A synthesis of the aplanatic lens with a two-dimensional gradient of index of refraction

A. S. Venetskiy, V. A. Kaloshin

Kotel’nikov Institute of Radio-engineering and Electronics of RAS

Received February 15, 2013  

Abstract: Two-dimensional problem of synthesis of media with two-dimensional gradient of a refraction index, transforming a field from a point source to a flat front with  of Abbe sine condition satisfaction is considered in a geometrical optics approach. The method of the given ray trajectories to find a refraction index distribution is used. The problem is reduced to a partial differential equation of the first order for the refraction index which is solved by the method of characteristics. Some realizations of media depending on a choice of the index of refraction distribution along the axis are given. The eikonal aberrations in the synthesized medium boundary for the source shifted from the focus are investigated. A comparison with Mikaelian lens characteristics is carried out.

Key words: geometrical optics, inhomogeneous media, lenses, synthesis.