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Physical Review A

Harmonic generation and multiphoton ionization near an autoionizing resonance

G. Alber, P. Zoller

Published Mar 1, 1983• 32 citations
Publisher

Abstract

We theoretically study intensity-saturation effects in resonant harmonic generation and multiphoton ionization. A first laser excites a two-photon resonance which is coupled by a second laser to an autoionizing state. Starting from an effective Hamiltonian for the three resonant atomic states, we derive a set of equations for the density matrix of the gaseous medium and the electromagnetic field within a semiclassical framework. We present and discuss analytical and numerical solutions of these equations which show a variety of line profiles depending critically on the intensities of the incident laser pulses.

DOI
10.1103/physreva.27.1373

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Physical Review A•May 1, 1974•14 citations
We theoretically study intensity-saturation effects in resonant harmonic generation and multiphoton ionization. A first laser excites a two-photon resonance which is coupled by a second laser to an autoionizing state. Starting from an effective Hamiltonian for the three resonant atomic states, we derive a set of equations for the density matrix of the gaseous medium and the electromagnetic field within a semiclassical framework. We present and discuss analytical and numerical solutions of these equations which show a variety of line profiles depending critically on the intensities of the incident laser pulses.
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.
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.
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.
Using the R -matrix Floquet theory we have carried out non-perturbative, ab initio one- and two-colour calculations of the multiphoton ionization of magnesium with the laser frequencies chosen such that the initial state of the atom is resonantly coupled with autoionizing resonances of the atom. Good agreement is obtained with previous calculations in the low-intensity regimes. The single-photon ionization from the excited state of magnesium has been studied in the vicinity of the autoionizing resonance at non-perturbative laser intensities. Laser-induced degenerate states (LIDS) are observed for modest laser intensities. By adding a second laser which resonantly couples the and autoionizing levels, we show that, due to the small width of the state, LIDS occur between this state and the state at intensities of the first laser below . We next investigate the case in which the first laser induces a resonant two-photon coupling between the ground state and the autoionizing state, while the second laser again resonantly couples the respective and autoionizing states. At weak intensities, our calculations compare favourably with recent experimental data and calculations. We show that when the intensity of the first laser is increased, the effect of an additional autoionizing state, the state, becomes significant. This state is coupled to the autoionizing level by one photon, inducing a triply resonant processes. We show that LIDS occur among the three autoionizing levels and we discuss their effect on the decay rate of the ground state. We consider dressed two- and three-level atoms which can be used to model the results of our calculations.
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.
The present paper applies the method of high-intensity quantum electrodynamics developed earlier to several problems of current experimental interest. In this paper the intensitydependent shifts and widths of atomic levels are calculated and applied to a given transition near resonance. The technique is demonstrated with three examples: the multiphoton ionization of atomic cesium and hydrogen in atomic beams and third-harmonic production in an atomic vapor. It is found that the multiphoton-ionization rate in a relatively weak laser beam (of order 108{10}^{8}108 W/cm2{\mathrm{cm}}^{2}cm2) is determined by the intensity-dependent level width (6f6f6f configuration) as well as the interference of the fine-structure states, and that the rates for hydrogen, in a much more intense beam (of order 1012{10}^{12}1012 W/cm2{\mathrm{cm}}^{2}cm2) are determined by both the intensity-dependent widths and shifts as‘\stackrel{\mathrm{`}}{\mathrm{s}}s‘ well as the wave-function renormalization constants. The agreement of these two examples of calculations with the experiments done recently is satisfactory. For third-harmonic production the role of two-photon resonance is emphasized, and the dependence of the generated third-harmonic intensity on the intensity and frequency of the fundamental is discussed. Near resonance, the ratio of third-harmonic intensity to fundamental intensity saturates.