COHERENT TECHNIQUES FOR MEASUREMENTS
WITH INTERMEDIATE CONCENTRATIONS
Thomas Dreier and Paul Ewart
1 Introduction
Coherent optical techniques contrast with those based on incoherent processes
such as laser induced fluorescence or spontaneous Raman scattering by emitting a
signal in a laser-like beam of radiation. For combustion diagnostics this presents
obvious advantages for efficient collection of the signal and discrimination against
background noise from scattered light or luminescence from the target gas. However
coherent emission requires that the emitting species be excited in a phased array or
that some process ensures phase coherence in the signal direction. This is usually
achieved in practice by a non-linear optical process that couples energy from incident
laser fields to the signal via the medium response. In gas phase media symmetry
considerations dictate that the third order susceptibility χ(3) is the lowest order that can
be employed. Thus the induced non-linear polarization will be described by a term of
the form
r
r
r
r
( 3)
P i( 3) (ω 4 , r ) = χ ijkl
(ω1 , ω 2 , ω 3 , ω 4 )E j (ω1 , r )E k (ω 2 , r )E l (ω 3 , r )
(1)
r
where E m (ω n , r ) are complex field amplitudes. This polarization radiates the signal
wave E(ω4) in the general process known as four-wave mixing. (For a detailed
treatment of the background physics of non-linear optics see the excellent text by
Boyd.1)
In this chapter we describe four different processes which belong to this
general class of non-linearity: (i) degenerate four-wave mixing DFWM, (ii) laser
induced thermal grating spectroscopy LITGS, (iii) coherent anti-Stokes Raman
scattering CARS and (iv) polarization spectroscopy PS. Figure 1 shows the basic
interactions involved in these processes.
The first three of these share a common physical interpretation in terms of
scattering from a grating induced by the non-linear response of the medium to the
interference pattern established by the overlap of the three incident fields E(ω1),
E(ω2) and E(ω3). DFWM (ω1 = ω2 = ω3) involves a stationary or standing wave
interference pattern created by the interference of a probe field, E(ω3), with either of
the two pump fields E(ω1) or E(ω2). The signal wave, E(ω4), is the result of scattering
of the other pump from the induced grating. The process of LITGS results from the
conversion of the induced stationary grating from a modulation of the molecular
population to a bulk gas modulation by processes of collision-induced relaxation. In
the case of CARS the Stokes wave at frequency ω2 creates a non-stationary
interference pattern with a pump wave at ω1 (= ω3). Scattering of the other pump off
this moving grating gives a Doppler shifted frequency corresponding to the antiStokes wave (ω4).
PS may be viewed as a four-wave mixing process in which two input fields
drive the populations of degenerate magnetic sub-states in the ground molecular level
into a non-equilibrium distribution. This population imbalance modifies the refractive
1
index for opposing states of circular polarization. The third, or probe, wave is linearly
polarized i.e. a superposition of right and left circular polarized components. As a
result of the different refractive indices for each component in the pumped medium a
polarization component is established which is orthogonal to the input state. This
orthogonal polarization provides the phased array to generate the forward scattered
signal beam.
Population
Grating
Population
Grating
ω1 ω2 ω3 ω4
Population
Grating
ω3 ω4
ω1
ω1 ω2
ω2 ω3
ω4
Collisional Quenching
Population
Grating - stationary
(a) DFWM
ω1
m-1
Thermal
Grating - stationary
(b) LITGS
Population
Grating - moving
(c) CARS
ω2
m
ω3 ω4
m+1
Degenerate sub-state
population transfer.
(d) PS
Fig.1 Coherent non-linear processes using resonant interactions; (a) degenerate four-wave
mixing DFWM, (b) laser induced thermal grating spectroscopy LITGS, (c) resonance
enhanced coherent anti-Stokes Raman scattering RE-CARS, (d) polarization spectroscopy PS.
Each of these processes will be significant only when χ(3) is resonantly enhanced by
appropriate choice of the input frequencies. It is this resonant enhancement that
provides the spectroscopic selectivity allowing their application in combustion
diagnostics. The parametric nature of the interactions demands that the input and
generated frequencies be governed by energy conservation. Each of the grating based
techniques requires the further condition of momentum matching or phase matching.
This matching is equivalent
to ensuring that the vector sum of the incident and
r
generated wave vectors k i is zero i.e.
r r r r r
r 2π
with k i =
∆k = k1 − k 2 + k 3 − k 4 = 0,
(2)
λi
In the case of PS conservation of angular momentum results in the change of
magnetic substate following absorption or stimulated emission of a photon carrying
one unit of angular momentum. Angular momentum is also conserved in the probe
and generated signal since the emergent othogonally polarized signal arises only from
a phase shift between the oppositely circularly polarized components of the incident
probe beam. The basic physics of each of these techniques is summarized in the
excellent review by Eckbreth.2
In the following sections we outline only briefly the underlying physics
involved and refer the reader to more particular expositions for information on
theoretical aspects and experimental details. Our concern here is to highlight the
peculiar features of each technique that offer promise for combustion diagnostics. We
indicate the possibilities by reference to only selected examples of applications since
space limitations preclude a comprehensive review. The focus is on progress made
toward quantitative measurements and issues relating to practical implementation. We
2
hope that this information will assist in choosing the most appropriate technique for
measurements with intermediate concentrations. In this context such concentrations
mean typically minor species that exist in the range of 10-4% to 1% (1ppm to
104ppm).
3.2 Degenerate four-wave mixing, DFWM.
The basic physics of DFWM has been presented in the context of optics and
spectroscopy3,4 and its application to combustion diagnostics has been reviewed by
several authors. ,5,6 The non-linearity responsible for coupling the pump and probe
beams may be due to several different physical mechanisms. In dilute absorbing gases
the primary mechanism is saturable absorption. Abrams and Lind7 developed a model
of this process, the A&L model, which has been widely used for analysis of DFWM
in absorbing media. This model is summarized by Eckbreth and only the main
features are outlined here. Much of the theoretical effort in the past decade has aimed
to understand more fully the physics of DFWM so that the signals may be interpreted
quantitatively in terms of important combustion parameters.
