  Angle-resolved spectroscopy 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 probe the texture of the Bloch wavefunction in
momentum-space, associated with Berry curvature and topological invariants.
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. In this Article, we introduce a
novel measurement methodology and observable in extreme ultraviolet
angle-resolved photoemission spectroscopy, based on continuous modulation of
the ionizing radiation polarization axis. By tracking the energy- and
momentum-resolved amplitude and phase of the photoemission modulation upon
polarization variation, we reconstruct the Bloch wavefunction of prototypical
semiconducting transition metal dichalcogenide 2H-WSe$_2$ with minimal theory
input. This novel experimental scheme, which is articulated around the
manipulation of the photoionization transition dipole matrix element, in
combination with a simple tight-binding theory, is general and can be extended
to provide insights into the Bloch wavefunction of many relevant crystalline
solids.
