Parallel-ray focusing with flat lens doublets

A doublet lens is proposed consisting of two plane parallel discs in contact and composed of nonhomogeneous refractive index media. In the first region incident rays are given an upward curvature by appropriate choice of refractive-index variation, and in the second region this is reversed up to the point where the rays are again parallel to the axis. The ray-tracing technique, for this form of focusing, relies upon the ray integral formula for nonhomogeneous media. A consequence of the design is a short focal-length beam expander with input and output rays parallel to the axis, with applications in laser and ultrasonic spot size reduction, junctions between multimode fibres of differing diameters and in integrated optics.