Lesina Antonino Calà, Vaccari Alessandro, Berini Pierre, Ramunno Lora
Opt Express. 2015 Apr 20;23(8):10481-97. doi: 10.1364/OE.23.010481.
Use of the Finite-Difference Time-Domain (FDTD) method to model nanoplasmonic structures continues to rise - more than 2700 papers have been published in 2014 on FDTD simulations of surface plasmons. However, a comprehensive study on the convergence and accuracy of the method for nanoplasmonic structures has yet to be reported. Although the method may be well-established in other areas of electromagnetics, the peculiarities of nanoplasmonic problems are such that a targeted study on convergence and accuracy is required. The availability of a high-performance computing system (a massively parallel IBM Blue Gene/Q) allows us to do this for the first time. We consider gold and silver at optical wavelengths along with three "standard" nanoplasmonic structures: a metal sphere, a metal dipole antenna and a metal bowtie antenna - for the first structure comparisons with the analytical extinction, scattering, and absorption coefficients based on Mie theory are possible. We consider different ways to set-up the simulation domain, we vary the mesh size to very small dimensions, we compare the simple Drude model with the Drude model augmented with two critical points correction, we compare single-precision to double-precision arithmetic, and we compare two staircase meshing techniques, per-component and uniform. We find that the Drude model with two critical points correction (at least) must be used in general. Double-precision arithmetic is needed to avoid round-off errors if highly converged results are sought. Per-component meshing increases the accuracy when complex geometries are modeled, but the uniform mesh works better for structures completely fillable by the Yee cell (e.g., rectangular structures). Generally, a mesh size of 0.25 nm is required to achieve convergence of results to ∼ 1%. We determine how to optimally setup the simulation domain, and in so doing we find that performing scattering calculations within the near-field does not necessarily produces large errors but reduces the computational resources required.
使用时域有限差分（FDTD）方法对纳米等离子体结构进行建模的情况持续增多——2014年发表了2700多篇关于表面等离子体FDTD模拟的论文。然而，尚未有关于该方法对纳米等离子体结构的收敛性和准确性的全面研究报告。尽管该方法在电磁学的其他领域可能已得到充分确立，但纳米等离子体问题的特殊性使得需要针对收敛性和准确性进行有针对性的研究。高性能计算系统（大规模并行的IBM Blue Gene/Q）的可用性使我们首次能够做到这一点。我们考虑了光学波长下的金和银以及三种“标准”纳米等离子体结构：金属球、金属偶极天线和金属蝴蝶结天线——对于第一种结构，可以与基于米氏理论的解析消光、散射和吸收系数进行比较。我们考虑了设置模拟域的不同方法，将网格尺寸变化到非常小的维度，比较了简单的德鲁德模型与添加了两个临界点校正的德鲁德模型，比较了单精度和双精度运算，还比较了两种阶梯状网格划分技术，即按分量和均匀划分。我们发现一般必须（至少）使用添加了两个临界点校正的德鲁德模型来避免舍入误差。如果要获得高度收敛的结果，则需要双精度运算。当对复杂几何形状进行建模时，按分量网格划分可提高准确性，但均匀网格对于完全可由Yee元填充的结构（例如矩形结构）效果更好。一般来说，需要0.25 nm的网格尺寸才能使结果收敛到约1%。我们确定了如何优化设置模拟域，并且在此过程中发现，在近场内进行散射计算不一定会产生大的误差，但会减少所需的计算资源。
