Open AccessTwo-dimensional fast marching for geometrical optics
Author(s) -
Amedeo Capozzoli,
Claudio Curcio,
Angelo Liseno,
Salvatore Savarese
Publication year - 2014
Publication title -
optics express
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.394
H-Index - 271
ISSN - 1094-4087
DOI - 10.1364/oe.22.026680
Subject(s) - eikonal equation , luneburg lens , physical optics , geometrical optics , discretization , ray tracing (physics) , optics , integral equation , physics , paraxial approximation , scattering , maxwell's equations , polarization (electrochemistry) , plane wave , inverse scattering problem , inverse problem , mathematical analysis , classical mechanics , mathematics , refractive index , beam (structure) , chemistry
We develop an approach for the fast and accurate determination of geometrical optics solutions to Maxwell's equations in inhomogeneous 2D media and for TM polarized electric fields. The eikonal equation is solved by the fast marching method. Particular attention is paid to consistently discretizing the scatterers' boundaries and matching the discretization to that of the computational domain. The ray tracing is performed, in a direct and inverse way, by using a technique introduced in computer graphics for the fast and accurate generation of textured images from vector fields. The transport equation is solved by resorting only to its integral form, the transport of polarization being trivial for the considered geometry and polarization. Numerical results for the plane wave scattering of two perfectly conducting circular cylinders and for a Luneburg lens prove the accuracy of the algorithm. In particular, it is shown how the approach is capable of properly accounting for the multiple scattering occurring between the two metallic cylinders and how inverse ray tracing should be preferred to direct ray tracing in the case of the Luneburg lens.