Dynamic programming revisited: a generalized formalism for arbitrary ray trajectories in inhomogeneous optical media with radial dependence

摘要

We present a formalism based upon dynamic programming (DP), to characterize light propagation in particular GRIN (gradient index) media by analyzing ray trajectories associated with skew-type rays. We study the conditions for the formation of periodic trajectories and stability of the system. We perform a comparative study with the classical formalism based on the Hamilton-Jacobi equation. The DP formalism allows representation in phase ( momentum) space.