Laser atomic spectroscopy in flames, gases and beams

J. Quant. Spectrosc. Radiat. Transfer Vol. 40, No. 3. pp. 385-402, 1988

Printed in Great Britain

0022-4073/88 $3.00+0.00 Pergamon Press pk

LASER ATOMIC SPECTROSCOPY IN FLAMES, GASES AND BEAMS C. Th. J. ALKEMADE Fysisch Laboratorium der Rijksaniversiteit Utrecht, Princetonplein 5, 3584 CC Utrecht, The Netherlands (Received 27 October 1986; receivedfor publication 16 November 1987)

Abstract--Some (partly unpublished) laser-induced fluorescence experiments made at our laboratory on the Na-D doublet in flames, gas-filled vapour cells, and an atomic beam/n vacuo are reviewed. These experiments relate to the following: the distortion of the fluorescenceemission spectrum of both doublet components by Mollow splitting at strong, near-resonant excitation of one component in an Ar-fiUed vapour cell; the distortion of the fluoreseenceemission spectrum of the laser-excited doublet component by (near-)resonant Rayleigh scattering in a N2-diluted H2-O2 flame; the distortion of the fluorescence-excitation spectrum of the laser-excited doublet component by partial atom trapping in a hyperflne level of the ground-state in an Ar- or N2-filled vapour cell; and finally the distortion of the saturation curve by similar atom trapping in an atomic beam and the influence of laser-polarization on this curve. Attention is given to the dependence of these effects on the ambient-gas conditions. Also the links between these effects and their possible relevancy for laser-based diagnostic techniques are indicated. The saturation curve of the Mollow triplet is discussed theoretically. A consistent definition of the terms fluorescence and scattering is proposed.

1. I N T R O D U C T I O N Because of their special properties lasers are suited par excellence to prepare an appreciable fraction o f free atoms or molecules in a specific state o f excitation and polarizationt and with a specific velocity component along the laser beam axis. This enables us to measure total or differential effective cross-sections for the transfer o f translational or internal energy, and of linear or angular momentum between the state- and velocity-selected particle (here called probe atom) and a collision partner. State- and velocity-selected chemical reactions or ionization processes can also be studied. Furthermore, a temporary collision complex (or quasi-molecule) in a selected state o f excitation, e.g. Na(3P) + Ar, can be prepared with a selected interatomic separation R by exciting a N a atom in Ar gas in the wing o f the collisionally broadened Na-D line. This enables us to investigate interatomic potentials by observing the Na-D fluorescence intensity (emitted after dissociation o f the unstable quasi-molecule) as a function o f laser detuning; the detuning is related to R through the difference of the excited-state and the ground-state potentials.' A laser beam, if intense enough, can not only change the population o f atomic states, but can also mod/fy the atomic properties (such as wave function, position and width of energy level, and polarizability). These modifications may be influenced by collisions and may therefore depend on the state o f the ambient gas. In our group o f the Atomic and Molecular Physics Department laser atomic spectroscopy has been applied mostly to free N a atoms in Ar- or N2-diluted H2-O2 flames at I a t m pressure, in gas-filled cetls, and in atomic beams in vacuo. The main aim was to understand the underlying mechanisms, to test existing or incite new theories, and to determine rate constants for stateselected collisional, chemical, and ionization processes (for a review, see Refs. 2, 3). Most o f our

fl'he polarization of an atomic state relates to the population distribution over its Zeeman substates characterized by their magnetic quantum numbers M. Special cases of atomic polarization are orientation and alignment. 385

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experiments were done by observing the spectral characteristics (such as intensity, excitation and emission spectrumt, and polarization) of Laser-Induced Fluorescence (LIF). Although we did not consider primarily the diagnostic application of laser-based techniques to plasmas, combustion systems, fluids, analytical excitation- or atomization sources, etc., 4-~zour basic LIF investigations may be of possible interest in this respect too. An unambiguous interpretation of diagnostic measurements (in terms of gas temperatures, gas pressures, flow velocities, concentrations of minor species, etc.) requires a proper understanding of the interactions of the probe species with the laser field and with the ambient gas, as well as knowledge of the relevant parameters (optical and collisional cross-sections, spectral line profiles, reaction rate constants, etc.). The optical and collisional interactions of the probe species are often considerably more intricate than is assumed in diagnostic applications in real-world systems. This may easily lead to misconceptions and pitfalls in the interpretation of the observations or to unawareness of the limitations of the applicability of laser techniques. Such pitfalls may be illustrated by considering, as an example, the well-known technique of density measurements of minor species by Saturated LIF Spectroscopy. 9-H Here one takes advantage of the fact that at the plateau of the (ideal) saturation curve (SC) the fluorescence intensity IF is independent of (fluctuations in) the laser beam intensity IL and of (spatial variations in) the quenching rate constant kq (cf. Appendix). Another advantage is that the saturated fluorescence intensity is simply related to the number density n2 of excited atoms and to the total number density nT of atoms in the laser-coupled levels. This holds at least if the atom has (effectively) only two energy levels. Absolute density values can be derived from absolute IF measurements if merely the Einstein transition probability A, the ratio of statistical weights gJgz, and the geometrical observation conditions are known (cf. Appendix). Neither the temperature, pressure and composition of the gas, nor IL or the spectral profiles of the laser and the atomic line need be known if a resonant broad-band laser is used. By restricting the observation volume to a small portion of a pencil-like laser beam, high spatial resolution can be achieved. However, errors may arise, for example, when one applies the idealized relationships between IF and n in the case when the observed fluorescence is polarized and thus anisotropic. These errors depend on the solid angle and mean direction of observation, the laser polarization, the rate of depolarization by collisions (which may locally vary with gas density and composition), and the polarization-dependence of the detection channel. Another, often more serious problem is that a strict saturation plateau occurs only rarely under realistic measuring conditions. ~3 Or, if it does occur, its position may deviate largely from that predicted by the idealized equations in the Appendix. In general, distortions of the SC can be produced by a great variety of (usually interwoven) effects, which depend on the measuring technique, the laser-excitation conditions, the physical and chemical interactions of the laserexcited species with the ambient gas, etc. Especially in diagnostic applications, these interactions can be a nuisance as they can depend on the gas pressure, composition, and temperature. Detailed kinetic data or additional test experiments are then required to assess them or to correct theoretically for the resulting errors. This applies, in particular, when pulsed lasers whose durations are comparable to the relevant relaxation times have to be used. Special caution should be exercised when one wants to derive the quenching rate constant kq from the saturation parameter, which is theoretically related to kq via the fluorescence efficiency Y [Eqs. (A2) and (A3) in the Appendix]. The saturation parameter marks the "knee" in the ideal SC, but the "knee" actually found may be shifted substantially from its true position by secondary effects. ~3 Essential errors in total density measurements may be produced when saturation results in a (partial) depletion of the probe species by laser-enhanced chemical reactions or ionization. The measured value then deviates from that existing in the absence of laser-excitation. In Sec. 2 of this paper we review a selection of our LIF studies on Na atoms in different experimental systems, while we indicate in Sec. 3 some of their mutual links and implications for laser-based diagnostics. Sections 2.1 and 2.2 deal with two effects that can distort the fluorescencetThe fluorescence-excitation spectrum is obtained by scanning the wavelength 2L of a narrow-band laser over the absorption line profile while measuring the spectrally integrated fluorescence intensity. The fluorescence.emission spectrum is obtained by analyzing the spectral profile of the fluorescence emission while keeping 2L fixed.

