Geodesic Lenses for Integrated Optics

Abstract

The authors present a procedure for the design of an aspherical, rounding-edge geodesic lens for integrated optics. The design, which is based on geometrical optics, makes use of the annulus technique, and of the principle of equivalent lenses.

In practice, the geodesic lens necessarily has an appropriate rounding-edge in order to reduce the scattering loss due to the steep rim between the waveguide and the lens. A numerical procedure has been devised to find the joint point between the rounding-edge and the inner part of the lens.

To facilitate the design, a relationship between the focal length, the effective aperture and the smoothness of the joint point has been found and represented in a graphical form. The tolerances achievable with the state-of-the-art technology are discussed.

Experimental results obtained in the authors’ laboratory for evaluation of the produced lenses are in good agreement with the numerical calculation.