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Physical Review A

Resonant enhanced multiphoton ionization studies in atomic oxygen

S. N. Dixit, Deborah A. Levin, B. V. McKoy

Published Jun 1, 1988• 21 citations
Publisher

Abstract

In this paper we analyze two-photon-resonant three-photon ionization of atomic oxygen via the 2${\mathit{p}}^{3}$${(}^{4}$S\ifmmode^\circ\else\textdegree\fi{})${\mathit{np}}^{3}$${\mathit{P}}_{0}$,1,2, and the 2${\mathit{p}}^{3}$${(}^{4}$S\ifmmode^\circ\else\textdegree\fi{})nf $^{3}$${\mathit{F}}_{2}$,3,4 states. The various atomic parameters required for calculating the resonant enhanced multiphoton ionization (REMPI) probabilities are obtained using quantum-defect theory. The infinite sums over nonresonant states are truncated at a finite number of terms. Our calculated two-photon excitation cross sections agree well with the results of other recent calculations and of experimental measurements. The photoionization cross section is calculated for various electron kinetic energies. The REMPI dynamics is analyzed by solving the density-matrix equations. This framework consistently takes into account the effects of saturation and ac Stark shifts. REMPI probability is seen to be quite sensitive to the initial detuning, the intensity, and the particular resonant state accessed. The photoionization cross sections also imply that due to the rapid falloff of the cross section, two-color REMPI schemes with a lower-frequency ionizing photon would increase the effective REMPI probability.

