Complete photoionization experiments via ultrafast coherent control with polarization multiplexing.

Photoelectron angular distributions (PADs) obtained from ionization of potassium atoms using moderately intense femtosecond IR fields (∼10^{12}  W cm^{-2}) of various polarization states are shown to provide a route to "complete" photoionization experiments. Ionization occurs by a net three-photon absorption process, driven via the 4s→4p resonance at the one-photon level. A theoretical treatment incorporating the intrapulse electronic dynamics allows for a full set of ionization matrix elements to be extracted from 2D imaging data. 3D PADs generated from the extracted matrix elements are also compared to experimental, tomographically reconstructed, 3D photoelectron distributions, providing a sensitive test of their validity. Finally, application of the determined matrix elements to ionization via more complex, polarization-shaped, pulses is demonstrated, illustrating the utility of this methodology towards detailed understanding of complex ionization control schemes and suggesting the utility of such "multiplexed" intrapulse processes as powerful tools for measurement.