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emission spectrum at high and moderate laser intensity, respectively. Section 2.3 describes a typical case o f a distorted fluorescence-excitation spectrum. Distortions of the SC measured for a selected hypertine transition under collision-free conditions are considered in Sec. 2.4. 2. R E V I E W OF L I F E X P E R I M E N T S ON T H E Na-D L I N E S

2.1. Experiment A: distortion of thefluorescence-emission spectrum by Mollow splitting in an Ar-filled cell The fluorescence-emission spectrumt of the Na-D doublet changes when one of its doublet components is excited by a strong, (near-) resonant laser beam. With the use of a broad-band laser (laser bandwidth ~VL>>atomic line width 6Vo), power broadening of the fluorescence emission profiles may take place, which increases proportionally to the spectral irradiance E~0 of the laser beam at atomic line centre v0.~;j5 Power broadening not only occurs in the laser-excited doublet component but also in the other component (be it to a lesser degree), when the latter is excited by doubletmixing collisions. 2 We have previously studied this effect in an Ar-diluted flame ~6 as well as in an Ar-filled vapour cell. 17 Here we want to report on our first attempts to demonstrate the Mollow-splitting (or a.c. Stark effect) o f the Na-D lines that is expected to occur with the use of a strong, narrow-band (~VL<<~V0) laser beam. When, for example, a linear-polarized laser beam with high irradiance E and frequency VL is tuned to near-resonance with the D~ line centre v0, the Dm fluorescence spectrum observed in the direction of the laser-polarization vector is split into three equidistant, unpolarized§ components. These components are located at frequencies VL, VL+ ~'/2n and VL-- f~'/2n, where t2' is given by

~ ' = ~ / t ~ + (2,~t~) 2.

(1)

Here A is the detuning ( = VL-- V0) and f~ is the circular Rabi frequency, which is proportional to the dipole matrix element and to ~/E. The MoUow component with frequency equal to VLis called the Rayleigh "line" (R)¶, the component with frequency nearest to v0 is called the fluorescence "line" proper (F), and the one on the opposite side of the Rayleigh line is called the three-photon "'line" (T). If (f~/A) e ~ 0, i.e. at low laser intensity, the F line centre approaches the (undisturbed) centre v0 o f the D~ component. In the lowest-order approximation, the emission of the T line may be conceived as part of a three-photon process in which simultaneously two laser photons are absorbed, raising the atom to the D~ state, while conserving energy. Subsequent spontaneous emission from this state produces the F line. (There is thus a time-ordering in the emissions of a F and a T photon. 2°,2t) In the presence of collisions, the D~ state can also be populated by one-photon absorption from the laser beam in the wing of the collisionally broadened D1 line. The energy difference h(vo- VL) is made up by kinetic energy. In the absence of collisions, as many T photons as F photons are emitted; since two laser photons are consumed in the three-photon process, the intensities of the T and F lines relative to that of the R line then vanish oc E when E ~ 0. In the presence of collisions, however, the F line grows with increasing gas pressure, whereas the T line weakens; the R line remains the same, but its incoherent part gains at the cost of its coherent part. Mollow splitting of an isolated atomic spectral line is a well-known phenomenon. 22,23We have studied, for the first time, the effect of Mollow splitting on the non excited Na-D doublet component t o o . 19'24'25 This component is seen in fluorescence when doublet-mixing collisions take place. In contrast to the laser-excited doublet component, the other component is predicted to be split in only two "lines". These lines are mutually separated by f~'/2n. The Mollow line located nearest to the D2 line centre v~ will here again be called a fluorescence line (F'); its central frequency approaches v~ when (f~/A) 2 --*0. The other Mollow line is called here the Raman line (Rm) as, in tAlso the absorption spectrum may change,m4but this will not be considered here. ~;Powerbroadening--which may be intuitively interpreted as resulting from broadening of the upper and lower energy levels due to the shortening of the optical lifetimesby the laser-induced transitionsmS--shouldbe well distinguished from saturation broadening of the fluorescence-excitation profile. 2 §When observedin an arbitrary direction, these components will be polarized and their radiations are thus auisotropic.TM ¶It has a coherent and an incoherent spectrally-broadenedpart. The former dominates at low, the other at high laser intensities.

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C . T h . J. ALKEMADE

lowest-order approximation, it is emitted from the De state under simultaneous absorption of a laser photon, while transferring the atom to the DI state. Its distance to the R line equals the D doublet splitting, if (f~/A)e<<1. The general theoretical description of the Mollow effect is based on the so-called dressed-atom model, in which atom plus quantized laser field are combined to a single quantum mechanical systemJ 4,e3,e6 The Mollow lines arise from spontaneous transitions between eigen-states of the dressed atom, whose energies depend on A and f~ (or E). In the above considered case of a linear-polarized laser beam tuned to near-resonance with the D~ component, the upper and lower states of the dressed atom consist each of two levels with the same energy separation hfY/2~. Optical transitions between these levels are allowed at three different frequencies, corresponding to the Mollow triplet. From the collisionally populated, unaffected/)2 state only two different transitions are allowed to the split lower state. We have tried to demonstrate the effects of Mollow splitting on the fluorescence spectrum of both Na doublet components by experiments in a Na-vapour cell filled with Ar (T -~ 450 K; argon density -~ 2 x 10~8cm-3). ~a5 A flash-lamp pumped, linear-polarized dye-laser was used with a pulse duration of 0.6/~s, a bandwidth of roughly 15 n ~ , and a variable detuning A from the D~ line centre. Time-resolved ( ~ 10 ns) fluorescence spectra were measured with the aid of a scanning Fabry-P6rot interferometer (finesse-~45; free-spectral-range-~ 6 5 0 n ~ ) and a fast transient digitizer, e7 Figure I shows a specimen of the emission profiles of the D, and De components (combined in one plot by utilizing aliassing) at a maximum available irradiance E - 200 kW/em e on the beam axis and IAI = 110 rn~. The R and F lines are clearly distinguished but the T line does not show up. The splitting observed at the D~ line is somewhat less than that at the De line. From Eq. (1) one calculates a splitting of 287m,~ for a uniform laser beam with E = 200 kW/em 2. The experimental splittings are evidently smaller, which can be explained by the inhomogeneity of the laser irradiance along the line of sight perpendicular to the beam axis. A quantitative comparison with theory is hampered by deviations from the idealized conditions assumed in the theory. The laser used was not strictly monochromatic, Doppler broadening was not negligible, and the irradiance was not uniform along the line of sight. The local value of ~2 ( ~ E) and thus offY 2 [Eq. (1)] drops gradually with increasing radial distance from the beam axis, whereas the fluorescence radiation emitted per unit volume element does not drop so much because

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Fig. 1. Fluorescence-emission spectrum of the Na-D doublet in an Ar-fdled vapour cell, recorded over about one free-spectral-range with a Fabry-P6rot interferometer, using a linear-polarized, narrow-band, pulsed dye-laser detuned by - 110 n ~ from the Di line centre with a peak irradiance E -~ 200 kW/crn 2 on the beam axis. The solid curve was drawn smoothly through the experimental points, some of which happen to be masked by the thickness of the line. Fluorescence was observed in a direction parallel to the laser polarization. The D-doublet components appear close together because of aliassing. R and F are the Rayleigh and fluorescence Mollow line of the Di component, respectively. The theoretically predicted position of the unobserved three-photon line T is indicated by an arrow. Because of aliassing, its position is shifted over one free-spectral-range to the right. Rm and F' are the Raman and fluorescence Mollow line of the D2 component, respectively. (According to measurements by A. R. D. van Bergen and H. van Halewijn at our Laboratory. ~5)

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atomic spectroscopyin flames, gases and beams

389

(near-) saturation persists far outside the beam axis. Consequently, the detected fluorescence radiation stems to a considerable extent from regions where the Mollow splitting is markedly smaller than on the beam axis. We have tried to take into account the inhomogeneity of E by computer simulation calculations, assuming a realistic model for the radial variation of E. The variation of fl 2 along the line of sight appeared to produce a shoulder in the outer wing of the fluorescence line, making it asymmetric and broader. Besides, the peaks of the R and F lines were found to lie closer to each other than one would expect for a uniform laser beam at E = 200 kW/cm 2. One can argue that the Mollow splitting of the D2 component was less affected by this inhomogeneity than that of the D~ component, in accordance with experiment. The peak of the T line, which was relatively weak in the presence of collisions, virtually disappeared because its profile became smeared out in the simulated compound spectrum. The intensity ratio of the F and R lines in the simulated spectrum agreed well with the experimental ratio, as long as the laser bandwidth was taken into account.

