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Resonance-enhanced coherent anti-Stokes Raman scattering in C2
B. Attal, D. Débarre, K. Müller-Dethlefs, J.P.E. Taran
To cite this version:
B. Attal, D. Débarre, K. Müller-Dethlefs, J.P.E. Taran. Resonance-enhanced coherent anti-Stokes Raman scattering in C2. Revue de Physique Appliquée, Société française de physique / EDP, 1983, 18 (1), pp.39-50. �10.1051/rphysap:0198300180103900�. �jpa-00245066�
Resonance-enhanced coherent anti-Stokes Raman scattering in C2
B. Attal, D. Débarre, K. Müller-Dethlefs
(*)
and J. P. E. TaranONERA, 29, Avenue de la Division Leclerc, 92320 Châtillon, France
(Reçu le 5 juillet 1982, accepté le 7 octobre 1982)
Résumé. 2014 Des spectres de Diffusion Raman Anti-Stokes Cohérente (DRASC) à la résonance électronique ont été
obtenus sur le radical C2 formé dans une décharge microonde et dans une flamme de chalumeau oxy-acétylénique.
La résonance électronique a été obtenue en accordant les lasers dans le système de Swan. Des spectres d’émission de C2 sur la bande de Swan avaient au préalable été enregistrés par spectroscopie à transformée de Fourier et
interprétés; ceci a permis de déterminer les conditions optimales d’enregistrement des spectres DRASC, puis d’interpréter ces derniers sans ambiguïté. Des simulations numériques ont été calculées; ces simulations prennent
en compte l’effet des populations des états vibrationnels supérieurs et de l’élargissement Doppler; elles sont en
bon accord avec les spectres expérimentaux. Les densités de C2 observées sont voisines de 5 x 1011 cm-3 dans la
décharge et 1013 cm-3 dans la flamme. Le seuil de détection est 1010 cm-3 avec notre instrument.
Abstract 2014 We have obtained resonance-enhanced Coherent Anti-Stokes Raman Scattering (CARS) spectra of the C2 radical formed in a microwave discharge and in an acetylene welding torch. Electronic resonance enhan-
cement was obtained in the Swan system. In order to prepare this work, Swan band emission spectra of C2 had
been recorded and assigned using Fourier-transform spectroscopy; this enabled us to determine the optimal
conditions for the CARS spectroscopy and to assign the CARS spectra unambiguously. Numerical simulations
were performed, with due account for the effects of upper vibrational state populations and for Doppler broadening;
the agreement with experimental spectra is fair. We deduce from the spectra C2 densities of about 5 x 1011 cm-3 in the discharge and 1013 cm-3 in the flame. The detection sensitivity is of the order of 1010 cm-3 for our system.
Classification
Physics Abstracts
07.65 - 33.10 - 33 . 20F - 33 . 20K - 33.35 - 33 . 70 - 33 . 80K - 42.65C - 47 . 80 - 51.70 - 52.80
1. Introduction. - Coherent Anti-Stokes Raman
Scattering
(CARS) is an attractivetechnique
forcombustion
diagnostics [1-5].
Itsdetectivity,
however,is limited
by
the existence of anon-vibrationally
reso-nant
background
of electronic nature which canpreclude the detection of trace
species,
i.e.species
withconcentrations below 1
% by
volume. Hence the interest in using the electronic resonance enhancement of the CARSsusceptibility,
from whichgains
of 10’to 108 should follow for the
detectivity.
ResonanceCARS has been studied
[6, 7]
and then observed, firstin
liquids,
then in gases[8-13].
In gases, resonance- enhanced CARS isextremely
difficult to observe.Several factors are
responsible
for thisdifficulty [14].
The main
difficulty
isone-photon
saturation which prevents us fromapplying large
power densities to thesample.
As a consequence, one is tempted to raise thegas
density
inorder
to have alarger susceptibility,
hence a
larger
sourcepolarization
and a stronger(*) Now at Institut für Physikalische und Theoretische Chemie, Lichtenbergstrasse 4, D-8046 Garching, Federal Republic of Germany.
signal.
