Macroscopic theory of optical phonons in superlattices

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Abstract
A macroscopic theory of optical-phonon modes in superlattices is developed. The Born-Huang equation is used with the inclusion of elastic force terms. The Hermiticity condition for the dynamical operator allows one to solve the eigenvalue problem uniquely without any particular boundary conditions at superlattice interfaces. The eigensolutions are classified according to their bulk and sheet sources and vortices. Eigenfrequencies and eigenvectors of confined bulk and interface modes are determined, and proven to form a complete orthonormal basis set. The results agree well with those from microscopic calculations, apart from certain singular wave vectors where a degeneracy takes place between confined bulk modes of equal polarizations or between confined and interface modes. The Fröhlich interaction Hamiltonians are derived for both types of modes.