High-Frequency Band Gap Design of Porous Phononic Crystals by Topology Optimization

Abstract Phononic crystals can control the propagation of elastic waves by their unique dispersion properties such as band gaps. In recent years, the application of phononic crystals for controlling high-frequency elastic waves, which is important for managing thermal conductivity in the nanoscale and for wireless communication, has been attracting attention. This research proposes a design method of phononic crystals which exhibit band gaps at high band order for the applications with high-frequency elastic waves. To consider manufacturability in nanoscale, phononic crystals made of a single material are assumed. A level set-based topology optimization is used for the design of phononic crystals. An objective function is proposed to achieve a band gap within an aimed range of frequency. As a numerical example, 2-dimensional silicon phononic crystal with hexagonal lattice is optimized. Our approach successfully generates a phononic crystal with a band gap at high band order.