  We study coupling of leaky Berreman modes in polar dielectric films (SiO2)
through a thin metallic layer (gold) and show the familiar signatures of normal
mode splitting. Due to very large negative real part of the dielectric function
of gold, the splitting shows up only for extremely thin coupling layers. In
contrast, coupling of Berreman modes through a dielectric spacer layer reveals
novel possibilities of having bound states in continuum, albeit in the limit of
vanishing losses. It is shown that the corresponding dispersion branches of the
symmetric and antisymmetric modes can cross. BIC is shown to occur on one of
these branches which is characterized by lower loss. In fact the BIC
corresponds to the point where the radiative losses are minimized. For thicker
layers (both spacer and the polar dielectric) BIC is shown to occur on the
higher order dispersion branches. The origin of BIC is traced to the
Fabry-Perot type mechanism due to the excitation of the leaky guided modes in
the central layer.
