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Applied Sciences

Photoelectron Angular Distribution and Phase in Two-Photon Single Ionization of H and He by a Femtosecond and Attosecond Extreme-Ultraviolet Pulse

Kenichi L. Ishikawa, Kiyoshi Ueda

Published Mar 5, 2013• 31 citations
Publisher

Abstract

We theoretically study the photoelectron angular distribution (PAD) from the two-photon single ionization of H and He by femtosecond and attosecond extreme-ultraviolet pulses, based on the time-dependent perturbation theory and simulations with the full time-dependent Schrodinger equation. The PAD is formed by the interference of the s and d continuum wave packets, and, thus, contains the information on the relative phase and amplitude ratio between them. We find that, when a spectrally broadened femtosecond pulse is resonant with an excited level, the PAD substantially changes with pulse width, since the competition between resonant and nonresonant ionization paths, leading to distinct from the scattering phase shift difference, changes with it. In contrast, when the Rydberg manifold is excited, and for the case of above-threshold two-photon ionization, and the PAD do not depend much on pulse width, except for the attosecond region. Thus, the Rydberg manifold and the continuum behave similarly in this respect. For a high-harmonic pulse composed of multiple harmonic orders, while the value is different from that for a single-component pulse, the PAD still rapidly varies with pulse width. The present results illustrate a new way to tailor the continuum wave packet.

DOI
10.3390/app3010189

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Journal of Physics B Atomic Molecular and Optical Physics•Nov 1, 2006•21 citations
We theoretically study the photoelectron angular distribution (PAD) from the two-photon single ionization of H and He by femtosecond and attosecond extreme-ultraviolet pulses, based on the time-dependent perturbation theory and simulations with the full time-dependent Schrodinger equation. The PAD is formed by the interference of the s and d continuum wave packets, and, thus, contains the information on the relative phase and amplitude ratio between them. We find that, when a spectrally broadened femtosecond pulse is resonant with an excited level, the PAD substantially changes with pulse width, since the competition between resonant and nonresonant ionization paths, leading to distinct from the scattering phase shift difference, changes with it. In contrast, when the Rydberg manifold is excited, and for the case of above-threshold two-photon ionization, and the PAD do not depend much on pulse width, except for the attosecond region. Thus, the Rydberg manifold and the continuum behave similarly in this respect. For a high-harmonic pulse composed of multiple harmonic orders, while the value is different from that for a single-component pulse, the PAD still rapidly varies with pulse width. The present results illustrate a new way to tailor the continuum wave packet.
We theoretically study the pulse-width dependence of the photoelectron angular distribution (PAD) from the resonance-enhanced two-photon single ionization of He by femtosecond (≲20 fs) extreme-ultraviolet pulses, based on the time-dependent perturbation theory and simulations with the full time-dependent Schrödinger equation. In particular, we focus on the competition between resonant and nonresonant ionization paths, which leads to the relative phase δ between the S and D wave packets distinct from the corresponding scattering phase shift difference. When the spectrally broadened pulse is resonant with an excited level, the competition varies with pulse width, and, therefore, δ and the PAD also change with it. On the other hand, when the Rydberg manifold is excited, δ and the PAD do not much vary with the pulse width, except for the very short-pulse regime.
Phase-shift differences and amplitude ratios of the outgoing sss and ddd continuum wave packets generated by two-photon ionization of helium atoms are determined from the photoelectron angular distributions obtained using velocity map imaging. Helium atoms are ionized with ultrashort extreme-ultraviolet free-electron laser pulses with a photon energy of 20.3, 21.3, 23.0, and 24.3 eV, produced by the SPring-8 Compact SASE Source test accelerator. The measured values of the phase-shift differences are distinct from scattering phase-shift differences when the photon energy is tuned to an excited level or Rydberg manifold. The difference stems from the competition between resonant and non-resonant paths in two-photon ionization by ultrashort pulses. Since the competition can be controlled in principle by the pulse shape, the present results illustrate a new way to tailor the continuum wave packet.
We study the ellipticity and the dependence on the phase lag (lead) (between the semimajor and the semiminor axes of the field components) of the photoelectron angular distribution (PAD) in the non-resonant two-photon ionization of atomic hydrogen. We establish exact analytical expressions for azimuthal PAD for 3s, 3p and 3d excited initial states, marked by the occurrence of an asymmetric term. This term gives rise to elliptic dichroism (ED), which can be obtained in two ways: either with the left (versus right) ellipticity, or with the phase lag (versus lead); for 3s and 3p initial states, it is shown that the quantum phase of continua is directly related to the phase lag, one-photon below-threshold ionization, and indirectly one photon above. Another important result is that the magnetic sublevels, m = 0, for 3p and m = ±1, for 3d, do not contribute to the azimuthal PAD. Our numerical results show, for 3s and 3d, and near-threshold ionization, that the PAD has maxima either along the semimajor or the semiminor axis, while for above-threshold ionization, they are always shifted from these axes. However, the maxima of the corresponding ED coincide with the PAD maxima, while for 3p, they are shifted from the PAD minima. A strong dependence of the ED sign is noted, regardless of the state or the process. However, strong ED signals are obtained for the 3s initial state and below-threshold ionization.
Ultrafast atomic processes, such as excitation and ionization occurring on the femtosecond or shorter time scale, were explored by employing attosecond high-harmonic pulses. With the absorption of a suitable high-harmonic photon a He atom was ionized, or resonantly excited with further ionization by absorbing a number of infrared photons. The electron wave packets liberated by the two processes generated an interference containing the information on ultrafast atomic dynamics. The attosecond electron wave packet, including the phase, from the ground state was reconstructed first and, subsequently, that from the 1s3p state was retrieved by applying the holographic technique to the photoelectron spectra comprising the interference between the two ionization paths. The reconstructed electron wave packet revealed details of the ultrafast photoionization dynamics, such as the instantaneous two-photon ionization rate.
The electron angular distribution after atomic photoionization by the fundamental frequency and its second harmonic is analyzed for a case when the frequency of the fundamental scans the region of an intermediate atomic state. The angular distribution and its left-right asymmetry, due to the two-pathway interference between nonresonant one-photon and resonant two-photon ionization, sharply change as a function of the photon energy. The phenomenon is exemplified by both solving the time-dependent Schr\"odinger equation on a numerical space-time grid and by applying perturbation theory for ionization of the hydrogen atom in the region of the $1s\text{\ensuremath{-}}2p$ transition for femtosecond pulses as well as an infinitely long exposure to the radiation. Parametrizations for the asymmetry and the anisotropy coefficients, obtained within perturbation theory, reveal general characteristics of observable quantities as functions of the parameters of the radiation beam.
The influence of laser-induced continuum structure on the angular distribution of photoelectrons is studied in the femtosecond time domain by direct numerical solution of the time-dependent Schrodinger equation. Control of the photoelectron angular distribution is demonstrated for the hydrogen atom by coherent population transfer from the initial S-state to an excited D-state via the p-continuum and further ionization into the f-continuum states. A direct optimization procedure is used to find a domain of laser parameters, for which the efficiency of the control with respect to the time delay and energy detuning between the laser pulses is maximized.