Laser-induced thermal acoustics (LITA), an optical four-wave mixing technique, has been used for sensitive measurement of the sound speed, thermal diffusivity, acoustic damping rate, and complex susceptibility of a gas. In LITA, laser-induced acoustic waves scatter laser light into a coherent, modulated signal beam. A simple expression accurately describes the signal. Atmospheric sound speeds accurate to 0.5% and transport properties accurate to 30% have been measured in a single shot without calibration. LITA spectra have been taken of weak spectral lines of NO2 in concentrations of less than 50 parts in 10^9. Signal reflectivities up to 10^4 are estimated

Cummings, E. B.

English

Caltech Authors - Main

September 1, 1994 / Vol. 19, No. 17 / OPTICS LETTERS
Laser-induced thermal acoustics: simple accurate
gas measurements
E. B. Cummings
Graduate Aeronautical Laboratories, California Institute of Technology, Pasadena, California 91125
Received February 17, 1994
Laser-induced thermal acoustics (LITA), an optical four-wave mixing technique, has been used for sensitive
measurement of the sound speed, thermal diffusivity, acoustic damping rate, and complex susceptibility of a gas.
In LITA, laser-induced acoustic waves scatter laser light into a coherent, modulated signal beam. A simple
expression accurately describes the signal. Atmospheric sound speeds accurate to 0.5% and transport properties
accurate to 30% have been measured in a single shot without calibration. LITA spectra have been taken of weak
spectral lines of NO2 in concentrations of less than 50 parts in 109. Signal reflectivities up to 104 are estimated.
A four-wave mixing (FWM) technique that the au-
thor proposes to call laser-induced thermal acous-
tics (LITA) has been applied for single-shot point
measurement of sound speed and thereby of tem-
perature, if the gas composition is known), thermal
diffusivity, and acoustic damping (and thereby of vis-
cosity) of a gas.' LITA signals arise from a sequence
of optoacoustic and acousto-optic effects, enhanced
by quenching. LITA's diverse capabilities, including
single-shot gas property, velocity, and multiplex spec-
tra measurement, portend a robust line of research
and application. A similar technique has been used
to measure sound speeds in crystals.2 Buntine et al. 3
first observed LITA signals from gases in delayed-
pump FWM experiments,3 and several groups of sci-
entists are studying thermal gratings (used in LITA)
in connection with degenerate FWM.
With cw argon-ion laser scattering off acoustic
waves excited by a 5-ns dye laser, the temperature
of the laboratory air was measured by uncalibrated,
single-shot LITA within 0.5%, limited by uncertainty
of the air composition and beam geometry. Trans-
port properties were measured within 30% of pub-
lished values, limited by a finite beam-size effect,
which was ignored. The two optoacoustic effects of
electrostrictiction and thermalization, proportional to
the real and the imaginary parts of the gas suscep-
tibility, respectively, produce different LITA signals,
permitting sorting of each effect. In this way LITA
was used to measure a spectrum of the complex
gas susceptibility showing weak visible lines of the
laboratory-air trace species NO2 (less than 50 parts
in 109). The absolute amplitude and time history of
LITA signals are accurately represented by predic-
tions of an analytical expression derived previously
from the linearized equations of light scattering and
hydrodynamics.'
LITA is a laser-induced dynamic grating tech-
nique that employs a combination of optoacoustic
and acousto-optic effects. Light from a short-pulse
driver laser (e.g., <10 ns) generates acoustic waves
by electrostriction and rapid thermalization. Elec-
trostriction, the tendency of polarizable molecules
to move toward regions of high optical electric-field
intensity,4 is proportional to the real part of the gas
susceptibility. Thermalization is a multiple-step col-
lisional process proportional to the imaginary part of
the gas susceptibility: molecules of the gas absorb
driver-laser energy; inelastic collisions convert part
of the excited-state energy into molecular kinetic
or rotational energy; finally, elastic molecular colli-
sions equilibrate the velocities of the molecules, rais-
ing the temperature. Acoustic waves are produced
efficiently when the drop in gas density accompa-
nying thermalization sharply lags that of equilibra-
tion. The density-perturbation field of the acoustic
waves generates a susceptibility-perturbation field
that scatters light from a long-pulse or cw source
laser, forming the LITA signal.
A forward-scattering FWM has been used for LITA.
The driver laser is split into two beams, which cross
at a small angle (0.5-5 deg) in the gas, where they
interfere with each other, forming an ellipsoidal
