Multiphoton ionisation of rare gases by a CO, laser: electron spectroscopy

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1 J. Phys. B: At. Mol. Opt. Phys. 21 (1988) L159L164. Printed in the UK LETTER TO THE EDITOR Multiphoton ionisation of rare gases by a CO, laser: electron spectroscopy W Xiongt, F Yergeaut, S L Chint and P Lavigne$ t Departement de Physique, UniversitC Laval, QuCbec, Canada GlK 7P4 $ INRSEnergie, Varennes, Canada JOL 2PO Received 25 January 1988 Abstract. Spectroscopy of the photoelectrons emitted in multiphoton ionisation of Xe and Ne by a COz laser has been performed. Highenergy electron peaks corresponding to the processes leading to the production of Xe+, Xe2+ and Ne+ have been observed. It is found that the ponderomotive potential plays a major role in determining the energy of these electrons, but that ATI may also be important. Abovethreshold ionisation ( ATI) has been the subject of many investigations since its discovery nearly ten years ago (Agostini et a1 1979). Soon after the initial observation, an experiment showed that the first peak in the electron spectrum could disappear at high enough intensity (Kruit et az1983b). The origin of this socalled peak suppression has been the subject of much discussion. One physical phenomenon which has to be at least part of the answer is the ponderomotive force. This pseudoforce, actually a mechanism that converts quiver energy into translational kinetic energy, can be calculated by the singleparticle theory of Kibble (1966): f= (e2/4mw2)ve2 (1) where Eo is the electric field amplitude and w the frequency of the laser. To this conservative force? can be associated a potential given by U,= e2ei/4mw2. (2) Up to now several investigations, both theoretical and experimental, have been made of the relationship between ATI and the ponderomotive force (Hollis 1978, Kruit et a1 1983a, Bucksbaum et a1 1987). All experiments, however, involved wavelengths near the visible range. At 1064 nm, an intensity of 1013 W cm2 yields a ponderomotive potential of about 1 ev. Moreover atoms are not ionised at intensities much larger than this (that is, the ionisation is saturated before the intensity can reach much larger values) so that large ponderomotive potentials are not accessible at these wavelengths. Equation (2), however, shows that the magnitude of the potential depends on the square of the wavelength used. Use of a longer wavelength offers the opportunity of t It is strictly conservative only when the radiation field is nontimevarying, but can be considered as such. if the particles leave the field before it has had time to vary appreciably: the highintensity case of Hollis (1978) /88/ IOP Publishing Ltd L159

2 L160 Letter to the Editor probing much larger ponderomotive potentials, with the possible benefit of shedding new light on the ATI process. In this letter we present our observation of highenergy photoelectrons created in the ionisation of Xe and Ne by a CO, laser at A = 10.6 pm. The laser facility we used has been described elsewhere (Yergeau et a1 1987). Briefly, a single pulse of 1 ns duration at A = 10.6 pm is isolated by a Pockels cell from the train produced by a modelocked TEACO, oscillator. Up to a few tens of joules of energy can be obtained after amplification. The beam is focused by a 250 mm NaCl lens into a vacuum vessel which is pumped down to 1.3 x lo* mbar by a turbomolecular pump. The sample gas is leaked into the chamber to bring the total pressure to about 1.3 x mbar. A retarding potential analyser was used to measure the energy spectrum of electrons (figure 1). An accelerating field of about 35 V cm was applied between the first two plates. After passing the potential barrier set between plates 3 and 4, the electrons were detected by an electron multiplier tube (EMT). Laser focus \ c3 Figure 1. Schematic of the experimental apparatus showing the electrode structure comprising the electron spectrometer. V, is the retarding potential applied to block lowenergy electrons. The laser propagation axis is perpendicular to the plane of the page. The amplitude of the EMT output, which is proportional to the number of electrons collected, was plotted against the retarding potential V,. Because the output energy was not very stable, we performed the following data reduction: for a given V,, we let the laser energy fluctuate around a certain value Eo. For each shot we recorded the laser energy E and the corresponding number of electrons n, and plotted log( n) against log(e). Fitting a straight line in this plot, we estimated the effective number of electrons N at laser energy Eo, which is thus an interpolation using data taken at energies straddling Eo. The resulting set of pairs V,N is then processed in the following way to account 1 for the peculiarities of the retarding potential method used: first, the abscissa is corrected for the acceleration imparted to the electrons by the voltage between the first two plates; the abscissa thus becomes E,, the electron energy. Second, the resulting spectrum is slightly smoothed, using the well known 121 numerical filter (Bevington 1969), to remove imperfections in the data due to the very limited number of laser shots available. Third, the derivative dn/de, is taken, since it is this quantity, not the integrated spectrum that the retarding potential analyser yields directly, that is pertinent.

