  Angle-resolved photoemission spectroscopy (ARPES) is the most powerful
technique to investigate the electronic band structure of crystalline solids.
To completely characterize the electronic structure of topological materials,
one needs to go beyond band structure mapping and access information about the
momentum-resolved Bloch wavefunction, namely orbitals, Berry curvature, and
topological invariants. However, because phase information is lost in the
process of measuring photoemission intensities, retrieving the complex-valued
Bloch wavefunction from photoemission data has yet remained elusive. We
introduce a novel measurement methodology and associated observable in extreme
ultraviolet angle-resolved photoemission spectroscopy, based on continuous
modulation of the ionizing radiation polarization axis. Tracking the energy-
and momentum-resolved amplitude and phase of the photoemission intensity
modulation upon polarization axis rotation allows us to retrieve the circular
dichroism in photoelectron angular distributions (CDAD) without using circular
photons, providing direct insights into the phase of photoemission matrix
elements. In case of two relevant bands, it is possible to reconstruct the
orbital pseudospin (and thus the Bloch wavefunction) with moderate theory
input, as demonstrated for the prototypical layered semiconducting transition
metal dichalcogenide 2H-WSe$_2$. This novel measurement methodology in ARPES,
which is articulated around the manipulation of the photoionization transition
dipole matrix element, in combination with a simple tight-binding theory, is
general and adds a new dimension to obtaining insights into the orbital
pseudospin, Berry curvature, and Bloch wavefunctions of many relevant
crystalline solids.