2.2. Experiment B: distortion of the fluorescence-emission spectrum by Rayleigh scattering at (near-)resonant excitation in flames When Na atoms in a gas are excited by an off-resonant laser beam (detuning IAl>>rv0), the

Rayleigh (R) line is well distinct from the collision-inducedfluorescence (CIF) lines of the D doublet. Whereas the CIF line intensities (and polarizations) depend on the gas pressure (through line-broadening, depolarizing, doublet-mixing, and quenching collisions), the R line intensity (and polarization) is independent of it. (We assume that IAI is still so small that Rayleigh scattering by Na atoms dominates over that by the gas.) However, at (near-)resonant excitation (IAI ~< 6v0), the R line appears as a bump on the top or flank of the CIF line. The resultant distortion of the fluorescence-emission profile depends on gas pressure (influencing the intensity ratio of the lines) and direction of observation (influencing the Doppler broadening of the R line and the line intensities if polarization occurs). At our laboratory, theoretical calculations of the fluorescence-emission profile and polarization at near-resonant excitation have been presented by Nienhuis 2s and experimentally verified, for the first time, by Nieuwesteeg et al) '29 Here we review the experimental procedure and results obtained. We chose as excitation medium a N2-diluted H2-O2 flame at atmospheric pressure and T = 1420 K, seeded with Na vapour by nebulizing a Na solution, because the intensity of the (weak) R line relative to the CIF intensity was improved by the small value of the fluorescence efficiency in this flame. ~ Moreover, in this flame a measurable degree of polarization of the CIF line was expected at D2 excitation. (The number of elastic depolarizing collisions during the lifetime of the excited state is reduced by the shortening of the lifetime due to quenching collisions.) The Na density was kept sufficiently low to avoid self-absorption, which could distort the emission spectrum. Thermal Na emission was negligible. Either of the doublet components was excited at near-resonance (IAI~ 80 mA) by a linearpolarized, narrow-band, cw dye-laser (Coherent Radiation, model 690), which produced laser radiation simultaneously in two axial cavity modes separated by 11 mA. The laser power was kept sufficiently low to prevent optical saturation as well as MoUow splitting (el. Sec. 2.1). Particulate scattering was proved to be negligible. The spectrum of the fluorescence emitted perpendicular to the laser beam and its polarization vector was analysed by means of the high resolution Michelson interferometer constructed in our laboratory with a maximum path-length difference of 1 m and a resolution of 1.3 mA at about 5000 A. 3° An analysing polaroid was used to measure the polarizations of the R and CIF lines. The solid curve in Fig. 2(a) shows a specimen of the spectral profiles of the two doublet components, obtained by Fourier transformation of the interferogram (for experimental details, see the figure caption). The R line appears as a small bump on the flank of the laser-excited doublet component, whereas the profile of the other component is not distorted, as expected. In order to make the R line stand out more clearly against the underlying CIF line, an additional recording was made with the laser detuned by the same interval IAI to the other side of the CIF line [see dashed curve in Fig. 2(a)]. The two spectra were normalized so that the spectrally integrated intensity of the other (undisturbed) doublet component was the same. In the difference spectrum,

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C. Th. J. ALKEMADE 8~ D2 / /

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Fig. 2. Fluorescence-emissionspectra of the Na-D doublet in a N2-diluted H2--O2 flame, recorded with a Miehelson interferometer by application of Fourier transformation. The wavelength scale refers to the D2 component, which was near-resonantly excited by a linear-polarized, narrow-band cw dye-laser; the D~ component was displaced to nearby the D2 component by aliassing. Fluorescence was observed in a direction perpendicular to both the axis and the polarization of the laser beam, while the analysing polaroid was oriented parallel to the laser polarization. The solid and dashed spectra in (a) were obtained with the laser detuned by +80 and -80mA, respectively, as indicated by the drawn and dashed arrows. The bumps on the flanks of the D2 line are caused by Rayleigh scattering. Figure (b) shows the differenceof the two spectra, in which the collisioninduced/)2 and D I fluorescence components are eliminated and only the Rayleigh lines (with opposite signs) appear. (Accordingto measurements by K. J. B. M. Nieuwesteeget al and reproduced from Ref. 3.)

the C I F line is absent and only two R lines are seen with opposite signs, separated by 2 x 80 m/~ [see Fig. 2(b)]. We found the R and C I F intensity ratios to agree with theory within the experimental error of 15% at either DI or D~ excitationt. The theoretical values were calculated taking collisional rate constants for quenching, mixing and disalignment of the polarized atoms from Ref. 31 and using the known absorption line profile. The experimental intensity of the/)2 component relative to that o f the D~ c o m p o n e n t was systematically larger by about 10% than the calculated value. Whereas no polarization occurred at D~ excitation, the degree o f linear polarization P r o f the R line (45%) and that o f the combined D2-CIF and R lines Po2 (9.2%), measured at D~ excitation, agreed with theory (60 and 8.9%, respectively) within the expected error margins. (The degree of polarization o f the D2-CIF line alone was a b o u t 4%. 31) These values relate to the special case when A = 0. The intensity ratio los/lot (where I is the spectrally integrated intensity including the superimposed R line) reflects directly the population ratio o f the doublet states 0nly if the DI component is excited by the laser. (The emissions of the unpolarized DI and D2 components are then isotropic.) At D~ excitation, we have ~9 ID2 _ riD2 =

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where z~2 and z2~ denote the rate constants for D2 ~ D~ and DI --, D2 mixing, respectively, divided by (A + k~) (defined in the Appendix). In the case o f D2 excitation, however, we have under the

tNote that a division bar is missing on the fight-hand side of Eq. (8a) in Refs. 3 (p. 139) and 29.

Laser atomic spectroscopyin flames,gases and beams

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2.3. Experiment C: distortion of the fluorescence-excitation spectrum by atom trapping in a ground-state hyperfine level in an Ar- or N2-filled cell In our studies of collisional line broadening we were faced with the distortion of the fluorescenceexcitation profile due to (partial) trapping of atoms in one of the two hyperline (hf) levels of the Na ground-state. 3'32As a consequence of hf splitting, which is caused by the nuclear spin (I = 3/2), each Na-D component appears as a doublet with a wavelength separation of about 20 mA. (The hf splitting of excited Na states is much smaller and may be disregarded in bulk-gas experiments.) If the laser bandwidth and the absorption line width are markedly smaller than the hf splitting, atoms are predominantly excited from one hf level when the laser is tuned to the corresponding hf line. However, the excited atom can return to either of the hf levels by spontaneous emission or a quenching collision. Those returning to the hf level that is not accessible to laser-excitation will be trapped there. The trapping effect is counteracted by hf-mixing collisions or diffusion of trapped atoms outwards the laser beam and their replenishment of fresh atoms by inward diffusion, which tend to restore the population-distribution over hf levels towards the initial distribution. When this restoration is incomplete, an underpopulation of the laser-excited hf level and an overpopulation of the other level will result, in the steady-state. Consequently, the laser-excitation rate and thus the fluorescence intensity IF will be less than expected at an equilibrium population distribution. The relative depression of IF will increase with increasing laser intensity and with decreasing detuning A2 from the hf line centre. This results in a distortion of the fluorescenceexcitation spectrum when we scan the laser wavelength successively over the two hf components. When the hf components overlap each other partly or the laser bandwidth is not small in comparison with their splitting (so that a smooth excitation profile with a single peak is observed), the distortion by atom trapping is seen as a symmetrical narrowing of this profile. This trapping effect has been investigated for the first time by Coolen et al in a Ne-filled Na vapour cell) 3 At our laboratory Jongerius32 has extended the theoretical analysis by including also stimulated emission, line broadening, and doublet-mixing collisions, and has made experiments in an Ar- and N2-filled vapour cell at higher gas pressures than were used in Ref. 33. He has also calculated, on the basis of these experiments, the (small) distortion effects that can be expected in Ar- and N2-diluted H2-O2 flames at 1 atm pressure. Figure 3 shows specimens of fluorescence-excitation profiles of the D: line, measured in a cell at an Ar density of 4 x l017 c m -3 and a temperature of 410 K. Similar profiles were obtained with N2 under the same conditions. The Doppler width was about equal to the hf splitting, whereas the coUisional line width was five times smaller. A narrow-band cw dye-laser, lasing unfortunately in two axial cavity modes (15 mA apart), was used at various power levels that were sufficiently low to avoid saturation broadening and hole burning.: The laser beam diameter was about 0.06 crn. The dot-dash curve in Fig. 3 represents the excitation profile in the absence of atom trapping. The hf structure was not resolved and produced only a shoulder on each side of the top that was located between the hf line centres. The distortion and particularly the narrowing of the excitation profiles with increasing laser irradiance are clearly seen. The narrowing is caused by the fact that the relative depression of the laser-excitation rate is largest when the laser is tuned to either of the hf line centres located on the flanks of the excitation profile. At the top of the profile, the depression is zero, as here no preferential population of either hf level occurs. The depression also disappears at the far wings of the profiles, as the laser-excitation rate becomes very small here. 2.4. Experiment D: dependence of the saturation curve on laser polarization and atom trapping in an atomic beam In a parallel beam of Na atoms in vacuo, crossing a resonant, monochromatic laser beam at right angles, one can excite a specific hf level of the/)2 state (with total atomic angular momentum F' = 0, 1, 2, or 3) from a specific hf level of the ground state (with F = 1 or 2). This holds because

