  In nanostructure electronic devices, it is well-known that the optical
lattice waves in the constituent semiconductor crystals have to obey both
mechanical and electrical boundary conditions at an interface. The theory of
hybrid optical modes, established for cubic crystals, is here applied to
hexagonal crystals. In general, the hybrid is a linear combination of a
longitudinally-polarized (LO) mode, an interface mode (IF), and an interface TO
mode. It is noted that the dielectric and elastic anisotropy of these crystals
add significant complications to the assessment of the electro-phonon
interaction. We point out that, where extreme accuracy is not needed, a cubic
approximation is available. The crucial role of lattice dispersion is
emphasised. In the extreme long-wavelength limit, where lattice dispersion is
unimportant, the polar optical hybrid consists of an LO component plus an IF
component only. In his case no fields are induced in the barrier, and there are
no remote-phonon effects.
