A method for calculating profiles of a dielectric thick lenses

Hasanov and Polat (see International Journal of Electronics and Communications (AEO), vol.54, no.2, p.109-113, 2000) investigated the transformation of a plane wavefront to another plane wavefront after passing through a thick lens and described the class of optical mappings realizable by means of such lenses. However, it is desirable to describe the class of optical mappings and calculate the lens profiles for a more general case when incoming and outgoing wavefronts have arbitrary shapes. For two reflecting surfaces a similar problem has been solved by Gasanov (1991). The aim of this paper is to provide a method for calculating the profiles of symmetric thick lenses which realize an a priori given optical mapping between spherical and plane wavefronts. It is shown that this mapping may be chosen freely and be used for various purposes such as satisfying Abbe´s sine law or Herscel´s condition exactly. We have shown, that calculating the profiles of lenses can be reduced to solving two first-order differential equations which can be solved separately. It is also shown that the geometry of the problem provides a natural condition to control the accuracy for the numerical solution of the obtained differential equations