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Fig. 3. Fluorescence-excitation profiles of the Na-D~ component, measured in a vapour cell filled with Ar gas at a density o f 4 x 101~cm -3 and a temperature o f 410 K by wavelength-scanning o f a low-intensity, narrow-band cw dye-laser. K(2) is a relative measure for the fluorescence-excitation rate as a function of laser detuning A~ from the centre o f the curves, whose top values were put equal to unity. The dot-dash curve represents the excitation profile in the absence o f atom trapping in either o f the two ground-state h f levels (see text). It shows that the hi" lines were not spectrally resolved. The three drawn curves, which are calculated best-fits to the experimental points, represent the distorted profiles at laser beam irradiance E = 3.0 x 10 -5, 1.7 x 10 -5, and 1.8 x 10 -I W/cm 2, respectively (from top to bottom). The profiles become narrower with increasing E-value because o f the dependence o f atom trapping on E. The relative effect o f atom trapping is largest at the flanks o f the profile where the two h f line centres are located. (From measurements by M. J. Jongerius 32 at our laboratory.)

Doppler-broadening and collision broadening are eliminated here, whereas the natural line width is less than the minimal distance between two neighbouring hf lines. Atom trapping in either of the hf ground-state levels can now be avoided by tuning the laser to the (F' = 3 *-- F = 2) hf line, in contrast to the case considered in Sec. 2.3. This is because atoms excited to the (F' = 3) level cannot make a radiative transition to the other hf level of the groundstate (which is inaccessible to laser excitation) as a consequence of the optical selection rule AF = 0 or ± 1. However, when the laser is tuned to the ( F ' = 2 , - F = 2) line, each excited atom can spontaneously decay to either of the hf ground state levels. Those decaying to the (F = 1) level will stay there forever, i.e., they are trapped. After a sufficiently large number of excitation-deexcitation cycles all atoms will become trapped. This number depends on the laser beam intensity and on the transit time ttr of the atoms through the laser beam. There is thus an upper limit to the total number of fluorescence photons that are emitted by each atom during ttr. This upper limit is reached at large values of laser intensity and/or ttr. The fluorescence emitted from the whole illuminated volume of the atomic beam will then no longer increase with increasing laser intensity. Consequently, a plateau is found in the saturation curve (SC), which lies below the plateau associated with optical saturation (cf. Appendix). When the laser intensity is not that high, the fluorescence emission will still grow with laser intensity, for a given value of ttr. Figure 4(a) shows SC's calculated under typical atomic-beam conditions; these curves relate the fractional excited-state density n2/n T to the spectral volume density Pv0 of a circular-polarized (¢ +) broad-band laser beam tuned to the (F' = 3 *- F = 2) line. (Here nT refers to the total density of atoms in the laser-coupled hf levels only.) The term broad-band means that the laser bandwidth is large relative to the natural line width but still less than the frequency separation of the hf lines. In the calculations we have taken into account the polarization of the laser-coupled degenerate F-levels, which consist of (2F + 1) Zeeman sublevels with magnetic quantum numbers M -- - F , - F + 1. . . . . F - 1, + F . t When an unpolarized atom enters the laserbeam, the Zeeman sublevels tAtom polarization is characterized by the relative population distribution over the Zeeman sublevels of a given level and relates to the directional distribution o f the atomic F-vector. Special cases are orientation and alignment.

Laser atomic spectroscopy in flames, gases and beams

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103mW/cm 2

"E Fig. 4. Saturation curves (SC) relating to an atomic N a b e a m / n vacuo orthogonal to a polarized cw laser beam tuned to one of the fiyperfine (hf) components of the Na-D 2 line. Figure (a) shows the fractional population n2/n T of the excited hf level, calculated as a function of the spectral volume density p,, in a o~+ polarized b r o a d - b a n d laser beam tuni~d to the (F' = 3 *- F = 2) fine. Curve I, which conforms to an ideal SC, was calculated assuming that the atom polarization has attained its steady-s~te (SS). Curve II relatesto the case of a finite transit time t, = 6/is of the atoms in the laser beam; in this case SS atom polarization is not reached on the Iow-inteusity branch, resulting in less efficient excitation. Dashed curve III is the fluorescence SC, calculated under the same conditions as the previous curve when the fluorescence is observed in a direction perpendicular to the laser beam. The plateau of curve lII is scaled to that of curve II. Its low-intensity branch deviates from that of curve II because the non-SS atom polarization and thus the anisotropy of the fluorescence emission vary with laser intensity. Figure (b) shows experimental SCs with a n a r r o w - b a n d , ~ + or ~ polarized cw dye-laser beam, as observed in a direction perpendicular to the laser polarization vector. (This vector is parallel and orthogunal to the laser beam axis in the case of o and ~ polarization, respectively.) The same relative fluorescence intensity (IF) scale is used for all curves. The experimental laser irradiance (E) scale has been matched to the P,0 scale at the top. Curve I ( O ) and curve 2 ( x ) relate to the case o f a ~r- and ~-polarized laser beam, respectively, tuned to the (F' ffi 3 *- F = 2) line, with ttr = 6 #s. The points (El) on curve 3 were measured using a ~-polarized laser beam tuned to the (F' - - 2 ~ F = 2 ) line, with ttr= 10#s. Drawn curve 3 is calculated while taking into account atom trapping in the (F = 1) hi' ground-state level, and fitted to the experimental points. Note the strong depression of the plateau and the apparent shift of saturation parameter of curve 3 in comparison with curve 1. Drawn curve 1 represents the best-fit of theoretical curve III to the experimental points. Dashed curve 2 is drawn smoothly through the experimental points only. Note the inversion at the high end of this curve, which is caused by partial atom trapping following spurious excitation of the ( F ' = 2) level due to spectral wing overlap. (According to calculations and measurements by H. A. J. Meijer at our laboratory and reproduced from Ref. 13.)

of each ground-state level are uniformly populated. Absorption of a ~ + polarized laser photon promotes the atom from any of the sublevels of the (F = 2) level to a sublevel of the (F' = 3) level whose magnetic quantum number M' is one unit larger (AM = + 1). This promotion to a higher M' number in combination with the selection rule A M = 0 to _+ 1 for spontaneous decay to the initial (F -- 2) level favours the population of sublevels with high M or M' numbers at the cost of those having low M or M' numbers. This population enhancement grows gradually with increasing number of repetitive excitation-deexcitation cycles experienced by the atom in the laser beam. A steady-state (SS) atom polarization is attained at sufficiently large values of laser intensity and/or tt,. In the above considered case all atoms are finally found in either the sublevel with highest quantum number M' -- + 3 of the (F" = 3) level or in the sublevel with highest quantum number M -- + 2 of the (F = 2) level. (The F-vectors are then oriented along the Z-axis.) The ideal SC

