Snell's law in multirefringent systems

TL;DR

This paper generalizes Snell's law for multirefringent systems with multiple propagating modes, demonstrating the formation of anomalous caustics through quantum mechanical calculations in electron-optical systems.

Contribution

It introduces a generalized Snell's law applicable to multirefringent systems with more than two modes, enabling the analysis of complex wave phenomena like anomalous caustics.

Findings

Confirmation of anomalous caustics in electron-optical systems

Generalized Snell's law for multirefringent media

Quantum mechanical calculations in multilayer graphene

Abstract

In anisotropic crystals, Maxwell's equations permit only birefringence for the propagation of light. Notwithstanding, multirefringent systems comprising more than two propagating modes exist, such as in electron optics and photonic crystals. It has been demonstrated that in such systems, the propagation of waves in the short wavelength limit results in the formation of anomalous caustics. To calculate these caustic curves, we generalized Snell's law valid for reflection and refraction in multirefringent systems possessing more than one propagating mode. The emergence of anomalous caustics in the wave function patterns obtained from rigorous quantum mechanical calculations in electron-optical systems is confirmed. These calculations were performed on electron scattering from circularly gated potential regions applied to multilayer rhombohedral graphene. Our results may generate further work to explore more complex phenomena in multirefringent systems.