We investigate the existence and behaviour of localized and resonant optical waves associated with the surface of a semi-infinite superlattice or its interface with a substrate, considering the case of transverse electric modes. In this paper, we present an analytic determination of the response function (Green function) for a semi-infinite superlattice with or without a cap layer, and for a superlattice in contact with a substrate. This calculation enables us to obtain both local and total densities of states as functions of the frequency and the wavevector (parallel to the interfaces). Besides the surface and interface localized modes which occur as delta peaks inside the gaps, one can also obtain resonant states as well defined peaks of the density of states inside the bulk bands of the superlattice. In particular, we emphasize the different types of mode induced by a cap layer. In addition, we show that the creation of a semi-infinite superlattice gives rise to delta peaks of weight -1/4 in the density of states at every edge of the superlattice bulk bands.

The existence of localized and resonant optical waves associated with the surface of a semi-infinite superlattice or its interface with a substrate is reported, considering the case of s-polarization (transverse electric modes). These modes appear as well defined peaks of the density of states, either inside the minigaps or inside the bulk bands of the superlattice. The density of states, function of the frequency ω, and the wave vector k∥ (parallel to the interface), are obtained from an analytic determination of the response function for a semiinfinite superlattice with or without a cap layer.

Two Green function techniques (the direct matching formalism and the interface response theory) are used to investigate the electronic structure of a semi-infinite GaAs/Ga1 − xAlxAs superlattice being in contact with a Ga1 − yAlyAs substrate. The effect of the superlattice termination on the formation of a surface state as well as on the density-of-states distributions is studied in a systematic way by varying the position of the superlattice surface (i.e. substrate/superlattice interface) within a superlattice period. It has been found that the occurrence, the position and the localization properties of surface states are very sensitive to the way the superlattice is terminated—they occur in particular mini-gaps only for some ranges of the outermost layer thickness. When this thickness is close to the value at which surface states merge into the mini-bands, the density-of-states distributions exhibit the most pronounced modifications.

The influence of capping layers on surface phonon polaritons in two-layer superlattices is investigated here theoretically. General analytical expressions are given. A few illustrative applications are presented afterwards, for p-polarized non-retarded polaritons within GaAs-InAs superlattices with or without an InP capping layer. A few dispersion curves for such polaritons are drawn. The variation of the frequencies of these polaritons with the thickness of the capping layer is given.

The existence of localised and resonant optical waves in semi-infinite superlattice with or without a cap layer is reported, considering the case of s-polarisation (transverse electric modes). These modes appear as well defined peaks of the density of states, either inside the minigaps or inside the bulk bands of the superlattice. The density of states, function of the frequency omega and the wave vector k(parallel to) (parallel to the interface), are obtained from an analytic determination of the response function for these heterostructures.

The interface response theory was recently presented for any composite material in discrete, continuous and mixed (partly discrete - partly continuous) spaces.The aim of this report is to show how this theory can be used for solving the Maxwell equations in any composite dielectric material. General expressions for the corresponding response functions are given. These results are illustrated by a general application to layered isotropic dielectrics and in particular simple derivations of the response functions for two media separated by an interface, for one dielectric slab sandwiched between two different semi-infinite dielectrics and for dielectric superlattices.