be approxi-
mately twice as large as r0. The model also uses the well-
known classical relations between the particle scattering
cross section and the particle radius, namely, σ ~ r6 for
r < λ and σ ~ r2 for r > λ. The model is implemented in
computer codes, which allows calculating all the param-
eters measured experimentally in [9].
For calculation of the scattered light power as a func-
tion of the laser power, we can use the following reason-
ing. Consider the energy balance equation for a laser
pulse propagating through the suspension. In the case of
linear attenuation of the laser beam, the following equa-
tion can be written
00
000 SA PPSFTSF ++= (1)
where F0 is the surface power density of the incident laser
beam, S is the laser beam cross area, T0 is the optical
transmittance of the cell at the laser wavelength at low
levels of the laser power density, 0
AP and 0
SP are, respec-
tively, the absorbed and scattered power of the laser beam
propagating through the cell. As far as the primary
mechanism of the self-induced attenuation of the laser
beam is the laser-induced scattering, to a first approxi-
mation we suppose that an increase of laser power does
not cause the increase of absorption in the suspension but
causes only the increase of scattering. Then, in the case
of non-linear attenuation of the laser beam in the suspen-
sion, the energy balance can be written
00
00 SA PPFSTSF ++= (2)
192
SQO, 7(2), 2004
S.E. Zelensky: Laser-induced non-linear light scattering in a suspension of �
where T is the optical cell transmittance which depends
on the laser power, PS is the scattered light power that is
a non-linear function of the incident laser power F0.
Now we introduce the following parameter
1000 )( −+= SAA PPPα , (3)
which is a measure of the absorption processes as com-
pared with the total attenuation of the laser beam propa-
gating through the suspension in the linear regime of in-
teraction. As far as the number density of particles in the
suspension remains constant, the introduced parameter
α is equal to the averaged ratio of absorption and extinc-
tion cross-sections of the particles. For example, for a
spherical carbon particle with the radius of 0.1 µm, the
absorption and extinction cross-sections at a wavelength
of 1.06 µm are respectively estimated as 3.68⋅10�14 m2
and 0.833⋅10�14 m2 [18], hence we can estimate α ~ 0.8.
By the order of magnitude, such an estimate is in agree-
ment with the results of direct measurements of scattered
laser power in carbon black suspensions [14].
With taking into account (3), equations (1) and (2)
result in the following expression for the scattered power
as a function of the incident laser power
)]1()(1[ 000 TaFTSFPS −−−= (4)
Expression (4) enables us to calculate the dependence
PS(F0) for a given dependence T(F0). The characteristics
PS(F0) calculated for various α are given in Fig. 1,b. The
linear transmittance of 2 cm-thickness cell is set to
T0 = 0.73. The calculations were performed with the use
of the dependence T(F0) (plotted in Fig. 1,a), which is the
best fit of the experimental data [9]. Circle points in
Fig. 1,b,c are the results of measurements of the scat-
tered light intensity at the wavelength of 1.06 µm and
pulse duration of 25 ns. The measurements were performed
in the same conditions as in [9]. The scattered light was
detected with a PMT tube (FEU-83) at an angle of scat-
tering of approximately π/2. As seen from Fig. 1,b, the
dependence of PS(F0) is essentially non-linear. At relati-
vely small levels of laser power density, F0 < 3 MW cm�2,
the slope of the curve PS(F0) equals to unity (in a log-log
scale). For the visualization, the dashed lines in Fig.1,b,c
are drawn with a unit slope. With the increase of F0 the
scattering becomes non-linear and the slope of the curve
increases up to approximately 2. Further increase of F0
leads to the decrease of the slope to nearly a unit.
As seen from Fig. 1,b, the experimental and theoreti-
cal data disagree. This disagreement can be explained
by taking into account the following circumstance. The
theoretical curves PS(F0) given in Fig. 1,b correspond to
the integral scattered laser power over the whole volume
and over all possible scattering angles, whereas the ex-
periments were carried out at a fixed scattering angle.
The considered mechanism of non-linear scattering im-
plies that the scattering indicatrix depends on the laser
power density and can change significantly during the
laser pulse due to the increase of vapor shells.