But a limit is soon reached where the one-photon absorption
attenuates the pump beams as wellas the signal,
yielding
distortedlineshapes
from whichthe proper line contours cannot be extracted. If one uses a shorter cell, a
background signal
isgenerated
in the windows, swamping the weaker lines or distort-
ing
them. This lastproblem
may be circumventedby . using
a cross-beam arrangement[15, 16],
which addssomewhat to the
experimental complexity.
In addition, resonance CARS spectra in gases are difficult to
interpret properly
since precise spectro-scopic
data are unavailable for the many molecules and radicals which are of interest in reactive media orplasmas.
Thisdifficulty
isaggravated by
the need touse two or three monochromatic and stable
pulsed
lasers which must be tuned
precisely.
Whentrying
todetect
tracespecies using
resonance CARS, the pro- blem isposed
inslightly
different terms since one is nottrying
toperform
ananalysis
ofspectral properties
of molecules, but to generate aslarge
asignal
aspossible.
Furthermore it can be shown that
high
power lasers tuned at a few linewidths away from theone-photon
resonances will
actually
generate moresignal [14];
frequency stability
then is less critical.Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/rphysap:0198300180103900
These reasons
largely explain
why so few papers in this field haveappeared
so far. The only speciesstudied or seen
by
resonance CARS are12
[10, 17, 18],C2
[12, 19] andN02
[ 1 l, 13], yet only12
spectra had beenthoroughly
understood. This work gives anaccount of a
C2 study
undertaken toprecisely
demon-strate the mechanism of electronic enhancement in the Swan system within the framework of the
multiple
resonance
theory
[10, 14]. In view of the absence ofspectral
data of sufficientquality
onC2,
we had to firstobtain emission spectra of the Swan system
using
ahigh
resolution Fourier-transform spectrometer[20].
To record the CARS spectra, two low power flash-
pumped
lasers were used which were tuned into aspectral region
so as tosatisfy
the condition of near-triple
resonance. Thanks to that consideration, some strong lines were found.Using
thefrequency
combi-nation which gave maximum
signal,
we were alsoable to detect
C2
in anoxyacetylene
flame.2.
Spectroscopy
ofC2.
- For the present work,resonance enhancement was
sought
from the Swan electronic transition (a3 llu-d 3 llg),
which lies in the visible. In order toprecisely
interpret the CARS spectral content, the positions of the emission lines had to be known to an accuracy of better than 0.01 cm-1. Since the information is not available from earlier work[21-23],
therecording of high
resolutionspectra
by
means of Fourier-transform spectroscopywas undertaken in collaboration with CNRS. That
study
hasprovided
us with accurateC2
emissionfrequencies, together
with anappropriate
set ofspectroscopic
constants,including
those for the A- typedoubling [24,
25].One-photon spectroscopy of C2.
- The Swansystem is
spread
all over the visible, with a maximumin the green at 516.5 nm [26, 27]. A stable emission
source was
developed
for this work, based on a micro-wave
discharge
in helium mixed withacetylene
andtraces of
02.
Several vibrational bands were recorded with the Fourier-transform spectrometer of Aimé-Cotton Labo- ratory between 420 and 600 nm. Part of the green sequence (Av = 0) is
displayed
infigure
1 under aspectral
resolution of 0.07 cm-1. It shows the charac- teristictriplet splitting
of each line and thestaggering
of the
triplet
components causedby
the absence ofone 039B doublet component
resulting
from the nuclearspin
statisticspertaining
to the zero nuclearspin
ofcarbon. An
improved
set ofspectroscopic
constantswas derived from the
positions
of these lines and of those seen in the rest of the spectrum ; these will bepublished
elsewhere[20].
