On Gradient Effective index Ray-Tracting in Planar Luneburg Lenses
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Date
1988-06
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Addis Ababa University
Abstract
The problem ,,1&r~ssed j.n the. thesis li(~E in the
field of integrated optics. }'or Hght propagation ill dielect.l'ic
,,,,aveguides interconnections are established bet\>leen the dispersion -"equation,
critical thickness and effective refractive index of the
film, electric field distl'ibution, power flow and a zig-zag
model of propagation. All existing types of planar lenses are
descrihed and critically analyzed, among them the generalized
Luneburg lenses seem to be one of the most advantageous for
applications in integrated optical cricui ts. Existing raY.-tracing
technique in such lenses is critically analyzed, A neH raytracing
approximation b'lsed on Fermat's principle is suggested.
The pr"",edure is successfully tested fm' a classical Luneburg
lens in which case the integrals are taken analytically. Some
detailed mathematical proofs have been relegated to the appendixes,
which, however, shOUld be regarded as integral parts of the paper
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On Gradient Effective index Ray-Tracting