Dispersion relations and the nonlinear generation ofC1-surface exciton polaritons in spatially dispersive ZnO

The recent experiments of DeMartini, Colocci, Kohn, and Shen [Phys. Rev. Lett. 38, 1223 (1977)] on the nonlinear generation of $C1\mathrm{}$- ($n=1\mathrm{}$ in the series) surface exciton polaritons in spatially dispersive ZnO are analyzed. It is shown for a prism-air-sample geometry that the air-gap thickness plays an important role in determining the polariton attenuation, and to a lesser degree the polariton energy. Reasonably good agreement with the experimental dispersion relations of DeMartini and co-workers is obtained by including spatial dispersion via the additional boundary condition (ABC) $\frac{\partial {\overrightarrow{\mathrm{P}}}_{\mathrm{ex}}}{\partial z}=0\mathrm{}$ for the excitonic polarization ${\overrightarrow{\mathrm{P}}}_{\mathrm{ex}}$ at the surface: The ABC ${\overrightarrow{\mathrm{P}}}_{\mathrm{ex}}=0\mathrm{}$ does not yield a good fit. The theory of the nonlinear generation of surface exciton polaritons in isotropic, spatially dispersive media is developed and applied to angle- and frequency-scanning experimental geometries. Numerical estimates of both the power radiated out via the prism (in the absence of surface roughness) and the line shape were also found to be in reasonable agreement with experiment for the ABC $\frac{\partial {\overrightarrow{\mathrm{P}}}_{\mathrm{ex}}}{\partial x}=0\mathrm{}$, but not for ${\overrightarrow{\mathrm{P}}}_{\mathrm{ex}}=0\mathrm{}$.