  We theoretically describe how fast electrons couple to polaritonic modes in
uniaxial materials by analyzing the electron energy loss (EEL) spectra. We show
that in the case of an uniaxial medium with hyperbolic dispersion, bulk and
surface modes can be excited by a fast electron traveling through the volume or
along an infinite interface between the material and vacuum. Interestingly, and
in contrast to the excitations in isotropic materials, bulk modes can be
excited by fast electrons traveling outside the uniaxial medium. We demonstrate
our findings with the representative uniaxial material hexagonal boron nitride.
We show that the excitation of bulk and surface phonon polariton modes is
strongly related to the electron velocity and highly dependent on the angle
between the electron beam trajectory and the optical axis of the material. Our
work provides a systematic study for understanding bulk and surface polaritons
excited by a fast electron beam in hyperbolic materials and sets a way to steer
and control the propagation of the polaritonic waves by changing the electron
velocity and its direction.