The A&L model considers two strong, equal intensity, pump beams and a
weak (non-saturating) probe beam interacting with stationary, two-level atoms. All
three beams are linearly polarized in the same plane, are monochromatic and suffer
negligible absorption and, in addtion, the pumps are assumed to be counterpropagating. The system is assumed to be in a steady state. In practical diagnostics we
have to deal with (i) saturation, including that by the probe beam, (ii) moving atoms
(iii) multiple and degenerate levels, (iv) forward pump phase-matching, (v) crossed
polarization of the input fields, (vi) non-monochromatic lasers, (vii) absorbing media
and (viii) laser pulses of short duration. Thus almost every aspect of the A&L model
requires considerable revision if measurements using DFWM are to be made
quantitative. In what follows we first summarize the main results of the A&L model,
highlighting the features of DFWM that make it attractive for combustion diagnostics.
We then deal with each of the features that must be addressed in practice for
quantitative measurements.
The A&L model is based on a perturbation theory expansion of the medium
susceptibility in terms of a strong field composed of the two pump beams of intensity
Ipump and a weak probe field Iprobe. The intensity of the signal beam, when integrated
int
and is given by analytic expressions in the two
over the atomic resonance line, is I sig
limiting regimes of weak and strong saturation by the pump:
µ12 N 2 k 2T12T23
8
I
int
sig
∝
[1 + 4 I
pump
I s (0)
]
52
2
I pump
I probe ,
(3)
when I pump << I s (0) and
int
−1 2
I sig
∝ µ 12 N 2 k 2T1−1 2T21 2 .I pump
I probe
3
(4)
when Ipump >> Is(0).
In these relations IS(0) = h2/(T1T2|µ12 |2) is the line-centre saturation
int
on the
intensity. Τhe medium influences the signal by virtue of the dependence of I sig
3
atomic number density N, the atomic dipole moment µ12 and the longitudinal and
transverse relaxation times T1 and T2 respectively. The signal can be characterised by
a reflectivity R = Isig/Iprobe.
The strong resonant enhancement of the reflectivity of DFWM in absorbing
gases is the basis of its sensitivity for detecting low concentrations of atomic or
molecular species. ,8,9 The dependence of the signal on N2, (the square of the
population of the initial level involved in the resonant enhancement) allows relative
and, in principle, absolute concentrations to be determined. For a gas in thermal
equilibrium, N is determined by a Boltzmann distribution and so the relative spectral
intensity of a DFWM spectrum indicates the temperature.10
Owing to the dependence of IS(0) on the collision induced relaxation rates, T1
int
to pressure can be dramatically reduced by operating
and T2, the sensitivity of I sig
with saturating pump laser intensities.11,12 The benefits of saturated DFWM are
discussed in detail by Lucht and co-workers13 and summarized by Eckbreth.
The A&L model has been modified to account for the effects of atomic motion
within the perturbation theory approximations, i.e. non-saturating beams.14 The effect
leads, firstly, to a wash-out of the induced gratings and effectively limits the crossing
angle α that can be used, since this angle determines the grating spacing (see figure
1). Secondly, there is an associated Doppler broadening of the atomic response. This
broadening effect depends on the size of the Doppler width, ∆ωD, relative to the
homogeneous width, ∆ωC, (determined by collisional or power broadening). Atomic
motion also affects the saturation behaviour of DFWM. The effect of the atomic
motion on the DFWM lineshape and intensity depends strongly on the phasematching geometry employed. The problem generally requires a numerical treatment
although in some cases approximate analytical solutions can be found.
Attal-Tretout and co-workers15,16 have given a non-perturbative treatment of
pump saturation in the forward phase-matched geometry. They included the effects of
atomic motion, level degeneracy, satellite lines and crossed laser polarizations
showing that for complex spectra saturation leads to significant changes in the
spectral lineshape and intensity.
Lucht and co-workers ,17,18,19,20 have developed a very powerful approach
based on direct numerical integration, DNI, of the density matrix equations for the
four-wave mixing polarization. This method lifts almost all of the major restrictions
of the A&L model and has been used to quantify the effects of collisions , , atomic
motion closely spaced resonances, level degeneracy, crossed polarization of laser
fields, and forward phase-matching geometry. The results of these calculations have
been well validated by comparison with experimental data from DFWM studies of
OH, NO and CH and have significantly enhanced our detailed understanding of the
basic physics of DFWM. They are, however, computationally expensive and time
consuming and so are not well suited for rapid or routine analysis of experimental
data. Accordingly, Reichardt and Lucht introduced an empirical relation for the
DFWM line-centre reflectivity R, which is a modified form of the Abrams and Lind
result:
R=
R hom
1 + (b∆ω D / ∆ω C ) 2
(5)
4
where Rhom is the reflectivity calculated from the A&L model. The empirical
parameter b is a function of the pump and probe intensity and characterises the
saturation level. This result was validated by comparison with the full DNI
calculation and with experimental data. It was possible to find transitions that yield
signals that, for constant laser power, are proportional to N2 over a wide range of
temperature. The validity of this result is qualified by the limitations of the A&L
model used to determine Rhom, in particular the restriction to a non-degenerate, twolevel atom and a non-saturating probe.
Crossed laser polarizations are often used to improve noise rejection. The
effect on the signal is described by a J-dependent geometrical factor G(J); a function
of the relative polarization and the ∆J of the transition, which modifies the basic A&L
result for both weak and strong pump fields.21
In practice it is also expedient to use saturating probe fields since the
maximum grating visibility, and hence scattering efficiency, will be produced by
equal intensity pump and probe fields. Saturation by the probe can be treated by
numerical techniques ,22,23 but again the method is not convenient for routine
diagnostic analysis. A non-perturbative analytical solution has been presented by
Bratfalean et al.24 that allows saturated lineshapes and a significant portion of a
molecular spectrum to be calculated on a PC within a few seconds. The validity of the
analytical result was checked by comparison with a full numerical calculation and by
comparison to DFWM spectra of C2 recorded in an oxy-acetylene torch flame.
The A&L assumption of monochromatic fields is also frequently invalid since
the fields from most pulsed lasers have a finite bandwidth and are composed of a
number of longitudinal modes. In general this presents an intractable problem and
only approximate solutions have been presented using mostly numerical methods.25,26
An approximate solution to the bandwidth problem is provided by the analytical result
derived by Bratfalean et al. Using an independent spectral response (ISR) model, in
which the field is considered to be made up of independent monochromatic
components, the DFWM line-shape can be found by integrating the molecular
response across the laser line-width for each value of the laser detuning. This
approach, however, is not valid for saturating intensities.
