An exact method, based on microscopic boundary conditions, is developed for calculation of the optical properties of exciton polaritons with spatial dispersion. The method is formulated in a general manner for an arbitrary electron-hole potential and probed in the approximation of the one-dimensional contact interaction, in half-space and slab geometries. Another approach, based on approximate boundary conditions applied to all exciton bound and scattering states, generalizes the concept of additional boundary conditions. This approach yields analytical results for semi-infinite semiconductors and semiconductor slabs and allows us to extract and analyze the contribution of the exciton continuum states to the optical spectra of semiconductors. A correlation between reflectivity and transmission calculated in two different approaches demonstrates the crucial role of the strict boundary conditions in the correct computation of optical spectra.
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Muljarov et al. (2002) studied this question.