Anisotropic Fermat’s principle for controlling hyperbolic van der Waals polaritons

Abstract

Transformation optics (TO) facilitates flexible designs of spatial modulation of optical materials via coordinate transformations, thus, enabling on-demand manipulations of electromagnetic waves. However, the application of TO theory in control of hyperbolic waves remains elusive due to the spatial metric signature transition from ( + , + ) to ( − , + ) of a two-dimensional hyperbolic geometry. Here, we proposed a distinct Pythagorean theorem, which leads to establishing an anisotropic Fermat’s principle. It helps to construct anisotropic geometries and is a powerful tool for manipulating hyperbolic waves at the nanoscale and polaritons. Making use of absolute instruments, the excellent collimating and focusing behaviors of naturally in-plane hyperbolic polaritons in van der Waals α – MoO 3 layers are demonstrated, which opens up a new way for polaritons manipulation.