Curved Space-Time for Light by an Anisotropic Medium: Media with the Variable Optical Axes

An optical impedance-matched medium with a gradient refractive index can resemble a geometrical analogy with an arbitrary curved space-time. In this paper, we show that a non-impedance-matched medium with a varying optical axis can also resemble the features of a space of non-trivial metric for the light. The medium with a varying optical axis is an engineered stratified slab of material, in which the orientation of the optical axis in each layer slightly differs from the other layers, while the magnitude of refractive index remains constant. Instead of the change in refractive index, the inhomogeneity of such a medium is induced by the local anisotropy. Therefore, the propagation of light depends on the local optical axis. We study the conditions that make the analogy between curved space-time and a medium with a varying optical axis. Extension of the transformation optics to the media with optical axis profile might ease some fabrication difficulties of materials with gradient refractive index.