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Physical Review A

Quantum theory of the competition between multiphoton ionization and third-harmonic generation

G. S. Agarwal, Surya P. Tewari

Published Apr 1, 1984• 42 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.29.1922

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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.
In connection with a recent experiment of vacuum-ultraviolet generation in multiphoton resonant ionization of xenon at increasing pressure, a model is elaborated to account for the simultaneous effect of a laser excitation tuned near a three-photon resonance and a pressure-induced emission from the resonant state to the ground state. Under certain assumptions usual in various super-radiance treatments, a system of Bloch equations is derived and numerically solved. The dependence of the ionization probability and third-harmonic production versus the interaction time, gas pressure, dynamical detuning, and laser intensity is extensively studied. A transition between a high and low ionization rate is observed when the pressure increases simultaneously with the disappearance of Rabi oscillations and a saturation of third-harmonic generation. An order-of-magnitude calculation reveals that such phenomena are accessible to experiment and a qualitative comparison with the above-mentioned results in xenon is found to be satisfactory.
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Three-photon resonance enhancement of third-harmonic generation and multiphoton ionization is treated for a slab geometry configuration. Striking pressure effects which become important at concentrations $n\ensuremath{\gtrsim}{10}^{12}$ /cm3{/\mathrm{c}\mathrm{m}}^{3}/cm3 for narrow-bandwidth short-pulse lasers are predicted for both the third-harmonic signal and the multiphoton ionization. For example, part of the third-harmonic signal exists the slab simultaneously with the laser pulse while another part is time delayed for small detunings from resonance. At intermediate detuning from the three-photon resonance the two parts can interfere. Multiphoton ionization yields near three-photon resonance are strongly suppressed under certain conditions, and peaks may occur for proper detunings on both sides of the three-photon resonance. A detailed experimental verification is suggested for Xe.
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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.
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.