These treatments of the laser bandwidth are relevant to line-shapes of DFWM
spectra generated by frequency scanning the laser across the atomic or molecular
resonance. Finding the lineshape of multiplex or broadband DFWM spectra27 presents
a different problem. In multiplex techniques a broadband laser field of width ∆ωL is
applied that spans the molecular resonance. The signal intensity and line-shape are
measured by spectrally resolving the signal with a high-resolution spectrometer.
Smith and Ewart28 treated the problem by finding the time-dependent solution
to the density matrix equations in the limit of large laser bandwidth, ∆ωL >> ∆ωD,
∆ωC. An analytical result was found in the extreme cases of dominant Doppler or
collision broadening. In general, however, a numerical solution was necessary
although the approximate analytical result was found to give a reasonable fit to
experimental data in an intermediate regime.
There is, as yet, no comprehensive theory of DFWM that can deal with
arbitrary bandwidth and intensity. As with the DNI method of Lucht et al., a
numerical approach is impractical for simulating multiplex DFWM spectra of
complex molecules. An alternative approach to calculating multiplex DFWM spectra
is to use the ISR model with the analytical expression for the signal intensity derived
by Bratfalean et al.. An important aspect of broadband excitation arises from the
5
possibility of non-degenerate FWM. The ISR approach can include such effects but
cannot simultaneously deal with saturation. In practice it is found preferable to
neglect treatment of non-degenerate contributions in favour of a more accurate
modelling of the saturation behaviour.
The effects of absorption on the relative intensities of DFWM spectra distort
measurements of temperature and concentration.29,30 In general their treatment
requires numerical calculation appropriate to the particular situation. Absorption will
reduce the intensity of the incoming pump and probe leading to reduced signal
generation. This signal reduction may be compensated by use of saturating laser
power. , Absorption of the signal beam may, however, remain a problem in some
situations.
Finally, we note that the restriction of the A&L model to steady state
interactions is overcome by the DNI method of Lucht et al. This approach may allow
quantitative analysis of DFWM with picosecond pulses31 and allow some of the
problems associated with collisions to be avoided. However, as Reichardt and Lucht32
point out, collisions still play a role in the DFWM signal generation even when the
laser pulse duration τL is less than τC the collision time (τC = ∆ωC-1).
3.2.1 Applications of DFWM to temperature and concentration measurement
Dreier and Rakestraw first showed that the temperature may be derived, using
a Boltzmann plot, from a DFWM spectrum by using the relative line intensity, with a
suitable power law, as a monitor of the initial state population. The power law
describing the signal dependence on the dipole moment33 may be determined
empirically or by comparing line intensities arising from the same initial state.34 The
question may, however, be avoided by using saturating intensities.
An alternative to the usual Boltzmann plot method is to fit the experimental
spectrum to a simulated spectrum using the temperature as the fitting variable. This
method is often used in thermometry based on multiplex DFWM spectra. Farrow and
Rakestraw, using the A&L model for the simulation of DFWM spectra of NO, have
found this method advantageous also for scanned spectra since it can treat a wider
range of saturation.35
Temperatures can be derived from scanned DFWM spectra only for stable
flames. Time resolved thermometry requires multiplex, or broadband, DFWM spectra
recorded in a single laser pulse. To date this technique has been applied only to OH ,36
and C2.37 Saturation is more readily achieved by using a laser bandwidth sufficient to
excite only two closely-spaced and temperature-sensitive lines. Mode fluctuations in
conventional lasers are, however, a severe limitation. Modeless lasers avoid this
problem and allow a large number of molecular levels to be probed.
In principle the accuracy and precision of broadband DFWM should be
improved by using broader spectral coverage to include more transitions in the
analysis. This would have the effect of minimizing the effects of laser spectral noise
in the same manner as broadband CARS. However, “optical dephasing” effects,
arising when transitions are excited that share common upper or lower levels, lead to
systematic errors when saturating intensities are used.38
The relative intensity of spectral lines generated by both scanning (narrowband) and multiplex (broadband) DFWM can be affected by absorption even for
minor species in flames. The degree of absorption varies with the lower state
population and so transitions from lower-J levels will appear weaker relative to
higher-J transitions. This gives the spectrum the appearance of corresponding to a
6
higher temperature and was identified as the principal cause of erroneous
temperatures derived from multiplex DFWM thermometry using OH in flames. In
order to account for the absorption it is necessary to know the temperature since the
lower state populations vary with temperature. This presents a problem if the spectral
intensities are themselves being used to determine the temperature. Smith and Astill
circumvented this problem by optimizing a linear regression fit to the data by varying
the exponent x in the dipole moment law. In practice absorption effects may be
ignored only when the integrated absorption is less than about 5%.
When absorption causes a dip in the incident intensity at line-centre, nondegenerate four-wave mixing, from spectral components in the wing of the transition
line-profile, will continue to generate signal at line-centre. These non-degenerate
contributions reduce the sensitivity of broadband four-wave mixing to absorption.39
The contribution of non-degenerate terms has been calculated only for non-saturating
intensities using the ISR model and the analytical result of Bratfalean et al., but the
results did show qualitative agreement with the experimental data. As yet there is no
comprehensive theory that includes all these effects of absorption, laser bandwidth,
non-degenerate FWM and saturation. In principle they could be included in the DNI
method of Lucht et al.
The general conclusion to be drawn from these findings is that DFWM is a
viable technique for thermometry using minor species and may be appropriate in
circumstances where more established methods such as CARS can not easily be used.
Accurate temperatures of stable flames can be derived from scanned spectra recorded
using saturating intensity. Saturation reduces the sensitivity of the signals to laser
intensity fluctuations, variations in collision rates and to absorption effects. Time
resolved temperatures in unstable flames can be derived from single-shot broadband
DFWM where again saturating intensity minimizes absorption effects.
Turning to the issue of concentration we will focus particularly on recent
attempts to obtain absolute measurements and extensions to 2-D mapping and
simultaneous measurements of both temperature and concentration.
