Multifocal three dimensional bootlace lenses

It is well known that a two dimensional (parallel plate configuration) bootlace lens can be designed to have more than one focal point. Wide angle scanning capabilities of these lenses in two dimensions is well established, being larger for higher numbers of focal points. However, no three dimensional bootlace lens having more than one focal point has been reported. It is the purpose here to report on three dimensional bootlace lenses having two, three, and four perfect focal points. Equations for lens surfaces are obtained for all three cases. An analysis shows that a lens with a larger number of focal points can be scanned to much larger angles in one plane at the expense of a modest decrease in scanning capability in the orthogonal plane. Computer simulations of radiation patterns for different scan angles are presented for all three lenses. These results also show that a lens with a higher number of focal points can be scanned to larger angles.