  Electron optics deals with condensed matter platforms for manipulating and
guiding electron beams with high efficiency and robustness. Common devices rely
on the spatial confinement of the electrons into one-dimensional channels.
Recently, there is growing interest in electron optics applications in two
dimensions, which heretofore are almost exclusively based on graphene devices.
In this work, we study band-inverted systems resulting from particle-hole
hybridization and demonstrate their potential for electron optics applications.
We develop the theory of interface scattering in an inverted-band $pn$ junction
using a scattering matrix formalism and observe negative refraction conditions
as well as transmission filtering akin to graphene's Klein tunneling but at
finite angles. Based on these findings, we provide a comprehensive protocol for
constructing electron optic components, such as focusing and bifurcating
lenses, polarizers, and mirrors. We numerically test the robustness of our
designs to disorder and finite temperatures, and motivate the feasibility of
experimental realization. Our work opens avenues for electron optics in two
dimensions beyond graphene-based devices, where a plethora of inverted-band
materials in contemporary experiments can be harnessed.
