Goos-Hänchen and Imbert-Fedorov shifts on hyperbolic crystals

We investigated Goos-Hänchen (GH) and Imbert-Fedorov (IF) shifts on a uniaxial hyperbolic crystal, where a circularly-polarized beam was incident on the crystal from the free space. The GH- and IF-shifts were analytically obtained and numerically calculated for the hexagonal boron nitride. Our results demonstrate that the GH- and IF-shift spectra are complicated and completely different in and out the hyperbolic frequency-bands (the reststrahlen bands in the infrared region). At the critical or Brewster angle, concisely analytical expressions of GH-shift was found, which explicitly state the optical-loss dependence of GH-shift at these special angles. We found the GH-shifts are very large at the critical and Brewster angles. It is very necessary to know these effects since hyperbolic materials are usually applied in the nano- and micro-optics or technology fields.