Resonance-enhanced CARS. - Resonance CARS studies in
C2
are made delicateby
numerous difficul-ties
experienced
inpreparing samples
of sufficient concentration or inavoiding
saturation of the one-photon
and Raman transitions in resonance with the fields. Since theobjective
is also to find conditionsappropriate
foroptimal
detectionsensitivity,
ouranalysis
was to concentrate on the transitions asso-ciated with the lower vibrational states (v 3) and
with rotational quantum numbers
containing
a suffi-cient fraction of the total
population
(J 40). Thediscussion will centre first on the main
spectral
featureswhich are contributed
by
the lower rovibrational levels 1 a ~. Then some attention will begiven
to the upper rovibrationallevels |b ~,
whichgive
corrective contri- butions of greatsignificance.
2.1 ANALYSIS OF LOWER LEVEL 1 a~ CONTRIBU-
TION. - The rules used in the
interpretation
of reso-nance CARS spectra have been discussed some time
Fig. 1. - Emission spectrum of C2 in a microwave discharge; 0-0 band of the d
303A0g-a 303A0u
Swan system ; instrumental resolution of inset spectrum : 0.07 cm-1.ago
[10, 14,
28]. In thefollowing,
we use the notations of these references. We recall that there are in generalthree types of lines associated with double resonances
pertaining
to the initial state |a ~ of the CARS energy level diagram, asdepicted
infigure
2. Two of these arefound when the pump
frequency
at 03C91is
in resonancewith a
one-photon frequency
03C9an, the third onebeing
obtained for Col =
úJn’b. It
is possible to visualizeFig. 2. - Energy level diagrams representing the states contributing to resonance-enhanced CARS in a diatomic molecule : (a) w"d enhanced fundamental (w = 1) vibrational
transition; (b) double electronic resonance with col = Wna and W3 = 03C9n’a; (c) Wn’a enhanced vibrational transition.
col, W2’ W3 are the familiar CARS frequencies [14].
the
susceptibility
in three dimensions as a function of parameters col - W2 and 03C91 ; cvl - C02 is the usual variable versus which CARS spectra aredisplayed,
and oei is the field
frequency usually
held fixed inresonance CARS.
Figure
3 illustrates atypical
case;the modulus of the
susceptibility
contribution from Paa has been calculatedassuming
úJn’n coba andFig. 3. - Three-dimensional plot of modulus of suscepti- bility proportional to paa VS- W 1 - w2 and 03C91. The condi- tions chosen for the frequencies .are similar to those pre-
vailing for the main lines of C2 studied below; i.e.
(On’n rr (O ba - 0. 8 cm-1, y rr 0.08 cm-1, no Doppler broaden- ing.
taking
the same value y for the threedamping
cons-tants. The relief is
composed
of threestraight « ridges »
each of which corresponds to a minimum in one of the
susceptibility
denominators. Theprojections
of thecrests of these
ridges
are close tostraight
lines havingthe
following equations :
These
straight
lines are shown infigure
4.Fig. 4. - Straight lines corresponding to the nulls in the denominators of the susceptibility. The intercepts corres- pond to the double resonances.
Well below electronic resonances
(03C91« wna)’ only
the
« ridge » corresponding
to the vibrational reso- nancegiven by equation
(1b) is seen in the spectra.If col is
made large enough(03C91
>con,a/2),
W3 can reachresonance with the lowest
level
|n ~ of the excitedelectronic state for W2 = 0, so that the anti-Stokes
resonance W3 = Wn’a appears at the
high frequency
end of the CARS spectrum (i.e. at col - W2 =
wn’a/2).
As col increases, this line is downshifted,
eventually crossing
the vibrational line when col = Wn’b where itgives
rise to the so-called anti-Stokes-enhanced Raman line. The other two double resonances arefound on col = Wna at :
and
Triple
resonances, i.e. lines obtained when the threeequations
(1) aresimultaneously
fulfilled, are for-tuitous, yet extremely
interesting
for thepotential gain
in detection
sensitivity they
afford. The three peaks offigure
3 then merge into a single and stronger maxi-mum. Triple resonances are
highly improbable
inlight
molecules or molecules like OH or
hydrogen
halideswhich have considerable line
spacing. They
are morelikely
to be found, however, in heavierspecies
like12.
