Topology Optimization of Photonic and Phononic Crystals and Metamaterials: A Review

This paper presents a comprehensive review of the literature and trends on the design of periodic microstructural composite materials including photonic crystals (PtCs), phononic crystals (PnCs), and metamaterials (MMs) by topology optimization. The properties of these materials rely highly on the constitutive materials and their spatial distributions and the resulting materials may exhibit various special properties, for example, photonic/phononic band gaps, negative permittivity/permeability, negative effective modulus, and negative refraction. Therefore, PtCs, PnCs, and MMs can be viewed as structural materials with periodic unit cells, the design of which is a typical topology optimization problem for desired properties or functionalities. In recent years, a great amount of research has implemented topology optimization for designing these structural materials as well as the associated functional devices. This review summarizes the most recent development in topology optimization of PtCs, PnCs, and MMs and the possible directions for future research are recommended.