Oscillations localized near impurity layers in a layered crystal

It is shown that the interaction between vibrational modes polarized parallel and perpendicular to the layers in a strongly anisotropic layered crystal is very weak for frequencies above the van Hove frequency, which corresponds to a transition from closed isofrequency surfaces to surfaces which are open in the weak-coupling direction. Such mode quasisplitting results in quasi-two-dimensional behavior of phonons polarized along layers and quasi-one-dimensional behavior of phonons polarized in a direction perpendicular to the layers and localized near light or strongly coupled impurity atoms or monolayers.