A molecule of intermediate characteristics like
C2 fortunately
offers a limited number ofnear-triple
resonances. The condition for a
triple
resonance toexist is
easily
seen to be :Wn’n = oeba
(2)
for the situation where excitation is done
using
twopump
frequencieswl and C02.
Note that the use of threeseparately
tunable sources would enable one to achievetriple
resonance conditions without restric- tions on any available molecular transition; thesepossibilities
as well as other aspects of resonance CARS spectroscopy aredeveloped
in[14].
Equa-tion (2) can be
expanded
as a function of the vibra-tional, rotational and
spin
quantum numbers v, J and 03A9respectively.
For thespecific
case of a fundamental vibrational transition we have Av = 1; in addition,the
one-photon
selection rules AJ = ± 1 and AQ = 0must be
respected [24].
Thesystematic
search for near-triple
resonancesusing equation
(2) thengives
thelines :
and
which are found in the spectrum at the positions :
and
respectively
for three sets of quantum numbers andterm indices i :
2.2 ANALYSIS OF UPPER ROVIBRATIONAL LEVEL |
b ~
CONTRIBUTIONS. - The
preceding
discussion has been devoted to spectral contributions from theground
vibrational level population paa. We cannot, however,
disregard
the contributions of upper rovibrationallevels b
~, since we aredealing
withdischarges
andflames wherein high
degrees
of vibrational and elec- tronic excitation will prevail. Furthermore, some of these contributions are known to beDoppler-free [29],
which is
likely
to enhance theirstrengths
relative tothe
ground
state ones. Some attention was thuspaid
to the main three terms contributed
by b
~.Several
general
remarks here have to be made withregard
to their actual existence and to theirspectral properties
when Dopplerbroadening
isnegligible.
As a matter of fact, the
reality
of those terms whichcontain resonances
pertaining
tounpopulated
mole-cular states has been the
object
of a controversy[14,
30,31].
Some terms of similar nature have beenexperi- mentally
shown to exist in other forms of four-wavemixing by Bloembergen
and coworkers using Navapour
[32-34] ;
thephysical interpretation
of the termsstudied
by
these authors has also attracted attentionrecently [35].
Fig. 5. - Diagrammatic representation of the major sus- ceptibility contributions proportional to pbb, and associated energy denominators.
The time-ordered
diagrams
for the pbb contribu- tions in CARS are shown infigure
5along
with theirresonance denominators,
giving
the fullexpression :
Under certain conditions on
damping,
it can be shown(Ref. [14], Appendix 1)
that these terms combine togive
a
single susceptibility
term of the form :Fig. 6. - Plots of modulus of susceptibility for three pbb contributions under same conditions as figure 3 and assum- ing the same value for pbb as for paa. Cases (a), (b), (c) cor- respond to figures 5a, b, c, respectively. The locuses of the minima in the energy denominators are also shown in the
projections. Those double-resonance lines which are Dop- pler-free are so marked (D.F.). The vertical scale is the same as in figure 3.
Several
damping
conditions can lead to this expres- sion :(i) if there are no collisions, with lifetime-broadened states;
(ii) if there are collisions and if the so-called damp-
ing
approximationis satisfied.
The
expression given by equation
(4) can also bederived using a
simpler
wavefunction (instead ofdensity
operator)representation
of the molecular system. The wavefunction approach is not appro-priate
at resonance since thedamping approximation
is often invalid. Well below electronic resonance,
however, the exact
expression
with the three terms ofequation
(3) and theapproximate expression
ofequation
(4)give
the same result. This is because the last two terms(Figs.
5b and 5c) almostexactly
canceland because the main term of
figure
5a tends to theexpression
ofequation
(4). At resonance, the terms offigures
5b and 5c(second
and third term of Eq.(3))
are as
important
as that offigure
5a(first
term of Eq.(3)).
