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Physical Review A

Near-threshold photoionization by pulses with modulated frequency

Andrzej Raczyński, Jarosław Zaremba

Published Mar 1, 1998• 1 citation
Publisher

Abstract

Model photoionization by a pulse with a modulated frequency is discussed. An approximation generalizing that of Weisskopf-Wigner is proposed, with a pole moving in the rhythm of the modulation. A model taking into account the ionization threshold is adopted, and relatively simple formulas for the nondecay probability and the photoelectron spectrum are obtained. A nonexponential character of the decay curves is demonstrated together with a raising and narrowing of the peaks in the photoelectron spectra.

DOI
10.1103/physreva.57.2243

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Model photoionization by a pulse with a modulated frequency is discussed. An approximation generalizing that of Weisskopf-Wigner is proposed, with a pole moving in the rhythm of the modulation. A model taking into account the ionization threshold is adopted, and relatively simple formulas for the nondecay probability and the photoelectron spectrum are obtained. A nonexponential character of the decay curves is demonstrated together with a raising and narrowing of the peaks in the photoelectron spectra.
The dynamics of the bound-state populations and the photoelectron spectra are calculated for model atomic systems irradiated by a pulse with a harmonically modulated frequency. For a system including a single bound state a model is adopted, which takes into account the threshold behavior typical of negative ions and admits continuum-continuum transitions. For a model one-dimensional atom the results are obtained through a numerical integration of the Schr\"odinger equation. The case of a resonant ionization is also considered. The modulation of the frequency results in changing the instantaneous rate of decay of the initial state, in inducing additional population oscillations for multilevel systems, and in additional peaks in the photoelectron spectra.
A model of atomic ionization by smooth pulses is solved with bound-continuum and energy-dependent continuum-continuum (C-C) dipole coupling. The rotating-wave approximation for the C-C transitions is avoided. In contrast with the flat continuum result, our ionization rate is independent of the C-C coupling. We also derive the photoelectron energy spectra and show that counterrotating terms make important contributions. Relation to above-threshold ionization experiments with two frequencies is discussed.
By solving the time-dependent Schr\"odinger equation in momentum space, the photoelectron emission from atoms under the irradiation of 400 nm sinusoidal phase-modulated shaped pulses was investigated. It was found that by controlling the phase and amplitude of the pulses in the frequency domain, in addition to the photoelectron peaks generated by the interference of multiple-cycle ionization, additional resonant peak structures and interference phenomena can be observed in the photoelectron emission spectrum. Through the analysis of photoelectrons from different subpulses within the shaped pulse, it was discovered that these structures arise from the modulation of ionization and excitation processes by multiple subpulses within the shaped pulse. This study demonstrates the significant importance of utilizing shaped pulses for the control of photoelectron emission.