Early studies of DFWM for combustion diagnostics included the detection of a
variety of important species. DFWM signals can be generated using pulsed lasers
from a point, a line or a 2-D surface giving temporal and spatial resolution. The
particular advantage of DFWM for concentration measurements lies in the possibility
of generating signals that are independent of spatially varying parameters such as
temperature, collision rate and gas composition. However, for quantitative
measurements the signals must be interpreted with due attention to all the effects
discussed previously that modify the A&L predictions of the DFWM intensity.
Attal-Tretout and co-workers have used DFWM to measure OH concentration
profiles in an oxy-acetylene flame for comparison with model predictions. They
found good agreement between experiment and theory for laser intensities I ~ Isat and
note that there is little to be gained by using intensities much greater than Isat.
The value of saturated DFWM for quantitative concentration measurements
has been studied in detail by Lucht and co-workers. ,40 Combustion environments can
present large variations in temperature and gas composition with concomitant
variations in the ratio of ∆ωD to ∆ωC leading to changes in the spectral lineshape and
saturation behaviour. Lucht et al. note that it is often possible to find a transition that
is relatively insensitive to temperature over the range of interest. They conclude,
however, that use of saturating intensities avoids the need to compensate for
variations in ∆ωD/∆ωC, minimizes the collisional effects and gives signals that are less
7
sensitive to laser intensity fluctuations and to absorption. Using saturated DFWM
they were able to measure the variation of OH concentration in a well-characterised
flame for a range of fuel equivalence ratios from 0.5 to 1.5.(see Fig. 2) The OH
concentration was found to vary by a factor of ~20 in agreement with model
predictions. By normalizing the experimental data to calculated values at one
equivalence ratio the concentrations were put on an absolute scale.
Figure 2. Experimental measurement of absolute OH concentration in a flame
using saturated DFWM (from reference [40], Courtesy of the Optical Society of
America).
Dynamical measurements have also been made using DFWM and CARS to
study flame-vortex interactions.41 In these experiments single-shot CARS was used to
determine the temperature and DFWM was used to monitor the concentration of NO.
The data acquired in point-wise measurements was used to construct a twodimensional map of the temperature and concentration distributions.
Single-shot two-dimensional mapping of concentration42,43 and temperature44
is possible using DFWM and has usually been achieved using the phase-conjugate
geometry with sheet-like pump beams interacting with a divergent probe. The lens
used to spread the probe over the mapped area then images the interaction region onto
a camera. Ewart et al.45 have shown that the coherent light forming the image does not
have the aberration correction usually associated with phase conjugation in DFWM.
Since there is then no advantage in the phase conjugating geometry the forward
geometry can be used. Owing to the small crossing angles required to produce
sufficient signal, the images are severely foreshortened and correction involves loss of
spatial resolution in the corresponding direction.
In practice imaging with DFWM presents several problems. A major concern
is the non-uniformity of the laser beams used. Spatial inhomogeneity is exacerbated
by the non-linearity of the process and this puts a premium on laser beam quality.
Some degree of correction for beam non-uniformity can be made by referencing the
target image to an image produced using the same beams in a totally uniform
medium.
8
The simultaneous mapping of both temperature and concentration in 1dimension has recently been achieved by Lloyd and Ewart46 using broadband DFWM
of C2 in an oxy-acetylene flame, as shown in figure 3. The signal from a line defined
by the intersection of sheet-like pump and probe beams from a broadband modeless
laser was imaged on to the slit of a spectrograph. The spectrum recorded at each point
on the slit yielded the temperature at the corresponding point on the line in the flame.
The intensity variation along the slit then yielded the relative lower state population
for each transition from which the total concentration could be derived using the
measured temperature and the partition function.
1.2
A
3800
B
1.0
Temperature / K
3600
-2
0
0.8
2
3400
0.6
3200
0.4
3000
0.2
Relative C2 concentration
C
0.0
2800
-2
-1
0
1
2
Distance / mm
Figure 3 Simultaneous measurement of relative concentration of C2 (solid line) and
temperature (open circles) in an oxyacetylene flame using broadband DFWM. The inset
shows concentrations recorded at increasing heights in the flame from A to C.
A potential advantage of DFWM is its ability to detect non-fluorescing
species; an advantage that has not yet been fully exploited. This potential is of
particular importance in utilizing infrared transitions of small molecules. To date only
stable species have been detected in cell based experiments in the infrared.47,48 A
major hindrance to DFWM in this spectral region is the present lack of narrow
linewidth lasers with adequate peak power to induce the non-linear optical process
involved.
Whereas molecules display strong absorption features in the infrared, atomic
radicals usually require excitation by vacuum ultra-violet radiation. The problem of
detecting atomic species may be addressed by using two-photon resonances to
enhance the DFWM process.49
3.2.2 Practical considerations and future applications
Our improved understanding of the detailed physics of DFWM has advanced
the technique from demonstrations of principle to applications in fundamental
combustion studies. Quantitative measurements of temperature, relative and absolute
concentration are now possible in specific situations and measurements have been
demonstrated in pointwise, 1-dimensional and 2-dimensional formats with both space
and time resolution. Scanned and multiplex DFWM provide average and timeresolved thermometry respectively, in situations where CARS may not be possible.
9
Such situations include flames, plasmas or materials processing environments where
N2 or other suitable Raman-active molecules are absent. DFWM offers advantages
over LIF for minor species concentration measurement since it can be made relatively
insensitive to collisions. Saturated DFWM has a reduced sensitivity to the ratio of
Doppler to collisional widths ∆ωD/∆ωC, and the ratio of quenching to dephasing
collision rates which may be unknown or difficult to determine in practical
applications. Thus concentrations may be measured in situations where the
temperature and gas composition vary significantly.
Applying DFWM to devices such as internal combustion engines presents
practical problems in attaining adequate signal-to-noise, S/N, ratio. Scattering from
windows, interference from non-resonant signals and thermal gratings occurring at
elevated pressures, common in such devices, make it more difficult to achieve a good
S/N ratio. Some progress is being made and detection by DFWM of combustion
generated NO in a firing spark ignition engine has recently been achieved.50 (see Fig.
4)
16
skip fire: 1 in 9
speed: 1200rpm
ignition: 40 deg bTDC
laser timing: BDC power stroke
14
DFWM Intensity (au)
12
10
8
6
4
2
0
226.10
226.12
226.14
226.16
226.18
226.20
226.22
226.24
226.26
226.28
Wavelength (nm)
Figure 4 DFWM spectra of NO in a firing, methane-fuelled, s.i. engine. From
reference [50] Courtesy of Springer-Verlag.
