  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.