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calculated [through Eqs. (A1) and (A2) in the Appendix with Y = 1 and g~ = g2 = 1] for this steady-state is shown by curve I in Fig. 4(a). At a restricted transit time, an SS atom polarization may not be attained in the range of low laser intensities; the atom polarization will then change with laser intensity. Since the so-called directional Einstein coefficients 13'34 for absorption- and stimulated-emission transitions between specific Zeeman sublevels depend on M and M ' , the overall rate constant for laser-induced (de-)excitation depends on the atom polarization. These overall rate constants are thus themselves functions of laser intensity through the laser-dependent atom polarization in the low-intensity range. This, in turn, distorts the shape of the SC. Curve II in Fig. 4(a) shows the calculated effects of non-steady-state polarization on the SC (for experimental details, see caption). Since in this case the excited-state population n 2 varies with time spent, or distance covered by the atom at constant velocity in the laser beam, we have plotted along the ordinate axis the time- (or volume-) averaged value of n2InT. This value is proportional to the intensity of fluorescence emitted from the whole illuminated volume of the atomic beam. The low-intensity branch of curve II, where SS atom polarization has not yet been attained, lies below that of curve I. This is explained by the fact that in this range the overall Einstein coefficient for absorption is smaller than the corresponding directional Einstein coefficient for the specific (F' = 3; M ' = + 3 ~ F = 2; M = + 2) transition that applies to curve I. The high-intensity branch of curve II (where a SS atom polarization is attained shortly after the atom has entered the laser beam) approaches to curve I. The saturation parameter of curve II is therefore apparently shifted to the right. Another effect of non-steady-state atom polarization occurs in tbefluorescence SC with I F being observed in a selected direction. The variation of atom polarization with time spent by the atom in the laser beam causes not only a time-variation of the polarization o f the fluorescence but also a varying directional distribution or anisotropy of its intensity. Curve III in Fig. 4(a) shows the calculated effect on the fluorescence SC (for assumed observation conditions, see caption). The low-intensity branch o f curve III, whose plateau is scaled to that of curve II, lies slightly above that of the latter curve. Curves 1, 2 and 3 in Fig. 4(b) are experimental SC's obtained with a ~r or it polarized narrow-band cw dye-laser beam tuned to either the (F' = 3 *- F = 2) or (F' = 2 , - F = 2) hf line (for experimental conditions, see caption). The experimental irradiance E scale is matched to the theoretical P,0 scale at the top, using the known spectral profile of the absorption line. No spectral selector was inserted in the detection channel so that all emitted hf lines were detected. Curve 1 fits well to curve III calculated under similar conditions, which proves that a t o m trapping was absent here. The strong effect of atom trapping in the (F = 1) hf level of the ground-state is clearly demonstrated by curve 3 representing the SC for the ( F ' = 2 , - F = 2) line. The plateau as well as the apparent saturation parameter of this SC lies about two orders below those of curve 1, in accordance with theoretical calculations (compare best-fit theoretical curve 3 with the experimental points). Saturation curve 2 was measured under the same experimental conditions as curve 1 except that here the laser was linear-polarized. The inversion at the high end o f curve 2 is explained by spurious atom trapping in the (F = 1) level following nonresonant excitation of the (F' = 2) level due to spectral wing overlap o f the (F' = 3 ,--F = 2) and (F' = 2 ,,-F = 2) lines. With a ~r+ polarized laser beam, this overlap does not lead to excitation of the (F' = 2) level because of the selection rule AM = + 1 and because at SS atom polarization all (F = 2) atoms are found in the (M = + 2 ) sublevel. For a more detailed discussion we refer to Ref. 13.

3. E P I L O G U E Here we present some annotations on the above described experiments and, more generally, on laser-induced fluorescence spectroscopy, and draw a few conclusions about their implications for

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laser-diagnostics. Since the items to be discussed are rather loosely connected with each other, we have grouped them under various subheadings, although some overlap could not be avoided.

3.1. Overall discussion 3.1.1. Intercomparison of the experiments. In each experiment the measuring conditions were chosen such that the effect studied stood out most clearly. Nevertheless, various effects may have concurred together in the same experiment. Here we discuss the extent to which they might have interfered with each other. ~ For example, the effects described in Secs. 2.3 and 2.4 are essentially based on and discussed in relation to the hf structure of the atomic states involved. The hf structure also could have had consequences for the distortions of the fluorescence-emission spectra discussed in Secs. 2.1 and 2.2. However, these distortions were measured at considerably higher gas pressures so that the structures found in the emission spectra were much broader than the hf splittings of the Na-D lines. Also, collisional mixing of the hf (sub)states swamped out here the trapping and polarization effects studied in the other experiments. Although the laser detuning A was about the same in experiments A and B, the intensitydependent Mollow splittings observed in A did not occur in the other experiment done at a much lower laser intensity. Only the Rayleigh line near the laser-excited doublet component persisted, whereas the Raman line near the other component was absent because its intensity drops more steeply than linearly with decreasing laser intensity. It can thus be assumed safely that the frequency distance fV/2n between the centres of the Rayleigh and adjacent fluorescence lines was indeed equal to IAI in experiment B [cf. Eq. (1)]. In experiment C relating to the distortion of the excitation profile, we measured the spectrally integrated emission intensity, including the Rayleigh and,CIF lines. It can be shown theoretically that this intensity is an unambiguous measure for the population of the Na-D level concerned, irrespective of the partitioning of the emission over the two lines3s'~9 Since the emission intensity was measured in a particular direction, the only assumption to be made at/)2 excitation was that the polarizations and thus anisotropies of the two components did not change with laser detuning. This assumption is reasonable in regard to the small detuning range used and the results reported in Ref. 31 on the A-dependence of the Na-D2 and Rayleigh polarizations in a N2-diluted flame. The typical effects of non-steady-state atom polarization on the fluorescence intensity, that occurred in atomic beam experiment D, are not likely to have played a role in the other, bulk gas experiments. The longer residence time of the Na atoms in the laser beam at gas densities above 3 x 10m7cm -3 and collisional mixing of the hf (sub)states are responsible for that. 3.1.2. Saturation curves (SC). In contrast to experiment D, which covered the SC from its initial linear asymptote to its final plateau, saturation was deliberately avoided in experiments B and C, whereas the Mollow splitting was observed m experiment A under saturation conditions. Here we discuss theoretically to what extent the effects A, B, and C might influence the shape of the SC. For simplicity, we assume that homogeneous (natural and/or collisional) line broadening is dominant over Doppler broadening. 2 The shape of the ideal SC and the position of its plateau are then independent of the spectral laser profile and are thus the same as described in the Appendix for a broad-band laser. However, when a narrow-band laser is used, the saturation parameter depends sensitively on the (fixed) detuning A, if it exceeds the width of the spectral line. Under the conditions of experiment C one could expect a distortion of the SC for the Na-D doublet, which sets in already at the linear branch. This holds because the relative effect of atom trapping on the fluorescence intensity increases with increasing irradiance before saturation is attained (see Fig. 3). This distortion is largest when the laser is tuned to one of the hf doublet components and is dependent on the gas pressure. At the plateau, the lifetime of the excited state is reduced by the enhanced rate of laser-stimulated deexcitation (which dominates the rates of spontaneous emission and quenching collisions). This could affect the plateau when the degree of polarization and thus the anisotropy of the fluorescence depend markedly on lifetime (of. See. 2.2) in case the fluorescence is observed, as usually, in a certain direction. Saturation can occur not only in CIF but also in scattering, even when more than one laser photon is involved in the latter process. We consider here the case of an atom with only two energy