electric-field intensity grating at their intersection.
Here, optoacoustic effects generate acoustic struc-
tures with modulation depths from 0.01% to 5%.
Electrostiction forms two traveling acoustic wave
packets (phonons) and a weak stationary isobaric
density grating (thermon), each with the wavelength
of the electric-field grating. Thermalization gener-
ates similar acoustic structures, but the thermon is
dominant. The phonons counterpropagate in the di-
rection parallel to the grating vector and decay by
acoustic damping, whereas the thermon (stationary
with respect to the fluid) decays by heat conduction.
Light scattered from the source laser by the acoustic
gratings emerges in a coherent signal beam when
the source laser is incident at the Bragg angle of the
grating. Light scattered by the phonons has Doppler
shifts relative to light scattered by the thermon of
plus and minus the Brillouin frequency, WB = csq,
q 2kd sin(0/2), where c8 is the speed of sound, q is
the grating vector magnitude, 0 is the driver-beam
crossing angle, and kd is the driver-beam wave-vector
magnitude. Beating between the light scattered by
these structures modulates the detected signal, which
0146-9592/94/171361-03$6.00/0 © 1994 Optical Society of America
1361
1362 OPTICS LETTERS / Vol. 19, No. 17 / September 1, 1994
sample
_ Dye Laser
550-800 nm
40 mJ _ 2xNd:YAG Laser
6 ns i I omJ
2 GHz LW.
Fig. 1. LITA experimental setup: f.l., focal length;
BPF, bandpass filter.
bears a dc component; a component at the Brillouin
frequency caused by phonon/thermon signal beating;
and a component at twice the Brillouin frequency
caused by beating of signals generated by the con-
jugate phonons.
Current experiments detect the relative Doppler
shifts of light scattered from a narrow-band source
laser. However, convection of the phonons and ther-
mon causes a common Doppler shift in the signal
beam that can be measured by optical heterodyne
techniques, permitting velocimetry by analogy with
laser-Doppler velocimetry. One may also use LITA
for single-shot spectral measurements by spectrally
resolving the LITA signal scattered from a broadband
source laser. Experiments to study both of these
LITA capabilities are under development.
An analytical expression previously derived for
the amplitude and time history of the LITA signal
allows the magnitude of LITA signals to be esti-
mated a priori and the actual LITA signal to be
interpreted quantitatively,' with very good experi-
mental agreement. The analysis treats the optoa-
coustic effects and the hydrodynamic evolution of the
acoustic structures, using the linearized hydrody-
namic equations.5 The perturbation solution for the
far field of light scattered off a dielectric disturbance
accounts for the acousto-optical effect.5 A simple
analytical result for the signal intensity, I(t), is ob-
tained for a short-duration Gaussian driver beam,
infinite-extent, monochromatic source beams, and
single-rate-dominated thermalization:'
l(t) o [Aexp(-DTq 2 t) +B cos(csqt + CF) exp(-rq2t)]2,
where DT is the thermal diffusivity, r is the acoustic
damping coefficient, and A, B, and 'D are simple al-
gebraic functions of gas and laser-beam parameters.
When the approximations listed above are not valid,
spatial and temporal convolutions of laser-beam
profiles and thermalization behavior augment the
analysis. The ratio of signal-beam to source-beam
intensity is of the order of 101 for room air with
a thermal modulation depth of 1% in a 2-mm-long
sample volume, without resonant enhancement at
the source-laser wavelength.'
Figure 1 is a schematic diagram of the experimen-
tal apparatus used in these LITA experiments. The
driver laser is a 2-GHz-linewidth (L.W.) dye laser,
which emits -40 mJ of light tuned between 587 and
592 nm in 5-ns pulses. 3-mm-wide driver beams are
formed from the dye laser emission by a 50% beam
splitter (B.S.) and a mirror (ml). The driver beams
intersect at the focus of the 400-mm lens, where they
approximate finite plane waves -200 Aum in diame-
ter. The beam-crossing angle is set by the distance
between the parallel beams, which is adjusted by use
of micrometer translation stages under mirrors m2
and M3 . Three-dimensional BOXCARS geometries6
with crossing angles ranging from 1.00 to 2.30 were
used in these experiments. The driver-beam pulse
triggers the acquisition of the LITA signal by means
of silicon P-I-N photodiode Pi (Thor Labs Model DET-
2SI). The source laser is a 1-W cw argon-ion laser op-
erating at 488 nm (Spectra-Physics Model 165). A
two-lens system adjusts the source beam diameter,
which ranged from -200 /uzm to 2 mm. Mirror m4
points the source beam to the sample volume. A sil-
icon P-I-N photodiode, P2, monitors the intensity of
the source beam.
The detection system consists of a fast photomulti-
plier tube (PMT) (Hammamatsu Model OPTO-8) with
