  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).