3 Letter to the Editor L161 Figures 2, 3 and 4 show the results of all this processing in three cases. The first two are with xenon as the sample gas and the third one is with neon. In all three figures, the top part shows the unsmoothed integrated spectrum, i.e. the raw data, while the bottom part shows the derivative of this spectrum after a small number of smoothing passes have been applied to it. The vertical scales for these two parts are both arbitrary. Figure 2 is for xenon when the laser energy is such that only single ionisation takes place. The spectrum consists of two peaks, one at low energy, and one spanning the range from about 250 to 350eV. The lowenergy peak is attributed to ionisation of impurities present in the vacuum chamber in addition to the Xe sample gas. We could actually vary its importance relative to the second peak by adjusting the purity of the xenon intake. The second peak is attributed to Xe itself. These two peaks are also found in figure 3, where the laser energy has been increased so that double ionisation could occur. Note that the two first peaks are wider and that a new peak appears, centred around loooev, which is attributed to the photoelectrons coming from the second ionisation of Xe. Figure 4 shows the case of Ne at a laser energy such that only single ionisation takes place. The lowenergy peak is still impurities, the wide peak around 1100 ev is that of Ne+ and the last one above 2000 ev is unaccounted for. Note that the poor quality of the data does not preclude the possibility of a single peak extending from 1000 to 2500 ev. How such spectra come about can be partly understood if one considers the following. Due to the very high nonlinearity of the ionisation process, an atom will be ionised as soon as the laser intensity at its location reaches the saturation value I,; below I, there is almost no ionisation at all and above I, there are almost no atoms c e C O a L Cl $ 1.5. m vl n LOO Electron energy lev) Figure 2. Spectrum of Xe at peak laser intensity of about 5x loi3 Wcm*. The top part of the figure shows the electron signal as a function of electron energy, processed as explained in the text but unsmoothed. The bottom part shows the derivative, still unsmoothed. 600 r ;i 200 c 3 F 100 e C O a L 0. e 1.5. m Y) I 1 I A Electron energy lev) Figure 3. Spectrum of Xe at a peak laser intensity of about loi4 Wcm2. The top part shows the unsmoothed integrated spectrum, while the bottom part shows the derivative after two smoothing passes.

4 L162 Letter to the Editor "B Electron energy (ev1 Figure 4. Spectrum of Ne at a peak laser intensity of about 1.3 x lol4 W cm2. The top part shows the unsmoothed integrated spectrum. while the bottom part shows the derivative after three smoothing passes. left to ionise?. Thus ionisation always occurs in a thin shell around the focal point in which Z = I,, and this shell expands with time during the rise of the laser pulse. At the moment it is ionised, an atom will eject an electron, which may have some translational kinetic energy, but will also be quickly accelerated by the ponderomotive force$. It is a simple matter to show that, in our case, the acceleration is large enough and the laser beam waist small enough that the electron moves out of the focal volume in a time much shorter than the pulse duration. Thus an elctron initially emitted at space coordinates (ro, zo) will be accelerated by a field 'frozen' at time to, with an intensity distribution Z(r, z, to) where to is determined by the relation Since the force is conservative in this case, the electron will acquire translational energy equal to the ponderomotive potential at point ( ro, zo), which can be estimated if we know the value of I,. This value for the first ionisation of Xe has been measured as I, = 1.88 x 1013 W cm2 at the slightly different wavelength of pm by Yergeau et a1 (1987), and is in good agreement with a statistical estimate made by Crance t This particular characteristic of multiphoton ionisation using a CO2 laser is fully supported in Yergeau et al (1987), in connection with ion yield experiments. $ Actually, the ponderomotive force will transfer the quiver energy that the electron must have to exist in the field into translational kinetic energy. 8 The actual values in our case are from a private communication.

Letter to the Editor L163 (1984a, b, c, d)o. The corresponding values for the second ionisation of Xe and the first ionisation of Ne are 8.75 x 10" and 7.0 x loi3 W cm2 respectively.

