European Journal of Applied Mathematics

Research Article

Optimal design of periodic antireflective structures for the Helmholtz equation

David C. Dobsona1

a1 Institute for Mathematics and its Applications, University of Minnesota, 514 Vincent Hall, Minneapolis, MN 55455-0436, USA

Abstract

We study the problem of designing a periodic interface between two homogeneous materials with different impedance properties, in such a way that time-harmonic waves incident on the interface over a given range of angles have minimal total reflected energy. It is shown that the problem can be ‘relaxed’ to include continuously varying profiles. A simple gradient descent minimization scheme is proposed and examples from several numerical calculations are given.

(Received July 08 1992)