Focal characteristics of spheroidal geodesic lenses for integrated optical processing

Abstract

Aspheric shaping of geodesic lenses in optical waveguides is suggested as a means for correcting spherical aberrations. The technique is complementary to the method of Spiller and Harper, in which geodesic lens aberrations are reduced by thickening the waveguiding layer in the lens region. The properties of a family of oblate-spheroidal lenses with no third-order spherical aberrations are described theoretically. Diffraction-limited performance over apertures up to one-half the full lens aperture is predicted for lenses with true <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</tex> /numbers (focal length divided by useful aperture) in the range 2-12. By combining spheroidal-shaping and mode-index correction techniques, geodesic lenses free from both third- and fifth-order aberrations can be designed. These lenses show diffraction-limited performance over apertures of a centimeter or more when true <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</tex> /numbers are in the range 1.5-9.5.