Geodesic optical waveguide lens analysis*

Abstract

In the geometrical approximation, ray paths over waveguide depressions (geodesic lenses) may be determimed by Fermat’s principle. In this paper an algroithm is derived, based on Fermat’s principle, to ray trace geodesic lenses with circular symmetry having an arbitrary generating curve. Ray tracing techniques are also presented for conical skirt mirror and toric edge rounding which are used to guide the rays into the geodesic lens. Furthermore, aspheric geodesic lens profiles are derived that provide perfect geometrical focusing with arbitrary focal length.