Magnetic-field controlled anomalous refraction in doped semiconductors

We predict here that a slab made of a doped semiconductor can exhibit anomalous refraction under the application of a static magnetic field. This anomalous refraction takes place in the far-infrared range and it occurs for any angle of incidence. We show that this effect is due to the fact that a doped semiconductor under a magnetic field can behave, to some extent, as a hyperbolic metamaterial. We also show that the occurrence of this anomalous refraction enables a semiconductor slab under a magnetic field to partially focus the electromagnetic radiation. The remarkable thing in our case is that we deal with naturally occurring materials and the anomalous refraction can be tuned at will with an external field.