5 Letter to the Editor L163 (1984a, b, c, d)o. The corresponding values for the second ionisation of Xe and the first ionisation of Ne are 8.75 x 10" and 7.0 x loi3 W cm2 respectively. For these values of I, and a wavelength of 10.6 pm, the kinetic energies acquired by the photoelectrons are 190,884 and 707 ev respectively for the three cases discussed. This means that we should observe peak suppression up to and including these electron energies. Actually our spectra show peaks beginning at energies above these thresholds; thus our data are compatible with the above model, but this is not the whole story. Peak suppression continues above the limit determined by the ponderomotive potential, even if uncertainties in both the retarding potential (due to the imperfectly known position of the focal point between the first two plates) and in the value of saturation intensity, are taken into account. Furthermore, the observed peaks are very broad, and this is not accounted for by our treatment since we assume that ionisation occurs at a well defined intensity, which implies a single value for the ponderomotive potential. There are two ways out of this problem: first, we can drop the idea that ionisation takes place at and only at saturation intensity. Even though this hypothesis works well to account for ion yields against intensity (cf Yergeau et a1 1987), electron spectroscopy may be more sensitive to slight departures from this ideal situation. Ionisation taking place in a narrow range of intensities would produce a corresponding range of ponderomotive accelerations and peak broadening would ensue. Second, we can *assume that some form of abovethreshold ionisation (ATI) comes into play here, where the expression ATI is taken at face value, that is, it denotes the presence of photoelectrons of energies larger than the minimum required by energy conservation considerations (including the quiver energy represented by the ponderomotive potential). Simply stated, the electron would have some variable initial kinetic energy when it is emitted, and this energy would contribute to the width of the peak. The actual mechanism of ATI in this case may be quite different from the more familiar one observed in shorter wavelength experiments, but the ionisation process itself is also quite different, since only nonperturbative theories can describe it with any amount of realism. Actually, it is our belief that the present measurements of photoelectron energy could help discriminate between the different theories now in existence. Theories involving a tunnellike mechanism (Keldysh 1964, Perelomov er al 1966, Ammosov er a1 1986) are still around, as well as the related nonperturbative treatment of Reiss (1980). A model involving plasmon excitation has been proposed recently (Faisal 1987), but electron energy distribution calculations are lacking. The inverse halfbremsstrahlung model of Kupersztych (1987) seems to have the right behaviour, but needs a correct ionisation rate to be plugged in to be applicable in our case. In conclusion, we succeeded in obtaining the energy spectrum of electrons from the ionisation of Xe and Ne by an intense CO, laser. The impressively high energy of the electrons can be explained by the acceleration due to the ponderomotive force together with the possible addition of some form of ATI. We are currently making some computer simulations to try to separate the contributions of ponderomotive acceleration and ATI to the peak width. This work was supported in part by the Natural Science and Engineering Research Council of Canada and in part by Le Fonds FCAR de la Province de Quibec. One of us (WX) acknowledges scholarships from Universitt Lava1 and LROL. We would like to thank Mr Y Fortier for his expert help in the construction of the experimental apparatus and Mr F Ltvesque of INRSEnergie for the operation of the laser system.

6 L164 Letter to the Editor References Agostini P, Fabre F, Mainfray G, Petite G and Rahman N K 1979 Phys. Rev. Lett Ammosov M V, Delone N B and Krainov V P 1986 Zh. Eksp. Teor. Fiz (Engl. Transl Sou. Phys.JETP ) Bevington P R 1969 Data Reduction and Error Analysisfor the Physicd Sciences (New York: McGraw Hill) Bucksbaum P H, Freeman R R, Bashkansky M and McIlrath T J 1987 J. Opt. Soc. Am. B Crance M 1984a J. Phys.: At. Mol. Phys. 17 L b J. Phys. B: At. Mol. Phys c J. Phys. B: At. Mol. Phys d J. Phys. E: At. Mol. Phys Faisal F H M 1987 J. Phys. B: At. Mol. Phys. 20 L299 Hollis M J 1978 Opt. Commun Keldysh L V 1964 Zh. Eksp. Teor. Fiz (Engl. Trans Sou. Phys.JEW ) Kibble T W B 1966 Phys. Rev Kruit P, Kimman J, Muller H G and Van der Wiel M J 1983a Phys. Reu. A Kruit P, Kimman J and Van der Wiel M J 1983b J. Phys. B: At. Mol. Phys. 14 L597 Kupersztych J 1987 Europhys. Lett Perlemov A M, Popov V S and Terent ev M V 1966 Zh. Eksp. Teor. Fiz (Engl. Trans Sou. Phys.JETP ) Reiss H R 1980 Phys. Rev. A Yergeau F, Chin S L and Lavigne P 1987 J. Phys. B: At. Mol. Phys

Non-sequential and sequential double ionization of NO in an intense femtosecond Ti:sapphire laser pulse

J. Phys. B: At. Mol. Opt. Phys. 30 (1997) L245 L250. Printed in the UK PII: S0953-4075(97)80013-2 LETTER TO THE EDITOR Non-sequential and sequential double ionization of NO in an intense femtosecond Ti:sapphire