Oscillations localized near impurity monolayers in a layered crystal

It is shown that in strongly anisotropic layered crystals the interaction between vibrational modes polarized along and perpendicular to the layers is very weak at frequencies above the Van Hove frequency which corresponds to the transition from closed isofrequency surfaces to those opened along the direction of weak coupling. This quasi-splitting of the oscillatory modes leads to a quasi-2D behavior of phonons polarized along the layers and to a quasi-1D behavior of phonons polarized in the direction perpendicular to the layers and localized near light or strongly bound impurity atoms or monolayers