Local-field effects, x-ray diffraction, and the possibility of observing the optical Borrmann effect: Solutions to Maxwell's equations in perfect crystals

Abstract

The electromagnetic normal-mode solutions to Maxwell's equations in perfect crystals are investigated including local-field effects by means of the dielectric-response matrix. The dynamical theory of x-ray diffraction is seen to be a special case thereof. At optical frequencies, a perturbation-theory expansion in q, the reduced wave vector, is solved and used to investigate the possibility that a microscopically varying component of the normal mode, $e^{i(\overrightarrow{\mathrm{q}}+\overrightarrow{\mathrm{k}})·\overrightarrow{\mathrm{r}}}$ ($\overrightarrow{\mathrm{K}}$ is a reciprocal-lattice vector), can transmit into the vacuum. The optimal effciency for this process is estimated to be 2.6 × ${10}^{-10\mathrm{}}$ for $\hslash \omega =1.5\mathrm{}$ eV in diamond. However, this process may be affected by the intrinsic irregularities, on an atomic scale, of the crystal-vacuum interface.