Interface response and rescaling approach to the eigenvectors of layered composite systems. I. Double-layer slab

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Abstract
We consider the eigenproblem of a composite system of two different layer subsystems, assumed to be coupled at their interface. General formulas for the eigenvectors and eigenvalues of the total system, as well as its response function, are derived and expressed in terms of matrix elements of the individual subsystem response functions and the interface coupling parameter. Explicit expressions for the case most frequently considered in the literature—that of homogeneous subsystems (with arbitrary asymmetrical boundary conditions)—are also given, illustrating the applicability of our general formulas to arbitrary double-layer systems.