Inhomogeneous waves and energy localization in dielectric superlattices

A study of inhomogeneous plane waves in two-dimensional infinite dielectric lossless media of alternating layers, periodic in one dimension, is carried out. It is supposed that one of the lattice layers has a negative dielectric permittivity in a certain frequency band whereas the other one is a usual dielectric. It is shown that under a certain configurational resonant condition, a wave having a complex wave number (the wave-vector component, which is parallel to the slab interfaces, is also complex) is an eigenmode of the structure. Properties of such eigenwaves, which differ from previously known ones, are investigated. Among them, the most important one is the energy localization of a wave inside the structure in a form of energy bullets. Natural modes of a periodic medium studied here result from translational symmetry of the problem. Therefore, the solution that we discuss is independent of the nature of waves and must exist for any periodic media, namely, dielectric, acoustic, etc.