INVERSE DESIGN OF DIELECTRIC MATERIALS BY TOPOLOGY OPTIMIZATION

Abstract

The capabilities and operation of electromagnetic devices can be dramatically enhanced if artiflcial materials that provide certain prescribed properties can be designed and fabricated. This paper presents a systematic methodology for the design of dielectric materials with prescribed electric permittivity. A gradient-based topology optimization method is used to flnd the distribution of dielectric material for the unit cell of a periodic microstructure composed of one or two dielectric materials. The optimization problem is formulated as a problem to minimize the square of the difierence between the efiective permittivity and a prescribed value. The optimization algorithm uses the adjoint variable method (AVM) for the sensitivity analysis and the flnite element method (FEM) for solving the equilibrium and adjoint equations, respectively. A Heaviside projection fllter is used to obtain clear optimized conflgurations. Several design problems show that clear optimized unit cell conflgurations that provide the prescribed electric permittivity can be obtained for all the presented cases. These include the design of isotropic material, anisotropic material, anisotropic material with a non-zero ofi-diagonal terms, and anisotropic material with loss. The results show that the optimized values are in agreement with theoretical bounds, conflrming that our method yields appropriate and useful solutions.