Level set-based topology optimization targeting dielectric resonator-based composite right- and left-handed transmission lines

In the last decade, metamaterials have been gaining attention and have been investigated because of their unique characteristics, which conventional materials do not have, such as negative refraction indexes. However, it is sometimes difficult to design metamaterials on the basis of experience and theoretical considerations because the relationship between their electromagnetic characteristics and structure is often vague. A mathematical structural design methodology targeting metamaterials may therefore be useful for expanding the engineering applications of metamaterials in industry. In this paper, a new level set-based topology optimization method is proposed for designing composite right- and left-handed transmission lines, each of which consists of a waveguide and periodically located dielectric resonators. Such transmission lines function as a fundamental metamaterial. In the proposed method, the shape and topology of the dielectric resonators are represented by the level set function, and topology optimization problems are formulated on the basis of the level set-based representation.