PERIODIC-ORBITS IN A SIMPLE RAY-SPLITTING SYSTEM

We study ray dynamics in a square billiard that allows mode conversion and is parametrized by kappa, the ratio of the velocities of the two modes. At kappa --> 1(+), conversion occurs at every reflection and pe riodic orbits proliferate exponentially. As kappa increases beyond roo t 2, the collection of daughter rays explore only three momentum direc tions and mode conversion is progressively inhibited. We provide an al gorithm for determining periodic orbits when kappa > root 2 and show n umerically that exponential proliferation persists around kappa simila r or equal to root 2 but as kappa increases, a crossover to subexponen tial behavior occurs for short periods. We discuss these results in th e light of conservation laws.