The keys to successful future applications in such hostile environments have
all been demonstrated in laboratory flames. Background noise from surface scattering
and thermal grating interference can be reduced or eliminated by using crossed
polarization between one pump beam and the probe. The calculations of Reichardt
and Lucht19 suggest that the signal penalty associated with the use of crossed
polarizations is reduced or eliminated under saturation conditions. Beam steering by
refractive index gradients is minimized by using the forward folded BOXCARS
geometry. Optimum S/N ratio is obtained by operating with I > Isat which also
reduces the signal sensitivity to collision effects. The requirements on the laser for
optimum efficiency include narrow linewidth (preferably single longitudinal mode)
and high frequency stability. Of great importance practically is good beam quality. A
uniform or Gaussian beam profile (TEM00) will optimize the wave mixing and spatial
filtering of unwanted light scatter. For multiplex DFWM the modeless laser is the
10
device of choice: it provides for excitation of a sufficient number of rotational
transitions to maximize accuracy and by mimizing mode noise it improves the
precision of measurements. Owing to the difficulty of frequency doubling broadband
light by critical phase-matching the bandwidth attainable in the UV is limited
typically to 0.1-0.2 nm. New developments in solid state laser materials e.g.
Ce:LiCAF offer the prospect of broadband laser emission directly in the UV and in
particular at the region of the strong (0,0) bands of OH. Applications in the infra-red
are also still dependent on development of suitable high-power narrow-linewidth
radiation sources.
3.3 Laser induced thermal grating spectroscopy, LITGS
Laser induced gratings have been widely exploited in studies of condensed
matter. These gratings arise from the spatial modulation of refractive index induced
by interfering pump and probe beams. In gas phase media the corresponding effect
arises from absorption of resonant radiation followed by collision induced quenching
leading to a stationary spatial modulation of temperature. The resultant density
fluctuation initiates two counter-propagating acoustic waves that traverse the
stationary temperature grating leading to periodic variation in the overall scattering
efficiency. The subsequent temporal evolution of the induced grating has been
modelled by Paul et al.51 and by Cummings52 using a one-dimensional model in
which a system of linearized hydrodynamic equations are used to describe the
normalized perturbations in density, velocity and pressure. Following excitation by a
short (nanosecond duration) laser pulse, the evolution of the grating may be
monitored by Bragg scattering of a c.w. probe beam. When the gas composition, and
hence the gas dynamic properties, is known the time behaviour of the scattered signal
may be used to derive the temperature and pressure.
Since the thermal gratings are created by resonant absorption, spectra may be
generated by scanning the wavelength of the excitation beams. Owing to uncertainties
in the collisional quenching rates, their variation with state and local gas composition
as well as saturation effects, it remains difficult to interpret the intensity of the signals
quantitatively in terms of species concentration.
3.3.1 Applications of LITGS to temperature and concentration measurements.
The potential of LITGS, or laser induced thermal acoustics LITA, for gasphase diagnostics was recognised by several workers.53,54 In contrast to DFWM the
signals from thermal gratings increase with increasing pressure which gives the
LITGS technique a potential advantage in high pressure situations. The capability of
LITGS to make such measurements has been demonstrated by Latzel et al.55 Using a
pulsed frequency doubled dye laser a thermal grating was excited in OH produced in
a high-pressure methane/air flame and probed by a c.w. Argon-ion laser. From the
temporal oscillations and the decay rate of the signal amplitude respectively the flame
temperature and pressure were derived from single pulse measurements over a range
of 10 to 40 atmospheres. (see Fig. 5)
Signals from LITGS may be parasitic on DFWM signals and will dominate at
high pressures. The relative contributions of LITGS and DFWM has been
investigated by Paul et al. In atmospheric pressure flames the thermal contribution is
usually small since the build-up time of the thermal grating may exceed the duration
of the nanosecond laser pulses usually involved in DFWM. The LITGS signal may be
eliminated by using crossed polarization of the pump and probe beams to leave the
11
DFWM signal free from interference. As noted above, the consequent decrease in
DFWM signal caused by the orthogonal polarization excitation may be counteracted
by use of saturating intensities.
Since LITGS offers essentially a spatially (and temporally) resolved
absorption measurement it may, in principle, be used for concentration measurements.
However quantitative interpretation of spectra generated using LITGS is currently
hampered by the lack of a general theoretical treatment that includes saturation effects
and the
variability of relaxation rates with local gas composition. However, future
applications may be developed for thermometry in high pressure situations and the
technique offers an optical method for measurement of pressure that does not rely on
spectral resolution of the lineshape.
1.0
LITGS of OH:
High pressure methane/air flame
0.8
Experiment
Simulation
Intensity
0.6
Fit temperature = 2014 K
Fit pressure
= 40.1 Bar
0.4
0.2
0.0
-25
0
25
50
75
100
125
150
Time / ns
Figure 5. LITGS signal from OH in high pressure flame showing experimental data (open
circles) and theoretical fit (solid line) using the model of Paul et al.[51] (from ref. [55])
Courtesy of Springer-Verlag.
3.4 Coherent anti-Stokes Raman scattering, CARS.
Since the pioneering work of Taran56,57 and Eckbreth58 CARS has evolved
from a non-linear optical "curiosity" into a practical spectroscopic tool for in-situ
combustion diagnostics. Although the technique requires a considerable theoretical
understanding, practical skill, and rather expensive equipment, precise pointwise,
single-pulse temperature and major species concentration measurements can be
routinely made in very harsh environments. Excellent review papers and textbooks
are available that deal with CARS theory and describe the numerous technical
approaches in practical measurement systems. ,59 As shown in Fig. 1 conventional
CARS is realized by crossing one “pump” beam (usually of a fixed frequency ω1),
with a tunable “Stokes” beam of frequency ω2, in the interaction volume. A second
pump beam at ω3 (= ω1), crossing the interaction region, engages in a four-wave
mixing interaction with the non-linear polarization of the medium to create a coherent
signal beam that is radiated at the anti-Stokes frequency 2ω1 – ω2. When the
frequency difference ω1 – ω2 equals a vibration-rotation (vibrational CARS) or a pure
rotational (rotational CARS) transition in the molecule the wave mixing is resonantly
enhanced. A CARS spectrum is generated by frequency scanning the Stokes beam
12
across these Raman-active transitions in the molecule. Alternatively, an entire CARS
spectrum can be generated within a single laser pulse when a broad-bandwidth Stokes
beam is employed and the generated signal is dispersed in a spectrometer and
detected with a CCD camera.
