A general analysis of nonplanar, two-dimensional luneberg lenses

A class of two-dimensional, nonplanar, modified Luneberg lenses is developed which generalizes the properties of many of the previously developed lenses. By this development the radiated beam can have an arbitrary direction relative to the plane of the lens as compared to previously developed designs in which the beam must lie in the plane of the lens. The lenses are of arbitrary contour; however, only the spherical and the planar contours are considered in detail.