Topology optimization for realizing tailored self-collimation in phononic crystals

Self-collimation is a phenomenon that the waves propagate through a narrow channel in phononic crystals (PnCs) without diffusion. Although different self-collimation PnCs configurations have been proposed with heuristic methods, it is still challenging to achieve a frequency-specified self-collimation. We propose a systematic topology optimization method to find the material distribution in PnCs for realizing a frequency-specified self-collimation within a wider incident wave angle range. To achieve the self-collimation effect, the weighted slope index of equi-frequency contours (EFCs) that effectively measures whether the wave propagation has a self-collimation effect is introduced as the objective function of the optimization model. The material-field series expansion (MFSE) technique is used to describe the complicated topologies of the unit cell with a low number of design variables. Then, the Kriging-based optimization algorithm with a self-adaptive strategy is adopted for solving the optimization problem. Numerical examples show that the optimized unit cell designs have flat EFCs within larger incident wave angle ranges and also demonstrate that the expected nondiffraction propagation characteristics can be achieved through optimization.