Conventional CARS employs an intense pump laser at a frequency ω1 that is
not in resonance with any transition in the molecule. The interaction thus proceeds via
a two-photon resonance to a real vibration-rotation or pure rotation level. The initial
one-photon pump interaction excites a virtual level (shown as a dashed line in Fig 1).
By tuning the interacting beams near to, or exactly on, a one-photon electronic
resonance in the molecular species (the dashed lines in Fig. 1(c) become real states)
the four-wave mixing interaction is enhanced significantly. This resonantly enhanced
CARS or RE-CARS allows the detection of minority species with ppm sensitivity,
similar to DFWM, albeit at the cost of increased theoretical and experimental
complexity.60,61
Theoretical treatments of CARS are presented in the literature cited above.
Here, only final expressions are given to highlight the important parameters that
determine the CARS signal intensity. Spectroscopically, the process can be
considered as a coherent variant of spontaneous Raman scattering and thus a CARS
signal can be generated for all molecular species that exhibit a varying polarizability
component during rotational and/or vibrational motion. Treating the electric fields
classically, the CARS intensity resulting from the induced polarization given in
equation (3.1), assuming single frequency laser sources, can be written as
I 4 = I CARS =
ω 42
n12 n2 n4 c 4 ε 02
I I χ CARS
2
1 2
⎛ sin(∆kl / 2) ⎞
l ⎜
⎟
⎝ ∆kl / 2 ⎠
2 2
2
(6)
where I1 and I2 are the intensity of the pump and Stokes beams respectively, l is the
interaction length, and ni are the refractive indices at frequency ωi. The maximum
signal is generated when the phase mismatch factor ∆k = 0 . The third-order
susceptibility, χ(3) = χCARS, in general consists of a non-resonant part χ nr(3) , which is
independent of the frequency of the exciting beams, and a Raman-resonant
contribution χ r(3) :
χ (3) = χ nr(3) + χ r(3)
(7)
From equation (6) the non-linear character of the signal is obvious as it
depends on higher powers of the intensities of pump- and Stokes lasers and the
squared modulus of the total third order susceptibility. Quantum mechanical
derivation of χ for molecular Raman transitions reveals the CARS intensity as
proportional to the square of the population difference between the lower and upper
Raman level involved , as well as the presence of the nonresonant background. The
spatial resolution of the technique is determined by the size of the interaction volume
which depends on the crossing angle and transverse mode structure of the laser beams
used. In order to accurately reproduce experimental data, the multi-longitudinal mode
nature of commonly employed laser sources as well as possible coherences in the
interacting beams need to be considered. Taken together with accurate values of
molecular parameters (energy levels, line broadening data, etc.) accurate modeling of
13
CARS spectral signatures of many major species of spectroscopic interest in
combustion diagnostics, such as N2, O2, H2O and others, may be obtained.
3.4.1 Applications of CARS to concentration measurements
Concentration measurements with CARS are feasible as long as some
characteristic parameter in the spectrum of the resonant species can be distinguished
above the noise level. The parameter that is chosen, such as peak amplitude,
integrated intensity or spectral shape must display a reasonable variability with
concentration, and signal intensities must exceed noise fluctuations such as those due
to detector shot noise, laser mode noise and simultaneously generated background
signals. At low concentrations the spectrally unstructured non-resonant background
signal from the bulk sample constitutes a fundamental limit to detection sensitivity. In
this case, spectral and intensity noise in the signal arising from pulse-to-pulse laser
energy fluctuations, mode beating and spatial beam pointing stability, coupled with
the high dependence of the CARS signal intensity on these parameters (see Eq. 3.6),
makes concentration measurements prone to systematic errors. Using broadband
CARS the spatially resolved detection of CO concentrations in flames using the
analysis of spectral line-shape has been demonstrated by Eckbreth et al.62 and Hahn et
al.63 down to concentration levels of 0.5-1.0%. This sensitivity is similar to that which
can be achieved when the non-resonant background is suppressed by exploiting the
polarization properties of the CARS signal field64. Referencing techniques, either inor ex-situ, by recording the simultaneously generated signal from the non-resonant
background or a resonant species in a sample cell can help in mitigating the effects of
signal intensity fluctuations.65,66
Sensitivity adequate for minor species concentrations can, however, be
obtained only in the RE-CARS technique. This has been applied successfully to
combustion relevant species by Attal et al. for C2 67 and OH.68 In a variable pressure
burner RE-CARS spectra for OH were obtained at “triple-resonance”, i.e. when all
laser fields in Fig. 1(c) are close to electronic transitions in the OH A2Σ-X2Π (0,0)
band and the vibrational Raman resonance is being scanned around 3065 cm-1.
Spatially resolved concentration profiles and temperature measurements in CH4-air
flames between 1 and 10 bar were possible with an estimated detection sensitivity of
1013 cm-3, or 2-4 ppm at 2400 K. The discrimination against fluorescence background
and saturation of the resonant transitions remain major challenges in attaining higher
detection sensitivities in RE-CARS. In addition, the complexity of the experimental
setup in combination with the need to have detailed knowledge necessary to calculate
the spectral structure are the main barriers to making RE-CARS a routine technique
for concentration measurements of minor species.
3.4.2 Practical considerations and future applications.
As discussed elsewhere in the present volume (see chapter 6) the main
application of CARS in combustion diagnostics so far remains in thermometry using
major species, such as N2, CO2 or H2. Scanned CARS is appropriate for stable flames
whereas broadband or single-pulse CARS is necessary for unstable situations or when
data acquisition time is a critical factor. The coherent character of the signal and its
relatively high intensity on a single shot basis for major species detection are
advantages in many technical combustion environments. Using well designed, i.e.
expensive instrumentation (lasers, optics and detection systems) concentration
measurements are feasible down to the 1% level. However for intermediate
14
concentrations of minor species down to the ppm range the only type of CARS that
can be feasibly used is RE-CARS.
