Minimax design of optically transparent and reflective coatings

We consider the design problem of creating coatings that are either highly reflective or highly transparent. The goal is to create an optical element, consisting of planar dielectric layers, that reflects (or transmits) energy over a given range of wavelengths and angles of incidence. The approach that we take is to formulate the problem as a minimax optimization problem. We demonstrate that the approach can be effective in producing coatings of a few layers with desirable properties.