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Physical Review Letters

Angular Distribution of Photoelectrons in Strongly Driven Multiphoton Transitions

S. N. Dixit, P. Lambropoulos

Published May 11, 1981• 36 citations
Publisher

Abstract

The behavior of photoelectron angular distributions in a strongly driven resonant multiphoton ionization process is discussed. It is shown that the angular distribution changes drastically with increasing intensity as a result of the ac Stark shifting of the levels. Moreover, under strong saturation conditions the distribution reaches a limiting form significantly different from the form predicted by perturbation theory. The effects of the laser bandwidth on the angular distribution are also discussed briefly.

DOI
10.1103/physrevlett.46.1278

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The behavior of photoelectron angular distributions in a strongly driven resonant multiphoton ionization process is discussed. It is shown that the angular distribution changes drastically with increasing intensity as a result of the ac Stark shifting of the levels. Moreover, under strong saturation conditions the distribution reaches a limiting form significantly different from the form predicted by perturbation theory. The effects of the laser bandwidth on the angular distribution are also discussed briefly.
In this paper, we present the theory of photoelectron angular distributions in resonant multiphoton ionization that rigorously takes into account the saturation, ac Stark-shift, and the laser-linewidth effects. The influence of these effects on the distribution is incorporated through the coupling equations between the angle-resolved ionization probabilities and the (time-dependent) bound-state density-matrix elements. General expressions for the angular distributions are derived and several properties of these distributions are arrived at from these expressions. Finally, numerical results are presented to illustrate the effects of saturation, of ac Stark shifts, and of the laser line shape.
The influence of the dynamic Stark effect on photoelectron angular distributions for two-photon-resonant three-photon ionization of sodium by way of the 42D4^{2}D42D fine-structure components has been investigated. Owing to the dynamic Stark shift of the atomic transition frequency, the angular distributions expected at low laser intensities were modified as different transitions were intensity tuned into and out of resonance with the laser frequency. The distributions are in good qualitative agreement with theory.
The influence of the ac-Stark shifts on the spin polarization (SP) of the photoelectron in a resonant multiphoton ionization is discussed. It is shown that the Stark shifts of various levels are different and this removes any initial fine-structure degeneracy of the excited states. This increased dynamic separation between the states increases the SP of the ejected photoelectron. Numerical results are presented to illustrate this effect. By expressing the equations of motion in the spin basis set the precise conditions necessary to observe nonzero SP are identified. It is shown on the basis of these conditions that although the removal of the fine-structure degeneracy occurs independent of whether the atom has any spin-orbit coupling, this does not induce any spin polarization if the atom has no spin-orbit coupling.
We present results from a time-dependent two-level-plus-continuum model of multiphoton ionization in order to better understand the short-pulse photoelectron spectrum resulting from multiphoton ionization and the role of intermediate states. Both resonant and nonresonant population transfer to the upper state are found to play an important role in the multiphonon ionization process. The dynamic modeling reveals the potential for broadening and shifting peaks in the photoelectron spectrum. However, we conclude that despite the complex dynamics of the excitation, short-pulse photoelectron spectra can be used to measure ac Stark shifts of both ponderomotively and nonponderomotively shifted states in strong laser fields.
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.
A theoretical investigation has been carried out on the dependence of the photoelectron angular distributions on laser intensity for the case of two-photon-resonant three-photon ionization of sodium. Good overall agreement is obtained with the experimental anisotropy parameters for ionization via the 4D3/2{D}_{3/2}D3/2​ and 4D5/2{D}_{5/2}D5/2​ intermediate states. The comparison of the theoretical results with the experimental data also clearly shows that the hyperfine splitting of the ground state has to be taken into account at high laser intensities although the low-intensity angular distributions do not depend on the initial ground hyperfine state.