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levels with statistical weights gm--g2--1, embedded in a gas and excited by a near-resonant monochromatic laser beam such that the Mollow fines are well separated. Expressions for the emission intensity as a function of laser intensity (oc fF; see Sec. 2.1) are presented in Refs. 14, 15 and 26. It follows from these expressions that the SC of the Rayleigh line(comprising both its coherent and incoherent parts; see Sec. 2.1) has the same shape as the ideal SC in the Appendix and is independent of collisions. The saturation parameter is given by (fF) s = (2~A) 2 (in the notation of Sec. 2.1), whereas the density n2 of excited atoms is half the total density nT at the plateau [cf. Eq. (A1) with gl = g2 in the limit of infinitely high laser intensity]. In the experiment described in Sec. 2.1 the ratio of the maximum fl value to A (both expressed in the same wavelength units without a factor 2~) was 2.4. The maximum laser intensity was thus six times larger than the saturation parameter, so that the Rayleigh line was fully saturated. (Under this condition the R line is also fully incoherent.) The SC of the Mollow triplet as a whole conforms to the ideal SC, whether line broadening collisions are present or not. In the latter case the saturation parameter is twice as large as that for the Rayleigh line alone. The saturation parameter decreases, however, with increasing collisional line width 70 (which is proportional to the gas density), since the rate of excitation in the line wing (JAJ>>70) increases with increasing 70 at fixed A. (The condition IAI >>70 is implied by the above assumption that the Moltow lines are well separated.) These considerations hold only in the impact limit of the collisional line broadening theory, which implies that both 12nAI and fl should be small compared with the inverse duration of a collision. ~4J5 Note that 2~0 is of the order of the inverse intercollision time, so that IAJ may still largely exceed 70. Also, the effect of quenching collisions was disregarded here. 3.1.3. Collision effects. Collisions played an important role in the appearance of the phenomena studied in Secs. 2.1, 2.2 and 2.3, whereas absence of collisions was a favourable condition for a clear demonstration and simple interpretation of the effects studied in the atomic beam experiment in Sec. 2.4. The roles played by the various kinds of collision processes were, however, quite different in experiments A, B, and C. In experiment A, Na-D doublet mixing collisions were essential to observe the Mollow splitting at the D line that was not directly excited by the laser. In flame experiment B, doublet mixing collisions were also essential to measure the intensities and degrees of polarization of both doublet lines at the same time when only one of them was laser-excited, in order to compare them with theoretical predictions. Besides, the intensity of the D line that was not laser-excited could here be used to normalize the CIF intensity of the other D line in the subtraction procedure (see Fig. 2). In experiment A a special kind of collision, called optical collisions, played a decisive role in the dependence of the total intensity of the Mollow triplet on the laser intensity. Quenching collisions were absent in experiment A where a noble gas was used, so that the experimental results could be compared with existing theoretical calculations. In experiment B partial quenching of the CIF line in the N2-diluted flame was essential in order to observe a non-zero degree of polarization of the laser-excited De line. Collisional line broadening was a prerequisite in experiment B in order to observe a CIF fluorescence line distinct from Rayleigh scattering. Without line broadening collisions, only a Rayleigh line with the same spectral profile as the laser profile would be observed (we disregard trivial Doppler broadening). This is a consequence of the energy conservation law when collisional energy cannot make up for the difference in energy of the absorbed and reemitted photons (see also Sec. 3.1.4). Line broadening collisions are also responsible for the enhancement of the intensity of the F line relative to that of the R and T lines in the Mollow triplet, as described in Sec. 2.1. (It is recalled that the R line intensity is not affected by collisions.) Collisional line broadening would also have suppressed the hf atom trapping effect investigated in experiment C, if the gas pressure was not chosen extra low. Gas-kinetic collisions, determining the diffusion coefficient of Na atoms in the gas, influenced the extent of the hf atom trapping effect in experiment C. This influence depends on the gas pressure, which was varied in the experiments fully reported in Ref. 32. Diffusion here, and in experiment B, also played a role in determining the residence time of the Na atoms in the laser beam and consequently in the attainment of a steady-state atom polarization (cf. Sec. 2.4).

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Collisional mixing of the Zeeman substates resulted in a partial depolarization of the C I F / ) 2 line at D, excitation in experiment B. The rate o f atomic disalignment (see also first footnote in Sec. 1) in N~-diluted flames has been determined from similar polarization measurements as in experiment B. 31

Finally, collisional mixing of the hfstates justified the neglect o f hf structure effects in experiments A and B, but was kept sufficiently weak in experiment C in order to demonstrate the effect of hf atom trapping on the fluorescence-excitation profile. In the interpretation of atomic beam experiment D the absence o f hf mixing was an essential condition. 3.1.4. Fluorescence versus scattering. In the literature there is some ambiguity in the use of the terms fluorescence and scattering o f radiation, as applied to free atoms or molecules. 2 In Ref. 7, for example, the former term is used when absorption o f a photon results in the population of a real atomic state, which may decay to a real lower state by spontaneous emission of a photon with the same or a different frequency. There is a delay between the absorption and reemission acts, which equals the lifetime of the upper state. The scattering term is then used when absorption of a nonresonant photon raises the atom to a virtual state, followed immediatelyt by, for example, the reemission of a photon with the same frequency (Rayleigh or elastic scattering) or a different frequency (Raman or inelastic scattering). In these examples scattering is thus a two-photon process leading to destruction o f a (laser) photon and creation o f a (Rayleigh or Raman) photon in a single step.:~ As an example of a three-photon scattering process we mention the emission o f the three-photon line (T) in a strong, near-resonant monochromatic laser field (see Sec. 2.1). By this process the atom is raised in a single step from the ground-state, via two virtual states, to a real excited state, from which it may return at a later instant to the ground-state under emission of a photon in the fluorescence line (F). The collision-induced fluorescence (CIF) emitted at the centres of the Na-D lines, after absorption of a nonresonant laser photon in the wing of the collisionallybroadened line profile, is another example in which the term fluorescence clearly applies. (Fluorescence is thus not restricted to the case of (near-) resonant excitation.) Only when the fluorescing species occurs in very low concentrations, resonant laser-excitation may be mandatory to obtain a detectable signal. Conversely, a detectable Rayleigh or Raman signal with a laser that is far off-resonant is usually obtained only with major species in flames or plasmas. (We disregard here the advantages of coherent Raman spectroscopy.) Problems as to the consistent distinction between fluorescence and scattering in terms of real and virtual intermediate states could arise when the exciting laser beam is tuned to resonance with an atomic transition (VL -- V0). The virtual state then coincides with the real excited state. In the case of a weak monochromatic laser beam (i.e., no Mollow splitting) and in the absence of collisions, then only a monochromatic Rayleigh line is emitted at v0 (we disregard trivial Doppler broadening). In contrast to the case of off-resonant excitation, there is now a delay time equal to the natural lifetime ~N ( = / l - I ) between absorption of a laser photon and subsequent emission of a Rayleigh photon. Emission o f a fluorescence line distinct from the Rayleigh line occurs only in the presence of line broadening collisions (as in experiment B). One should be careful in discussing delay times, because their measurement requires essentially some sort o f intensity-modulation of the incident beam, e.g., by a stepwise or pulselike function of time. The intensity-modulated beam is, however, no longer strictly monochromatic. In the case o f an off-resonant laser the spectral profile o f the modulated beam (determined by Fourier transformation of the modulation function) may extend over the atomic line. We can then expect in the scattering spectrum a component at v0, besides o f the Rayleigh line at VL ( # V0)- Whereas the delay time o f the Rayleigh component is still very short, that o f the former component equals ~s. One could measure the latter delay time separately, e.g., by choosing the width o f the modulation pulse long compared to the inverse detuning A- mbut still short compared to ~N. A filter tuned at v0 can then be used to select spectrally the component with the longer delay time from the Rayleigh component. tThat is, within a time interval of the order of A-I) 5 ~/Thepopulation and lifetimeof the intermediate (virtual) state of the bare atom (consideredseparate from the laser field --in contrast to the dressed-atom introduced in Sec. 2.I--and from any collision partner) are not well-defined.This state is assumed to lie above the initial state at a distance equal to the (mean) energy of the absorbed photon in order to obey the law of energy conservation. Q.S.R.T. 40/3--0

