Calvo Padilla, María LuisaPérz Ríos, Jesús2023-06-202023-06-202009-121464-425810.1088/1464-4258/11/12/125403https://hdl.handle.net/20.500.14352/44185© 2009 IOP Publishing Ltd. The financial support of the Spanish Ministry of Science and Innovation under Grant TEC2008-04125 and CAM-CG-300 is acknowledged. One of us (JPR) acknowledges the Consejo Superior de Investigaciones Científicas (CSIC) for the grant accorded (JAE-pre Fellowship). We are indebted to V. Lakshminarayanan for helpful suggestions and discussions.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.engjournal articlehttp://dx.doi.org/10.1088/1464-4258/11/12/125403http://iopscience.iop.org/open access535Gradient-Index MediaFermats PrincipleEikonal EquationÓptica (Física)2209.19 Óptica Física