Tracking optimization for propagation of electromagnetic waves for multiple wavelengths

Abstract

The purpose of our work is to design dielectric composite structures with specific qualities. In this paper we construct interfaces of given material components such that the originated structure attains desired properties. Propagation of the electromagnetic waves in the composite is described by the Helmholtz equation. Quality of the structure for a given set of wavelengths is enumerated by the tracking functionals that are to be minimized. Interfaces of the given materials are parametrized by the cubic B-spline curves. The design variables are afterwards the positions of B-spline control points. For cost functional evaluation one forward computation of the Helmholtz equation for each wavelength is needed. To get the sensitivity of the objective function we solve the backward (adjoint) equation. Several numerical simulations are presented. Finally three different designs are discussed.