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For a related quantitative discussion of the time- and frequency-dependence of nearly resonant light scattering, we refer to Ref. 36. Still in the absence of collisions but with a strong, monochromatic laser tuned to (near-)resonance, a distinct "fluorescence" line (F) may show up in the spectrum of the Mollow triplet (see Sec. 2.1). The appearance of this line requires the simultaneous absorption of two laser photons and emission of a T photon. It is thus essentially part of a scattering process that becomes relatively unimportant when the laser intensity is low. If the laser is in resonance with the atomic line centre, the distinction between an F and a T line actually becomes meaningless. These lines are then located symmetrically on opposite sides of the R line and thus of the atomic line centre, at a distance fl'/21r[ = f~/21r; see Eq. (1)] from v0, and have equal intensities. They merge with the R line when the laser intensity (ocfl 2) becomes low. It should be stressed that the theoretical description of the Mollow triplet at (near-)resonant excitation requires essentially the use of the dressed-atom model, in which a distinction between real and virtual states of the (bare) atom makes no sense at all. Because of the above mentioned failures to distinguish unambiguously, in the absence of collisions, a real state from a virtual one, at low as well as high laser intensities one should not use these concepts to distinguish between fluorescence and scattering processes. It is therefore proposed here to identify "true" fluorescence with collision-inducedfluorescence (CIF). It can be distinguished from "true" scattering by its collisionally broadened spectral profile and by the dependence of its excitation rate on the wings of the coUisi0nally broadened absorption line profile in case of non-resonant excitation and, possibly, by its dependence on quenching collisions. Line broadening collisions destroy also the coherence between the fluorescence radiation and the incident radiation. (This coherence is a characteristic of Rayleigh scattering.) The naming of the Mollow "fluorescence" line (F) at near-resonant, strong excitation has only a purely conventional meaning, at least in the absence of collisions. It is only based on the proximity of this line to the atomic line centre. Although the observability of the Raman line (Rm) at the D component that is not laser-excited depends on doublet-mixing collisions (see Sec. 2.1), its emission is still to be considered as a true scattering process. Mixing collisions are only prerequisite to prepare Na atoms in this D state. This state then acts as another initial state in the scattering process. Of course, mixing collisions may be accompanied by line broadening collisions (and may even contribute themselves, for a smaller part, to collisional line broadening2). But this introduces only a practical, not conceptual complication in the terminology. Finally, in the absence of collisions all reemitted radiation is to be called scattering. Absorption and scattering occur then in a single-step radiative process) although there may be a time delay between them at resonant excitation. The presence of a time delay does not exclude per se coherence between the absorbed and scattered radiations. One should only be cautious when one wants to observe this time delay without destroying coherence. In the case of resonant excitation, the usual term resonant Rayleigh (and Raman) scattering, in distinction from fluorescence, remains meaningful, when these terms are interpreted in the above proposed sense. Some authors use either the term fluorescence or scattering also in a broader sense to denote the total spectrum of the radiation emitted by the atom after absorption of a photon. In fact, we did so too, in the title of this paper and in Sees. 2.3 and 2.4, as the distinction here between fluorescence and Rayleigh scattering proper was irrelevant.

3.2: Implications for laser-diagnostics Collisions of the probe atom with the (major) gas constituents couple, on the one hand, the state of the atom to the state of the gas. On the other hand, collisions may influence the coupling of the atom to the laser field. Collisions thus play an important double role in laser-diagnostics, depending on whether one is interested in the state of the probe species themselves or in the state of the gas in which they are embedded. It is also important to know which laser-induced radiation processes are independent of (certain kinds of) collision processes. For example, the Rayleigh scattering and saturated fluorescence intensities are not influenced by collisions, at least if we exclude in the latter case certain collision processes or chemical reactions that may deplete atoms from the laser-excited level or affect the fluorescence anisotropy (cf. Sec. 1). We have therefore stressed in the foregoing discussions the influence of the gaseous environment

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on the reported LIF experiments. Here we summarize, point by point, the main conclusions that can be drawn with regard to the determination of Doppler temperatures and probe species densities. 3.2. I. Determination of Doppler temperatures. In the case of a Maxwellian velocity distribution, the width of a mainly Doppler-broadened fluorescence line or of a scattering line reveals the translational (or gas-kinetic) temperature of the gas. One can derive this width either in the emission mode by measuring the spectral emission profile (which may require a rather costly spectral analyser) or in the excitation mode by measuring the spectral excitation profile (which requires only a tunable narrow-band laser). In general, the use of a resonantly excited fluorescence line offers the advantage of higher intensity, but its line width has to be corrected, by deconvolution, for additional collisional (and natural) broadening or for partial overlap of neighbouring hf components. When a strong narrow-band laser is to be used, hole-burning in the velocity-distribution 2 could be a complication if the emission is not observed strictly at right angles to the laser beam. Mollow splitting at monochromatic, near-resonant excitation or power broadening with a broad-band laser can be easily avoided by restricting the laser intensity. But even in the case of a weak near-resonant, monochromatic laser the superposition of the Rayleigh line on the fluorescence line profile could be a nuisance, especially so when their line centres do not coincide (as in experiment B). However, if coUisional broadening is negligible and the observation direction is perpendicular to the laser beam, the resultant radiation has a single Doppler profile at resonant excitation. In the case of the Na-D doublet this problem can be avoided by analysing the spectral profile of the other D line that is excited by mixing collisions (see experiment B). Of course, the problem of contamination by a superimposed Rayleigh line in the emission mode can also be simply avoided by using off-resonant excitation, be it at the price of a much lower fluorescence intensity. When the Doppler width of a fluorescence line is to be determined in the excitation mode, the possible distortion of the excitation profile by hf atom trapping (see Sec. 2.3) should be attended to. This distortion can be simply suppressed by keeping the laser intensity sufficiently low, at the cost of fluorescence intensity. In the emission mode, Doppler temperatures are more straightforwardly determined by analysing the spectral profile of the Rayleigh line with the user of a monochromatic laser. Full Doppler width is, however, found only if the observation direction is precisely perpendicular to the laser beam. Off-resonant excitation is recommended to avoid overlap with the fluorescence line profile, but then the Rayleigh intensity drops ~ A -2. The Rayleigh intensity relative to the fluorescence intensity is also improved in strong-quenching milieus (cf. Sec. 2.2). The main advantage of this method is that the Rayleigh profile is not smeared out by collisional or natural line broadening. (The incoherent, broadened part of the Rayleigh line is negligible if (~/A)2<
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emitted radiation. Whatever method is used, one should avoid or correct for depletion of laser-excited atoms by certain coUisional and ionization processes or chemical reactions when one is interested in absolute density values (see Sec. 1). The use of Rayleigh scattering has the advantage that its intensity, polarization, and anisotropy are independent of collisions. Therefore, one does not need to know the gaseous conditions or collisional rate constants in the determination of absolute or relative densities. This advantage ceases to hold, however, when the Rayleigh line is (near-)resonantly excited, as its excitation profile then conforms to the absorption line profile, which depends on collision broadening (see Sec. 3.1). Rayleigh scattering is, in principle, also subjected to saturation at high laser intensities (f12 ~>A2). This offers the advantage of independence of (variations in) the laser intensity. But, since offresonant excitation, i.e. large A values are preferred (see preceding paragraph), the occurrence of saturation is not likely. Anyway, it may be wise to check the linear relationship between Rayleigh intensity and laser intensity when the usual equation for the absolute Rayleigh intensity is to be applied at high laser intensities. The determination of relative density values at constant laser intensity, no matter how large, is not affected by the onset of saturation. Hf trapping of atoms (accompanied by a Raman-like transition to the unexcited hf ground-state level of the Na atom) is unlikely to occur at off-resonant excitation (cf. Sec. 2.3). This holds true not only because the excitation rate is then low anyway but also because Raman scattering by atoms in either of the hf levels is then about equally strong. The use of a fluorescence line in density measurements is more precarious. The anisotropy of the fluorescence emission, associated with its polarization if any, may be influenced by depolarizing collisions, which should be allowed for when fluorescence is observed in a given direction (see Sees. 1 and 2). (The fluorescence power integrated over all space directions is, however, independent of such collisions.) Even when one wants to measure only the population ratio of the two Na-D levels, resulting from laser-excitation, errors may arise when the (possible) polarization of the D2 line is disregarded [see Sec. 2.2 and Eqs. (2) and (3)]. Saturated fluorescence spectroscopy is the method-of-choice in LIF for absolute or relative density measurements. Complications that may arise in its application to real-world systems have been exemplified in Sec. 1. In low-pressure gases, attention should also be given to the effect of hf atom trapping on the fluorescence intensity and to the other special polarization and trapping effects discussed in S¢c. 2.4. The trapping effects can be avoided by using a broad-band laser, however. When at near-resonant excitation a distinct Rayleigh line appears in the vicinity of the fluorescence line, one does not need to separate them spectrally; the intensity of the two lines together is a measure for the excited state density independent of their intensity ratio. The different polarizations and anisotropies of the lines should, however, be attended to when the direction of observation is changed (see above). This complication does not exist when the Na-DI line is (near-)resonantly excited by a linear-polarized laser beam; then the Rayleigh and fluorescence lines of both D components are essentially unpolarized. When a strongly polarized Rayleigh line is to be detected alone in diagnostic applications, in the presence of a neighbouring fluorescence line, a polaroid may be inserted in the detection channel that is oriented along the polarization axis of the Rayleigh line in order to improve the relative Rayleigh intensity. One should also attend to the optimal choice of laser polarization axis with respect to the observation direction. When combined with the spectral subtraction procedure mentioned in Sec. 2.2, one can so eliminate most efficiently the fluorescence line (or any other interfering line).

