Dynamic programming revisited: a generalized formalism for arbitrary ray trajectories in inhomogeneous optical media with radial dependence
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2009
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IOP Publishing Ltd.
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Abstract
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.
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© 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.