2021 Volume 2021 Pages 20210009
In this paper, we propose an optimization method for a unit cell structure of electromagnetic metamaterials using a level set-based topology optimization method incorporated with a high contrast homogenization method. The high contrast homogenization method can express wave propagation behaviors in metamaterials for a wide range of frequencies, and it can capture unusual properties caused by local resonances, which cannot be estimated by the conventional homogenization approaches. An optimization problem is formulated with an objective function composed of the homogenized coefficients, and a sensitivity analysis is conducted based on the concept of the shape derivative and the topological derivative. As numerical examples, we offer optimal configurations of unit cells exhibiting negative permeability. We examine wave propagation behaviors on the electromagnetic metamaterials composed of the optimized unit cells using the Helmholtz equation, and we confirmed that the obtained unit cell structures function as bandgap structures.
