COHERENT TECHNIQUES FOR MEASUREMENTS WITH INTERMEDIATE CONCENTRATIONS. Thomas Dreier and Paul Ewart

Transcription

1 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 (3) r (3) r r r P ω, ) = χ ( ω, ω, ω, ω ) E ( ω, ) E ( ω, ) E ( ω, ) (1) i ( 4 ijkl j 1 k l 3 r where E ( ω, ) are complex field amplitudes. This polarization radiates the signal m n wave E(ω 4 ) 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(ω 1 ), E(ω ) and E(ω 3 ). DFWM (ω 1 = ω = ω 3 ) involves a stationary or standing wave interference pattern created by the interference of a probe field, E(ω 3 ), with either of the two pump fields E(ω 1 ) or E(ω ). The signal wave, E(ω 4 ), 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 ω creates a non-stationary interference pattern with a pump wave at ω 1 (= ω 3 ). Scattering of the other pump off this moving grating gives a Doppler shifted frequency corresponding to the anti- Stokes wave (ω 4 ). 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

2 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 Population Grating ω 1 ω ω 3 ω 4 ω 1 ω ω 3 ω 4 ω 1 ω ω 3 ω 4 ω 1 ω ω 3 ω 4 Collisional Quenching m-1 m m+1 Population Grating - stationary Thermal Grating - stationary Population Grating - moving Degenerate sub-state population transfer. (a) DFWM (b) LITGS (c) CARS (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 generated wave vectors k r i is zero i.e. r r r r r r π k = k1 k + k3 k4 = 0, with k i = () 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. 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

3 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 10 4 ppm). 3. Degenerate four-wave mixing, DFWM. The basic physics of DFWM has been presented in the context of optics and spectroscopy 3, 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 Lind 7 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 I pump and a weak probe field I probe. The intensity of the signal beam, when integrated int over the atomic resonance line, is and is given by analytic expressions in the two limiting regimes of weak and strong saturation by the pump: I sig I int sig N k T1 T µ I I, (3) [ 1+ 4I I (0)] pump s 5 pump probe when I pump << I s (0) and I int sig µ N k T T 1. I I (4) 1 1 pump probe when I pump >> I s (0). In these relations I S (0) = h /(T 1 T µ 1 ) is the line-centre saturation intensity. Τhe medium influences the signal by virtue of the dependence of I on the int sig 3

4 atomic number density N, the atomic dipole moment µ 1 and the longitudinal and transverse relaxation times T 1 and T respectively. The signal can be characterised by a reflectivity R = I sig /I probe. 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 N, (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 I S (0) on the collision induced relaxation rates, T 1 int and T, the sensitivity of to pressure can be dramatically reduced by operating I sig with saturating pump laser intensities. 11,1 The benefits of saturated DFWM are discussed in detail by Lucht and co-workers 13 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, ω D, relative to the homogeneous width, ω C, (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-workers 15,16 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, 0 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 hom R = (5) 1 + ( b ω D / ωc ) 4

5 where R hom 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 N over a wide range of temperature. The validity of this result is qualified by the limitations of the A&L model used to determine R hom, 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. 1 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,, 3 but again the method is not convenient for routine diagnostic analysis. A non-perturbative analytical solution has been presented by Bratfalean et al. 4 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 C 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. 5,6 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 spectra 7 presents a different problem. In multiplex techniques a broadband laser field of width ω L 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 Ewart 8 treated the problem by finding the time-dependent solution to the density matrix equations in the limit of large laser bandwidth, ω L >> ω D, ω C. 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

6 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. 9,30 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 pulses 31 and allow some of the problems associated with collisions to be avoided. However, as Reichardt and Lucht 3 point out, collisions still play a role in the DFWM signal generation even when the laser pulse duration τ L is less than τ C the collision time (τ C = ω -1 C ) 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 moment 33 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 C. 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