Following the methodology developed in previous
papers [6,7,20], for subsequent analysis, we introduce
the factor of non-linearity for the scattered radiation as
follows
00 /
/
FdF
PdP SS
S =γ . (5)
The parameter (5) is a convenient dimensionless meas-
ure of non-linearity of the investigated process, which
can be easily determined from the experimental data re-
gardless of the units of measuring of PS and F0. With the
use of (4), by a little algebra, the following expression
can be derived
TT
TT
S −−−
−=
)1(1
1
0α
γ
γ , (6)
where γT is the following factor of non-linearity for the
optical transmittance
00 /
/
FdF
TdT
T =γ , (7)
which can be calculated from the known dependence
T(F0) . Equation (6) enables to calculate the dependence
Fig. 1. The optical transmittance (a) and scattered laser power
(b,c) as a function of the incident laser surface power density.
Circle points � experiment, solid lines � calculations. Dashed
lines indicate the unit slope. b � calculated according to equation
(4), c � calculated according to equation (8) from z1 = 0 to z2 =
= 0.05d for a cell thickness of d = 2 cm; α = 0.5 (1), 0.75 (2), 0.9 (3).
10
�3
10�2
10
�1
10
0
10
1
10
2
0.1 1 10 100
10
�3
10
�2
10
�1
10
0
10
1
10
2
b
1
2
3
F
0
, MW cm
P
,
a
.u
.
P
,
a
.u
.
T
S
S
�2
c
1
2
3
0.0
0.5
a
S.E. Zelensky: Laser-induced non-linear light scattering in a suspension of �
193SQO, 7(2), 2004
of γS(F0) with the use of T(F0) from Fig. 1,a. Fig. 2,b
shows the results of calculations for various values of α.
It is worth noting that the obtained dependence of γS(F0)
is a bell-shaped function, i.e. the investigated process is a
representative of the processes with variable factors of
non-linearity [20].
The experimental data for γS(F0) are given in Fig. 2,a.
These data were collected at the same conditions as the
data given in Fig. 1. As seen from Fig. 2,a, the experi-
mental dependence of γS(F0) shows a clear maximum;
this fact is in qualitative agreement with the calculations.
However, it should be noted that the position of the maxi-
mum in Fig. 2,a and its height differ from the calculated
values (Fig. 2,b). The observed disagreement can not be
explained only by the errors of measurements of the laser
surface power density. Thus, the situation requires addi-
tional analysis.
As it was already mentioned, the calculations account
the integral power of scattered laser light, whereas the
measurements were carried out so that the photodetector
collected the scattered light only from a small portion of
the laser-irradiated volume. The range of vision of the
photodetector covered only 5 to 10% of the length, d, of
the laser-irradiated track near the entrance window of
the optical cell. According to this, a computer program
was developed that calculates the power of laser light
scattered from a given region of the laser-irradiated
track. Denote z the coordinate along the laser beam axis.
Then, for a given range from z1 to z2, the scattered laser
power can be calculated as follows
∫∫= NtzFtzdtdzP
z
z
S ),(),(
2
1
σ , (8)
where N is the number density of particles in the suspen-
sion, σ is the scattering cross-section of a core-shell parti-
cle, it depends on the irradiation history of the particle
and therefore depends on z and t. For calculation of σ(z, t)
and F(z, t), the model [9] is employed. The integration
over t in (8) is performed within the extent of the laser
pulse, which is approximated by a Gaussian function.
The dependence of PS(F0), calculated according to (8),
was used for calculation of the factor of non-linearity,
γS, according to its definition (6), as a function of the
incident laser power density.
The theoretical curves γS(F0) calculated for the track
regions adjacent to the entrance window of the cell are
given in Fig. 2,c. By comparing Fig. 2,a and Fig. 2,c,
one can see that the theoretical curve γS calculated for
the range from z1 = 0 to z2 = 0.05d and for α = 0.5 is in
good agreement with the experimental data.
The proposed improved method of calculation of scat-
tered optical signals (8) enables to make a better fit of the
experimental data presented in Fig. 1. The theoretical
curves PS(F0), calculated for the range from z1 = 0 to z2 =
= 0.05d, are given in Fig. 1,c as solid lines. As seen,
good agreement between the calculated and experimen-
tal data is obtained for α = 0.5.
4. Concluding remarks
In this paper, we investigated some peculiarities of the
laser-induced light scattering in aqueous suspensions of
absorbing particles. The model of interaction of power-
ful nanosecond laser pulses with the suspensions is im-
proved. It is assumed that the primary mechanism of la-
ser-induced scattering is the rapid growth of vapor shells
around the suspended particles during the action of laser
pulses. Despite its simplicity, the model enables to calcu-
late all the experimentally measured characteristics of
the investigated object, with good agreement between the
experimental and calculated data.
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