Angle-resolved RABBIT: theory and numerics


Angle-resolved (AR) RABBIT measurements offer a high information content measurement scheme, due to the presence of multiple, interfering, ionization channels combined with a phase-sensitive observable in the form of angle and time-resolved photoelectron interferograms. In order to explore the characteristics and potentials of AR-RABBIT, a perturbative 2-photon model is developed; based on this model, example AR-RABBIT results are computed for model and real systems, for a range of RABBIT schemes. These results indicate some of the phenomena to be expected in AR-RABBIT measurements, and suggest various applications of the technique in photoionization metrology.


The RABBIT methodology - “reconstruction of attosecond harmonic beating by interference of two-photon transitions” (Muller 2002) - essentially defines a scheme in which XUV pulses are combined with an IR field, and the two fields are applied to a target gas. The gas is ionized, and the photoelectrons detected. In the typical case, the IR field is at the same fundamental frequency \(\omega\) as the field used to drive harmonic generation, and the XUV field generated is an atto-second pulse train with harmonic components \(n\omega\), with odd-\(n\) only. In this case, if the intensity of the IR field is low to moderate, the resultant photoelectron spectrum will be comprised of discrete bands corresponding to direct 1-photon XUV ionization, and sidebands corresponding to 2-photon XUV+IR transitions (Muller 2002). (The energetics of this situation are illustrated in fig. \ref{fig:pathways}.) Temporally, if the XUV pulses are short relative to the IR field cycle, the sidebands will also show significant time-dependence, since they will be sensitive to the optical phase difference between the XUV and IR fields, with an oscillatory frequency of \(2\omega\). In this case, a measurement which is angle-integrated, or made at a single detection geometry, can be viewed as a means to characterising the properties of the XUV pulses (spectral content and optical phase), provided that the ionizing system is simple or otherwise well-characterised (Muller 2002); RABBIT can therefore be utilised as a pulse metrology technique (Muller 2002, Krausz 2009), and this is the typical usage.

Conversley, RABBIT can also be regarded as a photoelectron metrology technique, since it is sensitive to the magnitudes and phases of the various photoionization pathways accessed. In contrast to most traditional (energy-resolved) photoelectron spectroscopy techniques, RABBIT has the distinction of interfering pathways resulting from different 1-photon transition energies: it is thus sensitive to the energy-dependence of the photoionization dynamics, as well as to the partial-wave components within each pathway. An angle-resolved (AR) RABBIT measurement is particularly powerful in this regard, since the partial-wave phases are encoded in the angular part of the photoelectron interferogram. Although this is a potentially powerful technique, the underlying photoionization dynamics may be extremely complicated, hence quantitative analysis of experimental results is challenging.