Electromagnetic wave propagation in metamaterials: a visual guide to Fresnel-Kummer surfaces and their singular points

TL;DR

This paper explores electromagnetic wave propagation in bianisotropic metamaterials using geometrical optics, focusing on Fresnel surfaces and their singularities, and unifies various wave surfaces through projective geometry of Kummer surfaces.

Contribution

It introduces a unified geometric framework for understanding Fresnel surfaces in metamaterials using Kummer surfaces and the Tamm-Rubilar tensor.

Findings

Collection of diverse Fresnel surfaces analyzed

Unified description via Kummer surface geometry

Insights into singular points of wave surfaces

Abstract

The propagation of light through bianisotropic materials is studied in the geometrical optics approximation. For that purpose, we use the quartic general dispersion equation specified by the Tamm-Rubilar tensor, which is cubic in the electromagnetic response tensor of the medium. A collection of different and remarkable Fresnel (wave) surfaces is gathered, and unified via the projective geometry of Kummer surfaces.