Extending the range of applications of CARS in combustion diagnostics will
depend on advances in laser technology and detection devices. For example, timedomain CARS, where the species specific spectral information is gained from the
transient signal response in a pump-probe experiment using ultra-fast (femtosecond)
laser pulses is an emerging development in laser spectroscopic diagnostics at least for
steady combustion events. Femtosecond-CARS temperature measurements using
nitrogen have been demonstrated recently by Beaud et al.69
3.5 Polarization Spectroscopy, PS.
In polarization spectroscopy, PS, a weak, linearly polarized probe beam is
crossed with a strong linearly or circularly polarized pump beam defining an
interaction length l. Both pump and probe beams have the same frequency ω close to
a resonant atomic or molecular transition. The strong pump beam induces
birefringence and selective absorption in the sample and, as a result, the probe
acquires a small ellipticity and rotation of its plane of polarization that is monitored
through a crossed analyzer. An introduction to the theoretical background of PS is
given by Demtröder in the context of high resolution spectroscopy70 and its
application to combustion diagnostics is reviewed by Eckbreth. Further details are
provided in the research paper of Teets et al.71 Shortly after Zizak et al.72
demonstrated that polarization spectroscopy provided a sensitive and spatially
resolved method for detecting atomic sodium seeded into a flame, Nyholm et al.73
extended the technique to monitor nascent OH in an atmospheric pressure flame.
As shown schematically in Fig. 1, when the laser frequency ω is tuned to a
molecular transition specified by angular momentum and magnetic quantum number J
and m, respectively, pump radiation is absorbed according to the selection rules ∆m =
m’ – m” = ±1 for left- and right-circularly polarized light. The m-level dependence of
the absorption cross section, σ(J”,m” Æ J’,m’), of the circularly polarized pump
pulse radiation leads to an uneven population of the degenerate magnetic sublevels,
and thus macroscopically to a partial orientation or alignment of molecular dipoles,
i.e., an induced optical anisotropy of the medium irradiated by the pump beam. Owing
to the resulting birefringence (∆n = n+ - n-) of the sample, the linearly polarized probe
wave experiences a slight rotation of its plane of polarization (relative phase shift for
right and left circularly polarized light), and simultaneously its ellipticity is changed
due to the difference in absorption coefficient (∆α = α+ - α-) for the respective
circularly polarized components of the probe light. After some algebra, and
neglecting terms of order smaller than (∆αl)2, one obtains for the signal intensity
transmitted through the analyzer to the detector
1 ϕ∆α ab l 1
x
1
1 ⎤
⎡
+ b∆α ab l
+ ( ∆α ab l ) 2
I PS (ω ) = I 0 ⎢ξ + ϕ 2 + b 2 +
2
2
2 1+ x
2
4
1 + x 2 ⎥⎦
1+ x
⎣
(8)
where frequency dependent terms, with x = 2(ω ab − ω ) / γ the frequency detuning
normalized by the collisional halfwidth γ, exhibit absorptive (Lorentzian) and
dispersive contributions to the total line shape. The first three, frequency independent,
terms in Eq. (8) are responsible for a constant background signal. They originate from
15
residual transmission of the polarizers (ξ), their accidental uncrossing (ϕ) and a
possible residual birefringence (b) from optical elements between both polarizers in
the probe beam path. (ξ + b2) normally is in the range 10-6. The differential absorption
coefficient for left and right circularly polarized light, ∆αab, at resonance (x = 0) is
given by
0
0
∆α ab ( x = 0) = ∆α ab
= α + − α − = α ab
S 0 ∆C JJ1
(9)
where α0 is the unsaturated absorption coefficient, S0 is the saturation parameter for
the pump wave and ∆C JJ1 are Clebsch-Gordan coefficients for the respective
transition and coupling case. ,
3.5.1 Applications of PS to temperature and concentration measurement
Advantages of PS for minor species measurements include the coherence of
the signal beam and the ability to detect species that exhibit no fluorescence spectrum
(e.g., many hydrocarbons). In addition, the technique offers high spatial, spectral and
temporal resolution as determined, respectively, by the crossing angle and focal
volume in the sample, and by the bandwidth and pulse length of the laser sources.
Furthermore, by using polarizers with high extinction ratio and low internal scattering
the signal can be observed against a dark background. The technique also has the
unique property of allowing identification of spectral branches by an evaluation of the
J-dependence of the absorption cross sections. Such identification is based on the fact
that for a linearly polarized pump wave Q-branch transitions with a Lorentz-profile
dominate the signal, whereas for a circularly polarized pump wave these transitions
are strongly suppressed and exhibit a dispersive line shape. Close to Doppler-free line
shapes can be achieved for nearly counter-propagating pump- and probe-beam
arrangements. However, sensitivity is then reduced since, for laser bandwidths
smaller than the Doppler width of the transition, only a small velocity subgroup is
probed.
PS was applied by several groups to OH ,74, NH and C275 excited via single
photon transitions and for CO and NH376 via two-photon transitions, the latter to
avoid excessive absorption and laser-induced chemistry in flame environments by
using deep ultraviolet radiation. Figure 6 shows polarization spectra of C2 recorded in
the flame zone of a premixed acetylene-oxygen welding torch and excited via its d
3
Πg-a 3Πu (0,0) band system at 516.5 nm. The detection sensitivity was estimated to
be better than 1018 m-3. The upper part of the figure illustrates the Lorentzian shaped
P- and R-branch lines when the two polarizers in the probe beam path are completely
crossed. On the other hand, dispersive line profiles dominate when some parallel
component of the probe light is allowed to leak through a slightly uncrossed analyzer
(lower part).
