Generalised additional boundary condition for non-local dielectrics. I. Reflectivity

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Abstract
The authors present a macroscopic non-local response theory which explicitly allows for scattering of the excitation at the surface of the medium. This response leads to one or two generalised additional boundary conditions (ABC). They derive compact and explicit formulae for the reflectivities (Rs and Rp), which depend on a surface-scattering parameter Uy (for s polarisation) or two parameters Ux and Uz (for p polarisation). By assigning Uy, or Ux and Uz different numerical values, they obtain results corresponding to different special cases of the ABC. The model employed is appropriate to an isolated excitonic transition in an insulating solid and is applied to calculate the reflectivity spectrum of a model semiconductor. They find that the p-polarised reflectivity is relatively insensitive to the value of the parameter Uz, which governs the behaviour of the normal component of the excitonic polarisation at the surface. As a rule, the greatest (smallest) deviations from local behaviour are found for the Pekar (Fuchs-Kliewer 1971) ABC. For the Agarwal et al. ABC (1981), non-local effects are of intermediate strength. The reflectivity for the Rimbey-Mahan ABC (1974), is nearly equal to that for the Pekar ABC and the same is true for the Ting et al. (1975) and Fuchs-Kliewer ABC. Results are presented for both frequency and angular scans.