Validity of the continuum approach to optical phonons in short-period superlattices

The authors report a strict comparison of long-wavelength optical lattice vibrations in a superlattice obtained with the macroscopic continuum model and a closely parallel microscopic model. It is shown that the proper envelopes of the atomic displacement patterns can be found if the uncertainties inherent in any dispersionless theory such as the continuum model are appropriately treated. Apart from small discrepancies due to the discrete nature of the matter and effective material layer thicknesses the main failure of the continuum theory is the neglect of bulk phonon dispersion.