Continuum theories of optical phonons and polaritons in superlattices: A brief critique

The controversy concerning the confinement of optical modes in superlattices concerns the use of electromagnetic (EM) or hydrodynamic (HD) boundary conditions and the roles of dispersion and retardation in continuum theories, and how continuum theories relate to microscopic models. In this paper we describe EM and HD continuum models and discuss recent attempts to reconcile the EM model with microscopic theory. We conclude that the lack of retardation and dispersion in the EM model results in a confusion between LO modes and polaritons. In particular, we question the attribution of LO-type Fr\"ohlich scalar potential to Fuchs-Kliewer interface polaritons.