Topology optimization of simultaneous photonic and phononic bandgaps and highly effective phoxonic cavity

By using the non-dominated sorting-based genetic algorithm II, we study the topology optimization of the two-dimensional phoxonic crystals (PxCs) with simultaneously maximal and complete photonic and phononic bandgaps. Our results show that the optimized structures are composed of the solid lumps with narrow connections, and their Pareto-optimal solution set can keep a balance between photonic and phononic bandgap widths. Moreover, we investigate the localized states of PxCs based on the optimized structure and obtain structures with more effectively multimodal photon and phonon localization. The presented structures with highly focused energy are good choices for the PxC sensors. For practical application, we design a simple structure with smooth edges based on the optimized structure. It is shown that the designed simple structure has the similar properties with the optimized structure, i.e. simultaneous wide phononic and photonic bandgaps and a highly effective phononic/photonic cavity, see Figures 8(b) and 8(c).