By using the non-dominated sorting-based genetic algorithm II, we study thetopology optimization of the two-dimensional phoxonic crystals (PxCs) withsimultaneously maximal and complete photonic and phononic bandgaps. Our resultsshow that the optimized structures are composed of the solid lumps with narrowconnections, and their Pareto-optimal solution set can keep a balance betweenphotonic and phononic bandgap widths. Moreover, we investigate the localizedstates of PxCs based on the optimized structure and obtain structures with moreeffectively multimodal photon and phonon localization. The presented structureswith highly focused energy are good choices for the PxC sensors. For practicalapplication, we design a simple structure with smooth edges based on theoptimized structure. It is shown that the designed simple structure has thesimilar properties with the optimized structure, i.e. simultaneous widephononic and photonic bandgaps and a highly effective phononic/photonic cavity,see Figures 8(b) and 8(c).
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