Flattened generalized Maxwell fish-eye lens limiting sub-unity refractive index regions

In this paper we propose the designs of three wide- band flattened generalized Maxwell fish-eye lenses. The designs were performed using transformation optics with quasiconformal mapping. This transformation allows not only to arbitrarily shape the lenses preserving the same electromagnetic response, but also to reduce the sub-unity regions which limit the bandwidth of operation. These devices have practical applications as wide-angle scanner and power divider matched in terms of the shape with conventionally planar receiver/transceiver arrays.