Acknowledgement--The authorwantsto acknowledgethe enlighteningdiscussionswithProfessorG. Nienhuisand A. R. D. van Bergen on some theoretical aspects of this work. REFERENCES 1. W. E. Baylis, Progress in Atomic Spectroscopy; Part A, pp. 207-261, W. Hanle and H. Kleinpoppen eds., Plenum Press, New York NY (1978). 2. C. Th. J. Alkemade, Tj. Hollander, W. Snelleman, and P. J. Th. Zccgers, Metal Vapours in Flames, Pergamon Press, Oxford (1982).

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3. K. J. B. M. Nieuwesteeg, Ph.D. Thesis (in English), Utrecht (1986). 4. S. S. Penner, C. P. Wang, and M. Y. Bahadori, Proc. 20th Symposium (International) on Combustion, pp. 1149-1176, The Combustion Institute, Pittsburgh, PA (1984). 5. M. Lapp and C. M. Penney, in Advances in Infrared and Raman Spectroscopy, Vol. 3, pp. 204-261, R. J. H. Clark and R. E. Hester eds., Heyden, London (1977). 6. M. C. Drake, R. W. Pitz, and M. Lapp, AIAA J. 24, 905 (1986). 7. Laser Probes for Combustion Chemistry, pp. 3-18, D. R. Crosley ed., American Chemical Society, Washington, DC (1980). 8. J. R. McDonald, in Laser Probes for Combustion Chemistry, pp. 19-58, D. R. Crosley ed., American Chemical Society, Washington, DC (1980). 9. Laser Probes for Combustion Chemistry, D. R. Crosley ed., American Chemical Society, Washington, DC (1980). 10. Analytical Laser Spectroscopy, S. Martellucci and A. N. Chester eds., Plenum Press, New York, NY (1985). 11. Analytical Laser Spectroscopy, N. Omenetto ed., Wiley, New York, NY (1979). 12. E. H. Piepmeier, Analytical Applications of Lasers, Wiley, New York, NY (1986). 13. C. Th. J. Alkemade, Spectrochim. Acta 4011, 1331 (1985). 14. G. Nienhuis, Acta Physica Polonica A61, 235 (1982). 15. G. Nienhuis, J. Phys. B 13, 2217 (1980). 16. R. A. van Calcar, M. J. G. Heuts, B. K. van Uitert, H. A. J. Meijer, Tj. Hollander, and C. Th. J. Alkemade, JQSRT 28, 1 (1982). 17. A. R. D. van Bergen, Tj. Hollander, and C. Th. J. Alkemade, JQSRT 33, 419 (1985). 18. C. Th. J. Alkemade, in 7th International Conference on Atomic Spectroscopy; Invited Lectures, p. 93, Sbornik VSCHT, Prague (1977). 19. A. R. D. van Bergen, M.Sc. Thesis, Utrecht (1980). 20. H. F. Arnoldus and G. Nienhuis, Opt. Commun. 48, 322 (1984) and 54, 95 (1985). 21. H. F. Arnoldus, Ph.D. Thesis (in English), Utrecht (1985). 22. B. R. Mollow, Phys. Rev. 188, 1969 (1969). 23. G. Nienhuis, Comments Atom. Molec. Phys. 11, 223 (1982). 24. A. R. D. van Bergen, Tj. Hollander and C. Th. J. Alkemade, in Proc, European Conf. on Optics, Optical Systems and Applications, Vol. 492, p. 110, SPIE, Bellingham, WA (1985). 25. A. R. D. van Bergen, Tj. Hollander, and C. Th. J. Alkemade, J. Phys. B., in press (1988). 26. G. Nienhuis, J. Phys. B 15, 535 (1982). 27. R. A. van Calcar, M. J. G. Heuts, B. K. van Uitert, H. A. J. Meijer, Tj. Hollander, and C. Th. J. Alkemade, JQSRT 26, 495 (1981). 28. G. Nienhuis Physica 95C, 266 (1978). 29. K. J. B. M. Nieuwesteeg, Tj. Hollander, and C. Th. J. Alkemade, IJQSRT 37, 141 (1987). 30. J. G. M. Em0nds, Ph.D. Thesis, Utrecht (1981). 31. K. J. B. M. Nieuwesteeg, Tj. Hollander, and C. Th. J. Alkemade, JQSRT 30, 97 (1983). 32. M. J. Jongerius, Ph.D. Thesis (in English), Utrecht (1981). 33. F. C. M. Coolen and N. van Schaik, Physica 93C, 261 (1978). 34. R. Altkorn and R. N. Zare, Ann. Revs. Phys. Chem. 35, 265 (1984). 35. G. Nienhuis, J. Phys. B 16, 2677 (1983). 36. G. Nienhuis, Physica 96C, 391 (1979). APPENDIX The observed intensity o f fluorescence IF induced by a resonant broad-band laser is proportional to the number density n2 (in cm-3) of excited atoms, if self-absorption is absent. In the steady-state, the dependence o f IF and n2 on the spectral irradiance E,0 (radiant power per unit frequency interval and per unit area) o f the laser beam is ideally given by 2't3

The constant o f proportionality between IF (expressed in photons per second) and n2 contains the Einstein coefficient for spontaneous emission A and purely geometrical factors, if we assume the fluorescence radiation to be isotropic. The quantity nr denotes the total density of atoms in the ground and excited state, while gt and g: are the corresponding statistical weights (a two-level atom model is assumed). The quantity ES~0, having the same dimension as Ev0, is given by E:o =

g---~

\ - - - ~ - ] -~.

(A2)

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C. Th. J. ALKEMADE

Here h--Planck constant, Vo= central frequency of the spectral line, c = light velocity, and Y = ej~ciency of fluorescence defined by A Y = .4 + k---~'

(A3)

where kq ffi (pseudo-)monomolecular quenching rate constant (in s -I). The above dependence of Ir or n2 on laser intensity is connected with the effect of optical saturation, caused by stimulated emission from the upper level, and is represented by the saturation curve (SC). The SC has a linear branch (IFocEvo) in the range of low laser intensities (Ev0<>E~0. According to Eq. (A1), n2--~ nTg2/(gl + g2) at the plateau. The SC attains half its plateau value at the "knee" of the curve where E~0 = ESv0; the saturation parameter thus marks the onset of saturation. The laser intensity may alternatively be expressed in units of radiant spectral volume density Pvo( =- E~o/c) or total radiant power P ( = E,0 integrated over the bandwidth and cross section of the laser beam). Experimental SCs are often plotted along a relative IF scale. When wavelengths are used instead of frequencies, the dimensions of the quantities marked by v are changed. Deviations from the ideal SC have been generally discussed in Ref. 13.