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

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dc.contributor.authorCalvo Padilla, María Luisa
dc.contributor.authorPérz Ríos, Jesús
dc.date.accessioned2023-06-20T03:39:36Z
dc.date.available2023-06-20T03:39:36Z
dc.date.issued2009-12
dc.description© 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.
dc.description.abstractWe 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.
dc.description.departmentDepto. de Óptica
dc.description.facultyFac. de Ciencias Físicas
dc.description.refereedTRUE
dc.description.sponsorshipMinisterio de Ciencia e Innovación (MICINN), España
dc.description.sponsorshipConsejo Superior de Investigaciones Científicas (CSIC), España
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/25450
dc.identifier.doi10.1088/1464-4258/11/12/125403
dc.identifier.issn1464-4258
dc.identifier.officialurlhttp://dx.doi.org/10.1088/1464-4258/11/12/125403
dc.identifier.relatedurlhttp://iopscience.iop.org/
dc.identifier.urihttps://hdl.handle.net/20.500.14352/44185
dc.issue.number12
dc.journal.titleJournal of Optics A. Pure and Applied Optics
dc.language.isoeng
dc.publisherIOP Publishing Ltd.
dc.relation.projectIDJAE-pre Fellowship
dc.relation.projectIDTEC2008-04125
dc.relation.projectIDCAM-CG- 300
dc.rights.accessRightsopen access
dc.subject.cdu535
dc.subject.keywordGradient-Index Media
dc.subject.keywordFermats Principle
dc.subject.keywordEikonal Equation
dc.subject.ucmÓptica (Física)
dc.subject.unesco2209.19 Óptica Física
dc.titleDynamic programming revisited: a generalized formalism for arbitrary ray trajectories in inhomogeneous optical media with radial dependence
dc.typejournal article
dc.volume.number11
dcterms.references[1] Bellman R E 1957 Dynamic Programming (Princeton, NJ: Princeton University Press). [2] Lee C L and Dana R A 2003 Dynamic Programming in Economics (Berlin: Springer). [3] Joseph S and Lakshminarayanan V 2002 Proc. 1st Int. Conf. on Quantum Limits to the Second Law AIP Conf. Proc. 643 297. [4] Edd S R 2002 BMC Bioinform. 3 18. [5] Sieniutycz S 2009 Appl. Math. Mod. 33 1457. [6] Calvo M L and Lakshminarayanan V 1987 J. Opt. Soc. Am. A 14 872. [7] Calvo M L and Lakshminarayanan V 1999 Opt. Commun. 169 223. [8] Lakshminarayanan V, Ghatak A K and Thyagarajan K 2002 Lagrangian Optics (Dordrecht: Kluwer). [9] Kalaba R 1961 J. Opt. Soc. Am. 51 1150. [10] Brandstatter J J 1974 J. Opt. Soc. Am. 64 317. [11] Sands P J 1983 Appl. Opt. 22 430. [12] Van Turnhout M and Bociort F 2009 Opt. Express 17 314. [13] Molloy J E and Padgett M J 2002 Contemp. Phys. 43 241. [14] Elsgoltz L 1996 Differential Equations and Variational Calculus (Russia: Mir) (in Spanish) The Lagrange-Sharpy method consists in transforming an initial equation in a Pfaff equation using an auxiliary scalar function Elsgoltz L 1962 Calculus of Variation (Reading, MA: Addison-Wesley) (in English). [15] Migayi H and Taniguchi T 1981 IEE Proc. 128 117. [16] Bociort F and Kross J 1993 Proc. SPIE 1780 216. [17] Marchand E W 1972 Appl. Opt. 11 1104. [18] Luneburg R K 1964 Mathematical Theory of Optics (Berkeley, CA: University of California Press). [19] Kline M and Kay I W 1965 Electromagnetic Theory and Geometrical Optics (New York: Wiley-Interscience). [20] Miñano J C, Benítez P and Santamaría A 2006 Opt. Express 14 9083. [21] Press W H, Flannery B P, Teukolsky S A and Vetterling W T 1986 Numerical Recipes, The Art of Scientific Computing (Cambridge: Cambridge University Press). [22] José J V and Saletan E J 1998 Classical Dynamics: A Contemporary Approach (Cambridge: Cambridge University Press). [23] Landau L and Lifschitz E 1994 Mechanics (Barcelona: Reverté) (Spanish edition). [24] Roberts M J 2003 Signals and Systems: Analysis of Signals Through Linear Systems (New York: McGraw-Hill Science Engineering). [25] See for example McNeillie F C, Thomsom J and Ruddock I S 2004 Eur. J. Phys. 25 479 ; Moore D T 1975 J. Opt. Soc. Am. 65 451 ; Ghatak A K and Sauter E G 1989 Eur. J. Phys. 10 136 [26] Moore D T 1993 Selected Papers on Gradient-Index Optics (SPIE Milestone Series vol MS67) (Bellingham, WA: SPIE Optical Engineering Press). [27] Gómez-Reino C, Pérez M V, Bao C and Flores-Arias M T 2008 Laser Photon. Rev. 2 203. [28] Murukeshan V M 2007 Biomedical fiber optics Optical Waveguides: From Theory to Applied Technologies ed M L Calvo and V Lakshminarayanan (Boca Raton, FL: CRC Press) chapter 10.
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