Multiscale topology optimization of electromagnetic metamaterials using a high-contrast homogenization method

Abstract

This study proposes a multiscale topology optimization method for electromagnetic metamaterials using a level set-based topology optimization method that incorporates a high-contrast homogenization method. The high-contrast homogenization method can express wave propagation behavior in metamaterials for various frequencies. It can also capture unusual properties caused by local resonances, which cannot be estimated by conventional homogenization approaches. We formulated multiscale topology optimization problems where objective functions are defined by the macroscopic wave propagation behavior, and microstructures forming a metamaterial are set as design variables. Sensitivity analysis was conducted based on the concepts of shape and topological derivatives. As numerical examples, we offer optimized designs of metamaterials composed of multiple unit cell structures working as a demultiplexer based on negative permeability. The mechanism of the obtained metamaterials is discussed based on homogenized coefficients.