Ideal-lens stars

Abstract

We recently showed how structures of ideal (thin) lenses can act as (ray-optical) transformation-optics devices. This was done by breaking the structure down into all sets of ideal lenses in the structure that share a common edge, and showing that these sets have very specific imaging properties. In order to start the development of a general understanding of the imaging properties of sets of ideal lenses that share a common edge, we investigate here particularly simple and symmetric examples of combinations of ideal lenses that share a common edge. We call these combinations ideal-lens stars. An ideal-lens star is formed by N identical ideal lenses, each placed such that they share a principal point (which lies on the common edge) and such that the angles between all neighbouring lenses are the same. We find that that passage through every single ideal lens in the ideal-lens star images any point to itself. Furthermore, light-ray trajectories in ideal-lens stars are piecewise linear approximations to conic sections. (In the limit of N approaching infinity, they are conic sections.)