Anastigmatic three-dimensional bootlace lens

A three dimensional lens adapted to have electromagnetic energy transmitted thereacross for use in a planar antenna array comprising:

• a first spherical concave cap section including a plurality of radiators defining feed ports directed toward its center of curvature;
• a second spherical concave cap section including a plurality of radiators defining lens ports directed toward its center of curvature;
• said concave cap sections facing each other and spaced apart on a central axis by a distance of S=R (2-.sqroot.2), where R is the radius of curvature of the concave cap sections;
• material filling the space between the facing concave cap sections having an index of refraction decreasing radially from the central axis according to the formula:
• n=2/(1+r.sup.2), where r is the radius from a point on the central axis midway between the cap sections;
• equal length coaxial transmission lines connecting the lens ports with the planar antenna array;
• whereby electromagnetic energy passing between said feed ports and lens ports is caused to take paths through the material whose lengths are varied due to the changing index of refraction of the material for improved off-axis focusing of the antenna array for forming simultaneous multiple directive beams.