Dependence of strong-field photoelectron angular distributions on molecular orientation

We have analysed angular distributions of the photoelectron yields arising from strong-field ionization of diatomic and polyatomic linear molecules using a leading-order intense-field S-matrix theory. For molecules with active π electrons the distribution is found to strongly depend on the degree of molecular alignment, showing a nodal minimum along the laser polarization direction as a characteristic signature. The nonlinear interaction of molecules with an intense laser pulse has attracted considerable experimental and theoretical interest recently (for reviews see, for example, [1, 2]). Singleelectron ionization is perhaps the most fundamental process initiated during the exposure of a molecule to a strong field. A number of phenomena, e.g. charge resonant enhanced ionization of molecular ions at critical internuclear distances or the suppression of ionization of a neutral molecule to that of an atom with the same ionization potential, have been observed and analysed. Most of the experiments have been performed on ensembles of molecules with random orientation. Just recently it has become possible to measure the orientation dependence of strong-field ionization in the case of N2 molecules [3]. The experimental observation supports theoretical predictions [4–8] that the total ionization rates of neutral diatomic molecules depend on the orientation of the molecular axis with respect to the laser field. The dependence of ionization yields and related observables, such as photoelectron energy spectra and angular distributions, on the spatial alignment of the molecule is important for an understanding of strong-field molecular physics. For example, high harmonic yields [9, 10] and molecular dissociation yields [11–13] are influenced by the angular dependence of the ionization process. Spatial alignment of molecules is furthermore of great interest in view of the variety of possible applications [13, 14], such as control of ionization and dissociation pathways, rotational cooling, molecular trapping and focusing, pendular-state 0953-4075/03/210375+06$30.00 © 2003 IOP Publishing Ltd Printed in the UK L375 L376 Letter to the Editor spectroscopy and the study of steric effects in chemical reaction dynamics. It is well known from excitation–ionization experiments at low laser intensities that, in particular, photoelectron angular distributions are sensitive to molecular orientation and provide a probe of the molecular structure, symmetry and orientation (for reviews see, for example, [15, 16]). In view of the recent experimental achievements in strong-field molecular ionization the question arises as to how the highly nonlinear electron–field interaction at peak intensities well above 1013 W cm−2 affects the angular distribution of the photoelectron yields depending on molecular orientation. Below we analyse the photoelectron angular distribution of linear molecules subjected to an intense linearly polarized laser pulse. It will be shown that, for molecules having an active π orbital, the degree of alignment of the molecular ensemble is reflected in the appearance of a nodal minimum along the laser polarization direction, as the cone angle of the distribution of alignments, β, decreases from β = 180◦ (random orientation) to β = 0◦ (complete alignment along the polarization axis). The origin of the minimum lies in the presence of a symmetryinduced node in the plane containing the molecular axis. Our analysis is carried out using an extension of the so-called KFR (Keldysh–Faisal–Reiss) theory [17–19] for atomic ionization in intense laser fields to the ionization of molecules [20–22]. It corresponds to the leading order of the ab initio intense-field S-matrix theory and involves nonresonant transitions of a molecule from the initial electronic ground state to the final state of the molecular ion and the field-dressed Volkov electron (e.g. [23]). The angular distribution of the ejected electrons, averaged over the distribution of the cone angles, can be given in terms of the rate of differential ionization per element of solid angle d along the axis of electron detection, as [20, 22]