In our calculations, the exactequation
(3)was
always
used.The
spectral
contours andstraight
linescorrespond- ing
to the nulls in the denominators are shown infigure
6. Theplots
arepresented
under conditions similar to those offigure
3.Figure
6a is associated withfigure
5a. Note that, in the limitof Doppler broadening,
two of the lines are
Doppler-free [29] ;
these lines aremarked on the
projection.
None of the lines infigure
6b(corresponding
to thefigure
Sb term) areDoppler-free,
but there are also two in
figure
6c. There are two lines (one inFig.
6a, one inFig.
6c) which are a factor of2 stronger than all other lines because the resonances are so
placed
that the real parts of the denominators not at resonance areonly
half aslarge.
In
figure
7, one can see the effect ofadding
the twoterms
having
the 03C9n’n resonance : the úJn’n resonance isseen to
rapidly decay
when 03C91 is tuned below cvn-bas noted earlier; this fact is consistent which the absence of upper electronic state vibrational reso-
Fig. 7. - Sum of contributions of figures 6b and 6c.
nances in conventional off resonance CARS spectra ; the two
Doppler-free
lines offigure
6c interfere cons-tructively
with the two lines having Col 1 = 03C9n’b infigure
6b, while the third lines of thesefigures,
whichare found for 03C91 = 03C9na, undergo near
complete
cancellation.
Adding
the contribution offigure
6a (term ofFig.
5a) furthercomplicates
the contours(Fig.
8).Fig. 8. - Sum of all pbb contributions.
The pbb contributions
naturally
interfere with that of paa. The correctionsthey
introduce become appre- ciable (>10%)
when the vibrational temperature exceeds 1 000 K inC2.
In addition, theDoppler
effect,if any, will reduce
predominantly
theamplitudes
ofthe lines of electronic character
(except
those in pbb which areDoppler-free).
A computer program was written in order to fit the
experimental
spectra. This program calculates the fourmajor susceptibility
contributions, one from paa and three from pbb with due account for the Dopplereffect. In the
spectral
window from 1611 to 1616 cm-1which has been studied in detail, 24 values of J are
taken into consideration, 3 of which (J = 18,19 and 20
as
explained
in section 2.1above)
havemajor
contribu-tions. For each value of J,
only
one set of states 1 a ~, |b
), n ), |n’ ~actually
is closeenough to
thesituation
of very
strong double or neartriple-resonance
and is accounted for.
No’convolution
is done with the laser linewidth function ; the width of the latter iscomparable
to or smaller than that of the CARS lines.3. Instrumental détails. - The CARS spectrometer is the one used for the work on
12 [10,
14], with someminor modifications. This is a system with flash-
pumped
lasersgiving
apulse
duration of 500 ns. Theentire
optical
set-up is mounted on a cast aluminium table of 0.5 m x 1.5 m. The elements of the two laser cavities are fixed on a ceramicglass
slab of 80 cmlength,
which is sunk into this table, and insures proper mechanical and thermalstability.
The twodye
cellsare attached to the
glass
bench and are enclosed in thesame
flashlamp
head, so thatsynchronous pulses
areemitted. Four water-cooled ablation flashlamps con- nected in parallel are used for the
pumping,
with aFig. 9. - Cross section of flashlamp head.
discharge
energy of 200-350 J,typically.
The capacitorhas a
capacitance
of 4.5 03BCF. The flashtubes are made of pure, fused silica, with 4.5 mm i.d. and 7.5 mm o.d.They
are mounted so as tocouple
thelargest possible
fraction of the output into the
dye
cells. The latter have a small bore (3.5 mm) and alarge
o.d. (8 mm) toincrease the apparent diameters of the
dye
flows(Fig.
9).Segments
of tungsten wire of 25 mmlength,
wound in coils over a 3.5 mm diameter
cylinder,
wereintroduced in these
dye
cells atregular
intervalsleaving
a useful aperture of 2.9 mm diameter.
They
reduceamplified
spontaneous emission veryeffectively.