Temperatures were determined by Nyholm77 from Boltzmann plots of R- and Qbranch line intensities in the OH A-X (0,0) band around 308 nm in acetylene-oxygen
and propane-air flames. At concentration levels around 1021 m-3 a signal-to-noise ratio
larger than 1000 was achieved using very low pulse energies (1.5 µJ in the pump- and
50 nJ in the probe beam) suggesting a detection limit of 1019 m-3. For the small
crossing angles normally employed in these experiments caution has to be exercised
since the extended interaction region may sample a non-uniform temperature
distribution giving rise to curved Boltzmann plots. In experiments on OH (see Fig. 7)
16
in CH4-air and NH in NH3-O2-N2 flames, Suvernev et al. have demonstrated that
temperatures can also be evaluated from accurate least-squares fits of theoretical
spectral signatures to experimental PS data
Signal Intensity [arb. units]
Signal Intensity [arb. units]
P(0,0)
1
2
3
41
40
39
R(0,0)
1
2
3
13
12
11
40
39
38
12
11
10
8
9
10
11
10
37
36
35
38
37
36
39
38
37
8
9
8
9
7
7
6
0
0
514.0
514.2
514.4
514.6
514.8
515.0
Wavelength [nm]
Fig. 6: Polarization spectrum of C2 obtained in an acetylene-oxygen flame for circularly
polarized pump beam. R-branch triplets are clearly resolved. Upper curve: the two polarizers are
crossed; lower curve: dispersive line profiles are obtained when the analyser is slightly opened
from the crossed position. The vertical scale is the same for both panels. From ref. [75] Courtesy
of Springer-Verlag.
Nyholm et al. obtained a two-dimensional distribution of C2 in a flame through
point-by-point measurements at several heights above the burner. Two-dimensional
single-pulse imaging of OH via PS is possible when the pump beam is formed into a
thin (<200µm) sheet (5 mm high) intersected by an expanded probe beam78.
Polarizers with large aperture and uniform optical quality for the passage of the
enlarged probe beam make these experiments more expensive. The “foreshortening”
of the image in the beam propagation direction also necessitates large crossing angles
(15o-30o) with a corresponding loss in signal intensity.
Single-pulse temperature imaging using OH was demonstrated by Nyholm et
al.79 by exciting the radical simultaneously on the Q1(2), Q1(9) line-pair (whose
thermal population exhibit sufficient temperature sensitivity) with a “dualwavelength” dye laser frequency doubled into the ultraviolet by two separate KDPcrystals. The two transmitted probe beams were spatially separated with a diffraction
grating and projected onto separate regions of a CCD camera chip. New et al.80
17
performed broadband PS thermometry on OH, where multiple lines of a spectrum can
be captured simultaneously using a broadband, modeless dye laser for the pump and
probe laser, and a fibre-coupled spectrometer with a CCD camera.
8
9
7
10
R1
11
7
PS-intensity
8
Q21
Diff x 10
3
PS-Signal
Simulation
8
4
0
-4
306.36
306.40
306.44
306.48
Wavelength [nm]
Fig. 7 Experimental PS spectrum of OH in a CH4-air flame showing a least squares fit (Tfit = 2120
K) of a theoretical spectrum to the experimental data. The small intensity Q21 transitions were not
included in the fit. From ref. [74] Courtesy of Springer-Verlag.
3.5.2 Practical considerations and future applications
Obtaining quantitative number densities from the PS signal in flames for a
wide range of collisional environments (i.e., pressures, species composition) and laser
intensities still is an area of active research. Saturated PS is a means to increase signal
levels and reduce the sensitivity of the signal to pulse-to-pulse energy fluctuations of
the laser source. By direct numerical integration (DNI) of the equation of motion of
the density operator for the system, Reichardt et al.81 predict that the PS signal can be
made less dependent on collision rate when a saturating pump beam is used. This
result is valid so long as the collisional width is smaller than the Doppler width of the
transition. To test the validity of these results the same authors performed saturated
PS measurements with OH in the near adiabatic H2-air flame of a Hencken burner82.
The signal intensity was measured as a function of equivalence ratio, Φ, and corrected
for probe beam absorption. Assuming a square root dependence of the signal intensity
on number density, the results were in good agreement with direct absorption
measurements as well as with predictions from a chemical equilibrium code in the
range Φ = 0.5-1.1.83 However if a linear dependence was assumed, deviations
between both methods appeared around Φ = 0.8.
Kaminski et al.84 conducted a systematic study of the pressure dependence of
the PS signal intensity of OH obtained in a variable pressure (10 – 900 mbar)
premixed methane-air flat flame as a function of height above the burner plate. A
specially designed burner housing with the two polarizers located inside the vacuum
chamber avoids the degradation of the polarization quality of the probe beam by
optical stress and birefringence in the entrance and exit windows.85 The OH height
profiles for two total pressures (30 mbar and 900 mbar) are depicted in Fig. 8,
18
together with corresponding linear LIF signal intensities acquired perpendicular to the
beams through a third window. The latter may be converted to OH number densities
when species specific quenching corrections have been applied, allowing a direct
comparison of PS with absolute number densities and future theoretical predictions
using numerical or analytic approaches.
120
ILIF, IPS
1/2
[arb. units]
100
80
LIF
60
40
(30 mbar)
1/2
(30 mbar)
(900 mbar)
1/2
(900 mbar)
PS
LIF
PS
20
0
0
5
10
15
20
Height [mm]
Fig. 8 Height profiles of PS (solid lines) signal intensities of OH excited in the A2SX2P (0,0) electronic band in premixed methane-air flames at two total pressures (30
mbar and 900 mbar, respectively) From ref [84]. Courtesy of C.F. Kaminskii.
3.6 Conclusions
The importance of minor species to the understanding of combustion has
motivated research in techniques for their detection. Coherent techniques based on
non-linear resonant interactions have proved to be viable for measurement both of the
trace concentrations involved and of the temperature. Although not discussed in detail
here some of these techniques have been applied to measurement of other relevant
parameters such as pressure and gas velocity.
Each of the techniques discussed here provides comparable detection
sensitivity but differs in the degree of complexity involved in both experimental
procedures and theoretical analysis. DFWM has been the most widely applied and
shows promise for providing absolute concentration and measurements in practical
devices such as engines. PS is experimentally simpler than DFWM but owing to
stress-induced birefringence in windows its use will probably be restricted mostly to
open flames. In addition the analysis of PS signals is complex and relies on
knowledge of relaxation rates that may not be known in a given situation. RE-CARS
has seen little application beyond the early demonstrations of principle owing largely
to the complexity of the experimental arrangement involving up to three
independently tunable lasers. LITGS remains a subject of continuing research since it
offers the prospects of measurements at elevated pressure where interpretation of
signals from the other techniques becomes problematic.
19
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1
2
3
4
5
6
7
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non-saturating laser powers. Appl. Phys, B 58 (1994): 459-466
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Measurements in a Flame. Opt. Lett. 17 (1992): 751-753.
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