Corrugated waveguide under scaling investigation

TL;DR

This paper investigates the scaling properties of classical light ray dynamics in a periodically corrugated waveguide using a nonlinear map, revealing mixed phase space characteristics and critical exponents.

Contribution

It introduces a simplified nonlinear map approach to analyze phase space mixing and scaling in corrugated waveguides, applicable to broader systems with mixed phase space.

Findings

Phase space is mixed with chaotic regions.

Critical exponents are connected by an analytic relationship.

Formalism applies to systems transitioning from integrability to chaos.

Abstract

Some scaling properties for classical light ray dynamics inside a periodically corrugated waveguide are studied by use of a simplified two-dimensional nonlinear area-preserving map. It is shown that the phase space is mixed. The chaotic sea is characterized using scaling arguments revealing critical exponents connected by an analytic relationship. The formalism is widely applicable to systems with mixed phase space, and especially in studies of the transition from integrability to non-integrability, including that in classical billiard problems.