Optimal Design of Broadband Absorbers with Multiple Plasmonic Nanoparticles via Reduced Basis Method

Abstract: In this paper, we propose a computational framework for the optimal design of broadband absorbing materials composed of plasmonic nanoparticle arrays. This design problem poses several key challenges: (1) the complex multi-particle interactions and high-curvature geometries; (2) the requirement to achieve broadband frequency responses, including resonant regimes; (3) the complexity of shape derivative calculations; and (4) the non-convexity of the optimization landscape. To systematically address these challenges, we employ three sequential strategies. First, we introduce a parameterized integral equation formulation that circumvents traditional shape derivative computations. Second, we develop a shape-adaptive reduced basis method (RBM) that utilizes the eigenfunctions of the Neumann-Poincar\'{e} operator for forward problems and their adjoint counterparts for adjoint problems, thereby addressing singularities and accelerating computations. Third, we propose a physics-informed initialization strategy that estimates nanoparticle configurations under weak coupling assumptions, thereby improving the performance of gradient-based optimization algorithms. The method's computational advantages are demonstrated through numerical experiments, which show accurate and efficient designs across various geometric configurations. Furthermore, the framework is flexible and extensible to other material systems and boundary conditions.