计算三维金属纳米结构非局域电磁效应的可杂交间断Galerkin方法
A hybridizable discontinuous Galerkin method for computing nonlocal electromagnetic effects in three-dimensional metallic nanostructures
摘要：
光与金属纳米结构的相互作用在金属表面产生电子的集体激发，也称为表面等离子体。这些集体激发导致共振，使光的限制在深亚波长区域，从而导致大的近场增强。等离子体共振的模拟提出了显着的挑战。从建模的角度来看，金属纳米结构中的导带电子的现实行为并没有被麦克斯韦方程组捕获，因此需要额外的建模。从模拟的角度来看，在长度尺度上的差异所产生的极端领域的本地化需要高效和准确的数值方法。在本文中，我们发展了一种可杂交的间断Galerkin（HDG）方法来求解贵金属导带电子流体力学模型下的Maxwell方程组。这种方法能够有效地模拟等离子体纳米结构，同时考虑电子和入射光之间的非局部相互作用。我们引入了一种新的后处理方案，以恢复超收敛的解决方案，并证明了所提出的HDG方法的收敛性的二维金纳米线和三维周期性环形纳米间隙结构的模拟。的流体动力学模型的结果进行了比较，一个简化的本地响应模型，显示它们之间的差异可以是显着的纳米尺度。
英文摘要：
The interaction of light with metallic nanostructures produces a collective excitation of electrons at the metal surface, also known as surface plasmons. These collective excitations lead to resonances that enable the confinement of light in deep-subwavelength regions, thereby leading to large near-field enhancements. The simulation of plasmon resonances presents notable challenges. From the modeling perspective, the realistic behavior of conduction-band electrons in metallic nanostructures is not captured by Maxwell's equations, thus requiring additional modeling. From the simulation perspective, the disparity in length scales stemming from the extreme field localization demands efficient and accurate numerical methods. In this paper, we develop the hybridizable discontinuous Galerkin (HDG) method to solve Maxwell's equations augmented with the hydrodynamic model for the conduction-band electrons in noble metals. This method enables the efficient simulation of plasmonic nanostructures while accounting for the nonlocal interactions between electrons and the incident light. We introduce a novel postprocessing scheme to recover superconvergent solutions and demonstrate the convergence of the proposed HDG method for the simulation of a 2D gold nanowire and a 3D periodic annular nanogap structure. The results of the hydrodynamic model are compared to those of a simplified local response model, showing that differences between them can be significant at the nanoscale.
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