Theactive
length
of theflashlamps
anddye
cells is 15 cm.A saturated copper sulfate water solution is circulated in the
flashlamps
forcooling;
this solution is intro- duced at the same temperature as thedye
solution.If the temperature différence exceeds 0.1 OC, the
resulting density gradients
in thedye
solutionkeep
thelasers from
emitting
in asingle
transverse mode and raise their thresholds. The temperature condition is fulfilledby maintaining
thedye
reservoirs in a tem-perature-controlled
bath. The coolants, as well as bothdye
flows afterpassing through
their pumps andMillipore
filters, arepassed
through heatexchangers
also
placed
in the bath. The copper sulfate serves two functions :by cutting
shortwavelength
UVbeyond
300 nm, it
improves
thedye
service life ;by cutting
thered and IR
beyond
700 nm, it also reduces thermal shocks in thedye
flows andimproves
beamquality
and
reproducibility.
The lasers are fired at a rate of 6 shots per minute.
Triggering initially
wasperformed
with anignitron.
A
grounded-grid hydrogen thyratron
was later intro- duced,giving
aslightly
shorterdischarge pulse
of1.5 J.1s.
Finally,
aprepulse
circuit was added, whichresulted in a 10
%
reduction in energy necessary forlasing.
The flashtubes are filled with 20 mbar of argon ; the gas is flown and evacuated from both endsusing
aprimary
pump. Argonslightly improves lasing.
If the pressure is
brought
below 2 mbar, flashtubefailures
quickly
occur, because thedischarge
energy does notsplit evenly
between them. The flashtube life is about 104 shots ; it is limitedby
a slow wall erosion whicheventually
leads to mechanical failure. The tungsten electrodes are mounted 4 mm away from thelamp
axes and 3 mm away from the tube ends. Thisprecaution taken in
conjunction
with argon gasflowing considerably
reducespollution by sputtering.
Two different
techniques
are used fortuning (Fig.10).
The « laser » at col is limited in bandwidth and tuned
by
means of an interference filter and solid 0.1 mm and 1 mm thick silica etalons of 83 %reflectivity,
whereasthe « Stokes » beam at (02 is tuned
by
a set of fourprism expanders
and onegrating
of 1 200g/mm
in Littrowmount blazed at 1 J.1m and tilted to second order. The
grating
rotation is entrainedusing
a carbon fibercomposite arm of 310 mm
length
and a differentialscrew. The
tuning
precision is 0.04 cm- l.Fig. 10. - Schematic diagram of resonance CARS spectro- meter ; DF : dichroic filter; DM : dichroic mirror; F : coloured filter (Schott GG 495) ; FP Fabry-Perot étalon ;
IF : interference filter ; G : grating ; M : monochromator and detector assembly; PE : prism beam expander; RC refe-
rence cell ; S : sample cell (flame or discharge).
Both oscillators
produce
beams 2 mm in diameter,with
divergence
less than 1.5 times the diffraction limit andpeak
power of 1-10 kW between 480 and 650 nm. The linewidth istypically
0.02 cm-’ at col and 0.07 cm-1 1 at úJ2. Both beams arehorizontally polarized.
Powers up to 100 kW can begenerated
withthese lasers at some cost in
spectral purity
and diver-gence. The
pulse
duration is about 0.5 03BCs. In order to obtain theseperformances,
it is necessary to use mix- tures of ethanol and waterby equal
volumes as thedye
solvent. COT is added as a
triplet quencher
and 1mole
%
Triton X100 to prevent dimer formation.Several
dyes
were tried in order to cover therequired spectral
ranges with goodefficiency. Satisfactory
results were obtained
by mixing
differentdyes,
one ofwhich acted as a fluorescent wavelength shifter which increased the energy available to pump the
lasing dye.
Output
energies
in the range of 1 to 5 mJ are emitted at col 1 = 19 494 cm-1 with a mixture of Coumarin 504 and Coumarin 450; Rhodamine 110 with LD 490 or Coumarin 480 gavecomparable energies
atúJ2 in
thevicinity
of 17 880 cm-1. Note that similar transfers have beenreported
forlaser-pumped dyes by
Coxand Matise