Goos–Hänchen shift on the surface of a polar crystal

We theoretically investigated the Goos–Hanchen shift (GHS) on the surface of a polar crystal, where a polarized beam was incident on the crystal from any positive permittivity medium. Attention was focused on GHS’s features for the incident-beam frequency lies near or in the reststrahlen band of the crystal. The GHS expressions were obtained for the s- and p-polarized incident beams, respectively. Our results demonstrate that the GHS properties are completely different for differently polarized incidences. The concise expression of GHS was obtained for the crystal with a low optical loss, accompanied by a large GHS in the vicinity of the critical or Brewster angle. In comparison with the optically lossless case, the effect of the loss on the GHS was clearly indicated. Unlike photonic crystals and metamaterials, the crystal used here is a natural material whose interesting frequency range is in the infrared region, and optical loss is much lower. The present GHS can be more easily observed and technically applied because the incident medium above the crystal surface can be any positive permittivity medium. The numerical results were obtained from the interface structure of the ZnS crystal and free space.