Topology optimization of phoxonic crystals for maximizing dual bandgaps using GA-SIMP method

Phoxonic crystals are photonic-phononic or optomechanical periodic structures that simultaneously exhibit dual bandgaps. This allows for the confinement of both optical and elastic waves in cavities and waveguides, providing a powerful platform for novel optomechanical devices and systems. The opening of dual bandgaps is crucial to these potential applications. Topology optimization offers maximum freedom in the dual bandgap structure design, however, relevant research is limited. We propose a two-stage algorithm to maximize the dual bandgaps, where a genetic algorithm is used to find the initial design, and then the SIMP method is employed to obtain the optimal solution. This GA-SIMP hybrid approach capitalizes on the global search capability of GA to explore the design space and identify potential configurations, while harnessing the computational efficiency and precision of SIMP to refine and converge to high-quality solutions. This strategy effectively balances global exploration with local refinement, addressing the trade-off challenges in dual bandgap optimization for phoxonic crystals. We demonstrate the design capability of the coupled methodology by opening bandgaps between different bands in the numerical examples, and the optimized structures show intermediate states between interconnected and mutually independent configurations.