Coupled interface-plasmon modes of a superlattice and doped overlayer

We calculate the energy dispersion relation of the local interface-plasmon modes of a semi-infinite periodic array of quantum wells coupled to the surface-plasmon mode of a doped overlayer. For equal dielectric constants, an exact solution for the interface-plasmon modes is obtained. In the limit that the distance d separating the superlattice and overlayer is zero, one interface mode is found. This mode exists only for wave vectors larger than a critical value dependent upon the ratio of the density of the quantum well to the density of the overlayer. For arbitrary separation d, two local interface-plasmon eigenstates are found that correspond to the symmetric and antisymmetric combinations of the semi-infinite superlattice plasmon and the surface plasmon associated with the doped layer. These modes are shown to have a very intricate energy dispersion. They are distinctly different from the surface modes of Giuliani and Quinn [Phys. Rev. Lett. 51, 919 (1983)], which do not exist in this case of equal dielectric constants.