Optimal design of an optical lens (Q1096796)

One considers a lens which focuses all rays from a given source onto a given focal point. The nonlinear differential equations which define the lens are first derived by using the Fermat principle of least time and then the existence and the uniqueness of the solution is considered. To this end, by using a fixed point theorem, one first constructs a local solution in a vicinity of zero, and then this solution is analytically extended. This is a global study of a system of two nonlinear functional differential equations.