  Advances in the ability to manipulate free electron phase profiles within the
electron microscope have spurred development of quantum-mechanical descriptions
of electron energy loss (EEL) processes involving transitions between
phase-shaped transverse states. Here, we elucidate an underlying connection
between two ostensibly distinct optical polarization analogs identified in EEL
experiments as manifestations of the same conserved scattering flux. Our work
introduces a procedure for probing general tensorial target characteristics
including global mode symmetries and local polarization.