at least a 500-MHz signal bandwidth and optical fil-
ters to prevent signal contamination and saturation,
including a 10-nm interference filter at 488 nm and a
40-mm lens 20-Am pinhole spatial filter. The PMT
dynode voltages are maintained during the signal
pulse by Mylar and silver-mica capacitors with av-
erage lead lengths less than 2 cm. The LITA sig-
nal path length to the detector is -2.5 m. Data
are recorded with a 1-GS/s, 8-bit, two-channel digital
storage oscilloscope (DSO, HP Model 54510A). This
records typically 500-2000 sample time histories of
signals from the PMT and P2.
In experiments using laboratory air, completely
nonresonant electrostriction generated a LITA signal
of roughly 30 photons /ns (reflectivity -101 with the
1-W source beam). An average of 256 shots yields
the nonresonant data plotted as the dotted curve in
Fig. 2. The frequency of the modulation is -26 MHz,
twice the Brillouin frequency, yielding a sound speed
accurate within the uncertainty of the knowledge of
the laboratory sound speed (-0.5%). The resonantly
0.9-
0.8-
,30.7
0.6
1. 3 
~0.4
0 so 100 5I0 200 250 300 350 400 450 500
time from driver laser fifing (ns)
Fig. 2. Nonresonant (dotted curve), near-resonant
(dashed curve), and resonant LITA (solid curve) signals.
September 1, 1994 / Vol. 19, No. 17 / OPTICS LETTERS 1363
0 200 400 600 800 1000 1200 1400 1600 1800 2000
time from driver laser firing (ns)
Fig. 3. Single-shot signal from N0 2-seeded air obtained
with a grating wavelength of 32.3 ,m.
Fig. 4.
tained
retical
0 50 100 150 200 250 300 350
tinie from driver laser firing (ns)
400 450 500
Four-shot average signal from seeded air ob-
with a grating wavelength of 14.5 ,Am and theo-
fit (dashed curve).
enhanced signal recorded near a weak line of NO2
appears as a dashed curve in Fig. 2 for comparison.
The signal recorded near the peak of the absorp-
tion line is the solid curve plotted in Fig. 3. On this
curve the dominant modulation is at the Brillouin fre-
quency, caused by interference between the signals
scattered by the phonons and the thermon. LITA's
good sensitivity is demonstrated since the ambient
air contained less than 50 parts in 109 of NO2 accord-
ing to the Southern California Air Quality Manage-
ment District.
Seeding the gas with NO2 vapors from a beaker
of nitric acid provided LITA signals that were sev-
eral orders of magnitude stronger than the signals
obtained from room air, with estimated reflectivi-
ties near 104. A sample single-shot LITA signal
appears in Fig. 3. The driver-beam crossing angle
was 1.04°, yielding a grating wavelength of 32.3
um and a Brillouin frequency of 10.7 MHz. At
high concentrations of absorbing species, thermal-
ization swamps electrostriction. Figure 4 shows a
four-shot average of the LITA signal obtained when
the beam-crossing angle was widened to 2.3° (grating
wavelength 14.5 gum; Brillouin frequency 23.9 MHz).
Damping of the waves occurs on a time scale pro-
portional to the square of the grating wavelength.
In Fig. 4 the theoretical LITA signal is plotted with
a dashed curve, showing excellent agreement with
experiment. The sound speed and transport coeffi-
cients used in the fit are published values for dry air.
Here, thermalization is resolved so the single-rate
model of thermalization is replaced by the super-
position of two-rate thermalizations: a fast -10-ns
process and a slow -100-ns process. One could ob-
tain a better fit to the data by adopting a more ac-
curate thermalization model and source-beam profile
model (a top-hat profile is assumed) and including
the effect of source-beam phase noise.
In conclusion, LITA has demonstrated excellent
sensitivity in the first round of experiments. In both
magnitude and time history, the LITA signal is ac-
curately represented by an analytical expression de-
rived from the linearized equations of hydrodynamics
and light scattering.
The author gratefully acknowledges the support
of the University Research Initiative in aerothermo-
chemistry sponsored by the U.S. Air Force Office of
Scientific Research. The author is also indebted to
the U.S. Office of Naval Research for its support of his
graduate education through its fellowship program.
References
1. E. B. Cummings, GALCIT Rep. FM 92-2 (California
Institute of Technology, Pasadena, Calif., 1992).
2. R. J. D. Miller, R. Casalegno, K. A. Nelson, and M. D.
Fayer, Chem. Phys. 72, 371 (1982).
3. M. Buntine, D. Chandler, and C. Hayden, "Detection
of excited-state absorption in water via laser-induced
grating spectroscopy," J. Chem. Phys. (to be published).
4. R. W. Boyd, Nonlinear Optics (Academic, New York,
1992), Chap. 8, pp. 327-331.
5. B. J. Berne and R. Pecora, Dynamic Light Scattering
(Wiley, New York, 1976), Chap. 10, pp. 229-232.
6. A. C. Eckbreth, Laser Diagnostics for Combustion
Species and Temperature (Abacus, Cambridge, Mass.,
1988), pp. 249-252.


