Interface plasmon modes of coupled semi-infinite superlattices

The energy dispersion relation of the local interface plasmon modes of two coupled semi-infinite periodic arrays of quantum wells separated by a distance d has been calculated. An exact solution is obtained when the two semi-infinite superlattices have equivalent periodicities and dielectric constants, but different densities. For the separation equal to zero limit, one interface plasmon mode is found. This mode exists only for wave vectors greater than a critical value depending upon the ratio of the densities of the two superlattices. For finite separation, two interface plasmon modes are found corresponding to the symmetric and antisymmetric combinations of the individual superlattice plasmon modes. These modes are found to exist only for separations less than some critical value depending upon the ratio of the separation distance to the superlattice periodicity.