Optimal design of periodic antireflective structures for the Helmholtz equation

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.