Abstract
Electromagnetic metamaterials are artificial materials with extraordinary physical properties not available in nature, such as a negative refractive index, that is, negative permittivity and permeability. This paper proposes a level set-based topology optimization method for the structural design of negative permeability dielectric metamaterials. The purpose of the optimization problem is to find the optimal layout of dielectric metamaterials that achieves negative permeability. The presence of grayscale areas in the optimal configurations significantly affects the performance of metamaterials. However these grayscale areas are impractical to manufacture, so an optimization method in which the boundaries of optimal configurations are clearly expressed is desirable, such as those provided by topology optimization methods utilizing level set-based boundary expressions. In this paper, first, the level set-based topology optimization method is explained, and the optimization problem that addresses the design of negative permeability dielectric metamaterials is then formulated. Finally, several numerical examples are provided to confirm the utility and validity of the proposed method.
