On Gradient Effective Index Ray-tracting In Planar Luneburg Lenses

The problem ,,1&r~ssed j.n the. thesis li(~E in thernfield of integrated optics. }'or Hght propagation ill dielect.l'icrn,,,,aveguides interconnections are established bet>leen the dispersion -"equation,rncritical thickness and effective refractive index of thernfilm, electric field distl'ibution, power flow and a zig-zagrnmodel of propagation. All existing types of planar lenses arerndescrihed and critically analyzed, among them the generalizedrnLuneburg lenses seem to be one of the most advantageous forrnapplications in integrated optical cricui ts. Existing raY.-tracingrntechnique in such lenses is critically analyzed, A neH raytracingrnapproximation b'lsed on Fermat's principle is suggested.rnThe pr"",edure is successfully tested fm' a classical Luneburgrnlens in which case the integrals are taken analytically. Somerndetailed mathematical proofs have been relegated to the appendixes,rnwhich, however, shOUld be regarded as integral parts of the paper

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