DOI
10.1103/physreva.37.4220

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In this paper we analyze two-photon-resonant three-photon ionization of atomic oxygen via the 2{\mathit{p}}^{3}$${(}^{4}S\ifmmode^\circ\else\textdegree\fi{}){\mathit{np}}^{3}$${\mathit{P}}_{0},1,2, and the 2{\mathit{p}}^{3}$${(}^{4}S\ifmmode^\circ\else\textdegree\fi{})nf ^{3}$${\mathit{F}}_{2},3,4 states. The various atomic parameters required for calculating the resonant enhanced multiphoton ionization (REMPI) probabilities are obtained using quantum-defect theory. The infinite sums over nonresonant states are truncated at a finite number of terms. Our calculated two-photon excitation cross sections agree well with the results of other recent calculations and of experimental measurements. The photoionization cross section is calculated for various electron kinetic energies. The REMPI dynamics is analyzed by solving the density-matrix equations. This framework consistently takes into account the effects of saturation and ac Stark shifts. REMPI probability is seen to be quite sensitive to the initial detuning, the intensity, and the particular resonant state accessed. The photoionization cross sections also imply that due to the rapid falloff of the cross section, two-color REMPI schemes with a lower-frequency ionizing photon would increase the effective REMPI probability.
We have studied two-photon resonant three-photon ionization of atomic sodium vapor. A dye laser tuned to either the 4d or 5s two-photon allowed transition was used to excite the atom and a second more intense laser (λ = 7000 Å) was used for ionization. The ion yield was measured as a function of resonant laser intensity and detuning, the nonresonant laser intensity, and the temporal overlap of the exciting and ionizing laser pulses. We have found1 that at high laser intensities the photoionization yield decreases as the nonresonant laser intensity is increased. When tuned to the 5s level a value of ~−0.6 was obtained for the exponential index even with the resonant laser tuned to maximize the ion yield. A theoretical model including the effects of Stark shift of the ground state, power broadening of the intermediate level due to saturation of the two-photon transition and by rapid transitions to the ionization continuum was used to predict the experimental results. Good agreement between theory and experiment required the use of a photoionization cross section for the 5s level which was ~20 times greater than the accepted value. Results for photoionization from the 4d level are also presented.
The resonantly enhanced multiphoton ionization of atomic hydrogen is studied for the case of four-photon ionization (three-photon resonant). The time-dependent probabilities, the shape of the resonance profile at different intensities, and the nonlinear index are computed for coherent light at frequencies around the resonance (365 nm). The systematic dependence of the cross section as a function of the principal quantum number of the resonant state (as this tends towards the Rydberg states) is investigated at zero detuning. The probabilities of absorption of one photon more than necessary for the four-photon ionization process (resonantly enhanced above-threshold ionization) is computed and the relevant branching ratios are examined. Then it is shown that the effect of the spatio-temporal structures of the laser pulse is to red shift the maximum of the resonance profile, whereas that of an ideal chaotic light is to blue shift and broaden the resonance peak. The shape, shift, and width of the profile resulting from both these effects are in very fair agreement with the experimental ones.
Two-photon-resonant three-photon ionization of atomic phosphorus is studied in the 298--306-nm wavelength range. P atoms are produced by Ar+{\mathrm{Ar}}^{+}Ar+ ion sputtering of an InP solid sample and the photoions are detected by a quadrupole mass spectrometer. The laser power dependence of the 3p4{\mathit{p}}^{4}p4S3/20{\mathit{S}}_{3/2}^{0}S3/20​--4 4S3/20^{4}\mathrm{S}_{3/2}^{0}4S3/20​ two-photon excitation and one-photon ionization of 4p4{\mathit{p}}^{4}p4S3/20{\mathit{S}}_{3/2}^{0}S3/20​ phosphorus is determined in the 10--200 MW/cm2{\mathrm{cm}}^{2}cm2 range. The cross section for the ionization step is estimated in the frame of the quantum-defect theory: \ensuremath{\sigma}\ensuremath{\sim}3\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}18}$ cm2{\mathrm{cm}}^{2}cm2. The two-photon Rabi frequency ${\mathrm{\ensuremath{\Omega}}}_{\mathit{R}}$ is deduced from the comparison of our experimental results with the extended two-level model developed by Eberly [Phys. Rev. Lett. 42, 1049 (1979)] to describe (m+n) resonant multiphoton ionization processes and with the rate equation approximation analysis. The best fit gives ${\mathrm{\ensuremath{\Omega}}}_{\mathit{R}}$(${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$)=8IL{\mathit{I}}_{\mathit{L}}IL​(W/cm2{\mathrm{cm}}^{2}cm2). This value compares relatively well with the theoretical estimate ${\mathrm{\ensuremath{\Omega}}}_{\mathit{R}}$=5.5IL{\mathit{I}}_{\mathit{L}}IL​ obtained by limiting the perturbation-theory summation to the dominant intermediate states. The combination of well-characterized Ar+{\mathrm{Ar}}^{+}Ar+ ion sputtering of a solid sample with resonant photoionization is used to perform actual trace analysis of materials. For example, 0.5 ppm of phosphorus in a silicium sample was measured by this method with a lateral resolution of \ensuremath{\sim}300 \ensuremath{\mu}m.
We present both experimental and theoretical studies of resonantly enhanced multiphoton ionization of cesium atoms. Photoelectron angular distributions for two-photon ionization via the one-photon-allowed 7p2P12,327p^{2}P_{\frac{1}{2},\frac{3}{2}}7p2P21​,23​​ and 8p2P12,328p^{2}P_{\frac{1}{2},\frac{3}{2}}8p2P21​,23​​ intermediate states and three-photon ionization via the two-photon-allowed 8d2D52,328d^{2}D_{\frac{5}{2},\frac{3}{2}}8d2D25​,23​​ resonant intermediate states are reported. The photoelectrons are energy analyzed with a spherical-sector electrostatic energy analyzer with an energy resolution of ~ 0.1 eV and angular resolution of ~ \ifmmode\pm\else\textpm\fi{}2\ifmmode^\circ\else\textdegree\fi{}. A straightforward calculation based upon a finestructure scheme gives excellent agreement with the measured angular distributions for the 2P12^{2}P_{\frac{1}{2}}2P21​​ states. The laser pulse duration is comparable to the hyperfine precession period which allows the hyperfine coupling to partially destroy the anisotropy initially produced in the 2P32^{2}P_{\frac{3}{2}}2P23​​ resonant intermediate states. Quantitative calculations including hyperfine coupling take this into account and provide an expression which gives a reasonable fit to the 2P32^{2}P_{\frac{3}{2}}2P23​​ data.
Two investigations are reported on the application of resonantly enhanced multiphoton ionization (RMPI) to gaseous mixtures of an atomic vapor and a few Torr of argon. Photon fluxes large enough to ionize atoms by RMPI were produced by focussing down the light from a tunable pulsed dye laser. The irradiances generated were of the order of 500MWcm⁻². Ionization was detected by a voltage biased wire electrode that simply collected the photoelectrons either directly or after some gas multiplication. One investigation was the measurement of the dependence of RMPI processes in mercury on the polarization of the incident light for comparisons with theoretical calculations. The processes were four-photon resonant absorptions to either a ¹S₀ or ¹’³D₂ level followed by single photon ionization. Complete photoionization of all atoms excited to the resonant levels is established and the measured polarization dependences are found to agree with the calculated polarization dependence for the resonant excitation step of the RMPI process. Unexplained observations of the distortions in the polarization dependence of the ion yield and the absorption linewidth of the 6d ¹D₂ resonance are discussed. The second investigation was a study of the density dependent electric dipole forbidden two-photon resonant transition ²S → ²P in three-photon RMPI spectra of the Rydberg states of potassium. Stark interactions are shown to be unlikely and too weak. From the characteristics of the spectra, the excitation process is identified as a laser-assisted collision interaction.
The infinite summations over the complete set of unperturbed atomic states appearing in the NNNth-order perturbation theory for multiphoton ionization are performed using the Dalgarno-Lewis method. The relevant transition matrix elements are written in a closed integral form exhibiting all the analytic properties of the amplitude as a function of incident photon energy. The cross sections for two- and three-photon ionization for atomic hydrogen are calculated for both linearly and circularly polarized light with a wide range of photon energy spectrum including the near resonance, and numerical comparison is made with the values obtained by different methods.