Analytical inversion of dielectric matrix of electron gas with one-dimensional inhomogeneity

In the framework of classical electrodynamics by analytical inversion of dielectric matrix simple expressions are derived for macroscopic dielectric function and function of energy losses. The electron density of systems under study is arbitrary function of one coordinate. Fourth scattering of incident electrons is treated. The theory is applicable to foils, surfaces and structures of one-dimensional periodicity. The model calculation is presented, where the importance of non-diagonal elements of dielectric matrix (local-field effects) is explicitly demonstrated.