Extraordinary reflection and refraction from natural hyperbolic materials

The reflection and refraction were theoretically investigated for a linearly-polarized wave incident upon the surface of a naturally hyperbolic material. We proposed that this material is uniaxial and possesses two hyperbolic-frequency bands (HB-I and HB-II), whose optical axis is arbitrarily pointed. We paid our attention to reflective and refractive features in the HBs and predicted some extraordinary phenomena. The double reflection was found, where the reflective wave contains a transverse electric branch and a transverse magnetic branch with different amplitudes and phases. The asymmetry of reflection exists and the reflective coefficient abnormally decreases as the incident angle is enlarged. The double refraction inside the material means two refractive branches (the o-wave and e-wave). For the e-wave, there is a special frequency point (SP) in either HB, depending on the orientation of the optical axis. The e-wave and reflective wave exhibit completely different behaviors on the two sides of the SP. The e-wave is a normal refractive wave on the left side of the SP, but it is an evanescent wave on the right side. Its energy-flux seriously deviates from the incident plane and is highly condensed at the inner surface near the SP. It is more interesting that the energy-flux density of the e-wave in the HB-II can even be much larger than that of the incident wave and is opposite in direction on the two sides of the SP, which means an evident radiation-switching effect. The o-wave is a normal refractive wave in the HB-I, but it is an evanescent wave in the HB-II. The above results and conclusions were obtained from the hexagonal boron nitride (hBN). These unique properties may be very useful in optical or optoelectronic technology.