The Hyperbolic Nature of Hyperbolic Polaritons.

Polaritons travelling along a hyperbolic medium's surface have recently sparked significant interest in nanophotonics for the unprecedented manipulation ability on light at the nanoscale in a planar way, promising potential nano-optical applications, especially in 2D circuitry. Despite the widespread use of the term "hyperbolic polariton," the hyperbolic nature has predominantly been inferred from numerical solutions of implicit eigenmode equations, rather than established through an explicit analytical isofrequency relation. In this work, we propose an analytical form for describing the iso-frequency contour of the hyperbolic polaritons, showcasing their strictly hyperbolic nature. Such an analytical form is obtained based on the focusing behavior of the hyperbolic polariton and verified by both numerical simulations on commonly used hyperbolic media systems of the hyperbolic polaritons and experimental characterizations on a hyperbolic metamaterial film. The results present a concise and intuitive physical image of its propagation behavior with the angular dispersion, revealing the fundamental mechanism governing the realization of the deeply sub-diffractional volume-confined polariton and provide a groundbreaking methodology in developing novel hyperbolic polaritons-based optical devices.