7 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 -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 -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 ~ I sat and note that there is little to be gained by using intensities much greater than I sat. 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 ω D to ω C 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 ω D / ω C, minimizes the collisional effects and gives signals that are less 7

8 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. ) The OH concentration was found to vary by a factor of ~0 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. 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 concentration 4,43 and temperature 44 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

9 The simultaneous mapping of both temperature and concentration in 1- dimension has recently been achieved by Lloyd and Ewart 46 using broadband DFWM of C 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. Temperature / K C B A Relative C concentration Distance / mm 0.0 Figure 3 Simultaneous measurement of relative concentration of C (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 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 -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

10 Such situations include flames, plasmas or materials processing environments where N 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 ω D / ω C, 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: 100rpm ignition: 40 deg btdc 14 laser timing: BDC power stroke 1 DFWMIntensity (au) 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 Lucht 19 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 > I sat 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 (TEM 00 ) will optimize the wave mixing and spatial filtering of unwanted light scatter. For multiplex DFWM the modeless laser is the 10

11 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 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 Cummings 5 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 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

12 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 LITGS of OH: High pressure methane/air flame Intensity Experiment Simulation Fit temperature = 014 K Fit pressure = 40.1 Bar 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 Taran 56,57 and Eckbreth 58 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 ω 1 ), with a tunable Stokes beam of frequency ω, in the interaction volume. A second pump beam at ω 3 (= ω 1 ), 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 ω 1 ω. When the frequency difference ω 1 ω 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 1

13 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 ω 1 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 = 1 ω 4 4 n n n c ε 4 0 I 1 I χ CARS sin( kl / ) l kl / (6) where I 1 and I are the intensity of the pump and Stokes beams respectively, l is the interaction length, and n i are the refractive indices at frequency ω i. The maximum signal is generated when the phase mismatch factor k = 0. The third-order susceptibility, χ (3) (3) = χ CARS, in general consists of a non-resonant part χ nr, which is independent of the frequency of the exciting beams, and a Raman-resonant (3) contribution : χ r χ χ nr + χ r (3) (3) (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

14 CARS spectral signatures of many major species of spectroscopic interest in combustion diagnostics, such as N, O, H O and others, may be obtained 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. 6 and Hahn et al. 63 down to concentration levels of %. 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 field 64. 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 C 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 A Σ-X Π (0,0) band and the vibrational Raman resonance is being scanned around 3065 cm -1. Spatially resolved concentration profiles and temperature measurements in CH 4 -air flames between 1 and 10 bar were possible with an estimated detection sensitivity of cm -3, or -4 ppm at 400 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 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 N, CO or H. 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

15 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 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 spectroscopy 70 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. 7 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 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), one obtains for the signal intensity transmitted through the analyzer to the detector I PS 1 ϕ α abl 1 x 1 1 ( ω ) = I 0 ξ + ϕ + b + + b α + ( ) abl α l ab (8) 1+ x 1+ x 4 1+ x where frequency dependent terms, with x ( ω ω) / γ the frequency detuning = ab 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

16 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 + b ) normally is in the range The differential absorption coefficient for left and right circularly polarized light, α ab, at resonance (x = 0) is given by α ab ( x = 0) = α ab = α α = α abs 0 C JJ 1 (9) where α 0 is the unsaturated absorption coefficient, S 0 is the saturation parameter for the pump wave and are Clebsch-Gordan coefficients for the respective C JJ 1, transition and coupling case 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 C 75 excited via single photon transitions and for CO and NH 76 3 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 C recorded in the flame zone of a premixed acetylene-oxygen welding torch and excited via its d 3 Πg-a 3 Πu (0,0) band system at nm. The detection sensitivity was estimated to 18-3 be better than 10 m. 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 Nyholm 77 from Boltzmann plots of R- and Q- branch line intensities in the OH A-X (0,0) band around 308 nm in acetylene-oxygen and propane-air flames. At concentration levels around 10 1 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 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