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Physical Review A

Resonance-enhanced multiphoton ionization: Interference effects due to harmonic generation

Douglas Jackson, James J. Wynne, Peter H. Kes

Published Aug 1, 1983• 96 citations
Publisher

Abstract

A general theoretical model for the treatment of multiphoton ionization is presented. In this treatment, we have explicitly included coherent effects resulting from harmonic generation. The predictions of this model are in agreement with experimental observations that we present in this paper. In addition, the model is contrasted with much earlier theoretical treatments of multiphoton ionization and accounts for the anomalous multiphoton-ionization behavior reported by others in the literature.

DOI
10.1103/physreva.28.781

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A general theoretical model for the treatment of multiphoton ionization is presented. In this treatment, we have explicitly included coherent effects resulting from harmonic generation. The predictions of this model are in agreement with experimental observations that we present in this paper. In addition, the model is contrasted with much earlier theoretical treatments of multiphoton ionization and accounts for the anomalous multiphoton-ionization behavior reported by others in the literature.
The effect of temporal coherent control on the two-photon-resonant third-harmonic generation and multiphoton ionization into the continuum states of an atomic system is experimentally and theoretically investigated by means of a pair of partially incoherent, identical laser pulses. The evidence of quantum interference as a function of the delay between the pulses is reported. The transition from the resonant to the nonresonant case is also shown. The obtained results agree with the prediction of a theoretical model showing that the onset of quantum interference appears to be related to the coherence time of the laser radiation, which is much shorter than the pulse duration.
Several extensions are made in theoretical studies of multiphoton ionization associated with third-harmonic fields that are generated near three-photon resonances in gaseous media. The treatment includes the strong coherent cancellation effect which occurs between three-photon pumping of a resonant level and pumping by the third-harmonic field that is generated in the same medium. The incomplete spoiling of the cancellation effect with counterpropagating beams is quantitatively described. Also, treatment of the multiphoton-ionization problem involving phase-matched, third-harmonic fields is generalized to include quantitative effects of index changes due to a buffer gas, absorption due to dimers, and collisional dephasing of coherent excitations. Finally, we show how measurements of linewidths, phase-matching positions, and pressure dependences of ionization yields associated with third-harmonic generation and subsequent absorption can be used to determine oscillator strengths of a resonant level, absorption coefficients for a resonant species and a buffer-gas species, and the refractive index of the buffer gas at the third-harmonic frequency.
Harmonic-generation processes at high laser intensity are strongly affected by resonant multiphoton ionization. In this paper coexistence of these phenomena at low pressure and high intensity is taken into account with use of a mean-field theory. New consequences of this model are derived, especially for resonances strongly damped by ionization. Available experimental data on mercury agree qualitatively with this model. A second approach, called the quasistatic approximation, is used to get analytical solutions for mean-field equations, in good agreement with numerical results. Furthermore, possible applications of the quasistatic approximation to the study of harmonic generation at both high pressure and high laser intensity are mentioned.
A quantum-mechanical formulation for the generation of third-harmonic radiation in an atomic medium undergoing three-photon resonant multiphoton ionization is given. The generation of the third harmonic is treated as a cooperative emission and its pressure dependence is shown to be in agreement with experiments. The formulation is general enough to include both transient and steady-state phenomena and includes both traveling-wave and standing-wave cases. A comparison of the results of the present theory with those of Jackson and Wynne is given.
Multiphoton ionization in the region near a three-photon resonance is treated for focused, plane-polarized Gaussian beams with diffraction-limited beam divergence. In this situation, a third-harmonic field is generated within the laser beam. At, and very near, three-photon resonance the driving rate for the upper-state probability amplitude due to one-photon absorption of third-harmonic light becomes nearly equal to the corresponding three-photon rate due to the laser field, but these effects are 180\ifmmode^\circ\else\textdegree\fi{} out of phase. As a consequence of this cancellation between two pumping terms, the three-photon resonance line essentially disappears at moderate concentrations and the observed ionization has a line shape that is close to the phase-matching curve for third-harmonic generation. The ionization signal, near but not on the resonance, is due almost entirely to absorption of third-harmonic photons plus other laser photons; three-photon resonantly enhanced multiphoton ionization by the laser is much weaker. This is particularly true on the blue side of the three-photon resonance at detunings where phase matching occurs. The problem is treated quite generally with predictions of the full line shape for nnn-photon ionization and third-harmonic light generation near three-photon resonance, including the rather strong influences of positively dispersive buffer gases. We also show that the cancellation between the one-photon and the three-photon process is partially spoiled in the presence of a counterpropagating beam at the same frequency.
We investigate theoretically a particular case of doubly resonant multiphoton ionization. More precisely, we consider two levels quasi-resonant with two successive harmonics of the field frequency. The method used is based on the effective operator formalism first introduced for this problem by Armstrong, Beers and Feneuille. The main result is to show the possibility of observing large interference effects on the width of the resonances. Moreover this treatment allows us to make more precise the connection between effective operator formalism and standard perturbation theory.