Propagation of rays in 2D and 3D waveguides: a stability analysis with Lyapunov and Reversibility fast indicators

TL;DR

This paper analyzes the stability of ray propagation in 2D and 3D waveguides using Lyapunov and Reversibility indicators, revealing different error growth laws for regular and chaotic orbits and relating capacity scaling to waveguide corrugation.

Contribution

It introduces a stability analysis framework for waveguide ray propagation using Lyapunov and Reversibility errors, linking chaos, regularity, and channel capacity.

Findings

Error growth is power-law for regular orbits.

Error growth is exponential for chaotic orbits.

Capacity increases with corrugation depth following an approximate scaling law.

Abstract

Propagation of rays in 2D and 3D corrugated waveguides is performed in the general framework of stability indicators. The analysis of stability is based on the Lyapunov and Reversibility error. It is found that the error growth follows a power law for regular orbits and an exponential law for chaotic orbits. A relation with the Shannon channel capacity is devised and an approximate scaling law found for the capacity increase with the corrugation depth.