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

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.

Chaos Detection by Fast Dynamic Indicators in Reflecting Billiards

“…For a single orbit, the dependence on n can be investigated and the limit , limit of , provides the maximum Lyapunov exponent. has been shown to be very sensitive to multi-dimensional problems, such as chaos detection in planetary systems (see, for instance, [ 32 ]) and in 2D and 3D waveguides (see [ 33 ]). In Section 3 , we present a numerical analysis of the 2D reflection map in a convex domain, given by a deformed circle.…”

Ray transport and chaos detection in cavities via dynamic indicators

“…In particular, we develop two dynamic indicators from LRT: The Lyapunov and reversibility error. We then present a numerical analysis of: i) a 1D reflection map in a corrugated waveguide [3,4]; ii) a 2D reflection map in a convex billiard given by a deformed unit circle [5], via computation of the two dynamic indicators. We compare the phase portraits with the colour plots of the Lyapunov and reversibility errors [6] computed in a regular space grid in the ray dynamical phase space.…”