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Journal of Modern Optics

Multiphoton Ionization of Atoms by Two Radiation Fields: Theory and Calculations for Hydrogen

C. Leone, Saverio Bivona, R. Burlon, G. Ferrante

Published Jul 1, 1989• 3 citations

Abstract

An approximate non-perturbative theory of multiphoton ionization of a hydrogen atom by two strong radiation fields is outlined. The special case is then considered for when one of the fields is of low intensity and high frequency and the other field is of high intensity and low frequency. A set of representative calculations has been performed for this case; that is, (a) angular distributions for given numbers of absorbed and emitted low-frequency photons and different geometries; (b) total cross-sections versus the strong-field intensity; (c) angular distributions summed over all the low-frequency photon exchanges, showing a fourfold symmetry in a geometry in which each ionization channel exhibits, instead, only a twofold symmetry; (d) the average energy gained by the ejected electrons. Calculations are performed for a strong low-frequency field of arbitrary polarization. In many respects, the present calculations are expected to complement those of single-field multiphoton ionization. It is hoped that the results of the calculations reported here may prompt systematic measurements also in this new class of processes, as the predictions are well within the state of the art of present multiphoton-ionization experiments.

DOI: 10.1080/09500348914550981

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An approximate non-perturbative theory of multiphoton ionization of a hydrogen atom by two strong radiation fields is outlined. The special case is then considered for when one of the fields is of low intensity and high frequency and the other field is of high intensity and low frequency. A set of representative calculations has been performed for this case; that is, (a) angular distributions for given numbers of absorbed and emitted low-frequency photons and different geometries; (b) total cross-sections versus the strong-field intensity; (c) angular distributions summed over all the low-frequency photon exchanges, showing a fourfold symmetry in a geometry in which each ionization channel exhibits, instead, only a twofold symmetry; (d) the average energy gained by the ejected electrons. Calculations are performed for a strong low-frequency field of arbitrary polarization. In many respects, the present calculations are expected to complement those of single-field multiphoton ionization. It is hoped that the results of the calculations reported here may prompt systematic measurements also in this new class of processes, as the predictions are well within the state of the art of present multiphoton-ionization experiments.

The strong-field multiphoton ionization of atoms is considered and a theoretical approach dealing nonperturbatively with the radiation field formulated. The general computational scheme is the conventional perturbation theory, but the intermediate states are dressed by the field. We present in detail a method to dress the continuum states and to study the dipole transitions within the continuum. In the high-frequency domain, the proposed procedure rapidly converges over a wide range of field intensity and offers an interesting framework for calculating ionization rates for arbitrary numbers of absorbed (above-threshold) photons and field polarization.

This paper illustrates the study on asymmetry of the angular distribution of the ejected electrons in a multiphoton process from the ground state of a hydrogen atom. General expressions for the multiphoton ionization rates have been derived based on a variation of the Dalgarno–Lewis method for the evaluation of matrix elements in higher order perturbation theory. In addition, these analytical expressions for the various multiphoton transition rates and their variation as a function of polarization, phase, frequency and intensity of the incident radiation have been studied extensively. The general expression obtained can be used to analyse any number of incident beams with arbitrary polarization, phase and intensity.

We have discussed the problems of non linear interaction between electromagnetic radiations with atoms from semi-classical point of view. Time dependent Schrödinger equation for single electron system is solved by using perturbative technique to obtain transition probability. Higher order perturbation is also discussed which is used in multiple processes, in which two or more quanta are emitted instead of a single photon. The theory is based on assumption that the perturbation is small. From this transition probability ionization rate and absorption cross-section of hydrogen atom is calculated. Its variation with photon energy and field strength is analyzed which agrees very well with experimental observations.The Himalayan PhysicsVol. 3, No. 32012Page : 40-43

Based on analytical equations valid in perturbation theory, we study the process of ionization of the ground state of the hydrogen atom by the absorption of three photons, two of them being of the same frequency. Results are given for the total ionization rate and for the angular distribution of the ejected electrons, in a regime of frequencies in which two-colour two-photon ionization is not possible. The case of orthogonal photon polarizations, investigated in some detail, displays a strong dependence on the electron direction.

A nonperturbative method is used to study the two-color multiphoton ionization of atoms by solving the Schr\"odinger equation in momentum space, which facilitates the extraction of the rapidly varying part of the wave function. Our method generalizes the problem for cases where an arbitrary number of ionization photons are absorbed, and also takes into account the threshold shifts due to both the high- and low-frequency fields. The photoelectron energy spectra of the hydrogen atoms are calculated and the dependence on the laser field strengths and frequencies is discussed. \textcopyright{} 1996 The American Physical Society.