Laser-induced thermal acoustics: simple accurate gas measurements

Laser-induced thermal acoustics (LITA), an optical four-wave mixing technique, has been used for sensitive measurement of the sound speed, thermal diffusivity, acoustic damping rate, and complex susceptibility of a gas. In LITA, laser-induced acoustic waves scatter laser light into a coherent, modulated signal beam. A simple expression accurately describes the signal. Atmospheric sound speeds accurate to 0.5 % and transport properties accurate to 30 % have been measured in a single shot without calibration. LITA spectra have been taken of weak spectral lines of NO2 in concentrations of less than 50 parts in 109. Signal reflectivities up to 104 are estimated. A four-wave mixing (FWM) technique that the au-thor proposes to call laser-induced thermal acous-tics (LITA) has been applied for single-shot point measurement of sound speed and thereby of tem-perature, if the gas composition is known), thermal diffusivity, and acoustic damping (and thereby of vis-cosity) of a gas. &apos; LITA signals arise from a sequence of optoacoustic and acousto-optic effects, enhanced by quenching. LITA&apos;s diverse capabilities, includin

E. B. Cummings

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Laser-Induced Thermal Acoustics: Simple Accurate Gas Measurements

Detection of excited-state absorption in water via laser-induced grating spectroscopy,&quot;

Dynamic Light Scattering

Laser Diagnostics for Combustion Species and Temperature (Abacus,

Nonlinear Optics (Academic,

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