Forestiere Carlo, Iadarola Giovanni, Rubinacci Guglielmo, Tamburrino Antonello, Dal Negro Luca, Miano Giovanni
Department of Electrical Engineering, Università degli Studi di Napoli Federico II, via Claudio 21, Napoli 80125, Italy.
J Opt Soc Am A Opt Image Sci Vis. 2012 Nov 1;29(11):2314-27. doi: 10.1364/JOSAA.29.002314.
Numerical formulations based on surface integral equations (SIEs) provide an accurate and efficient framework for the solution of the electromagnetic scattering problem by three-dimensional plasmonic nanostructures in the frequency domain. In this paper, we present a unified description of SIE formulations with both singular and nonsingular kernel and we study their accuracy in solving the scattering problem by metallic nanoparticles with spherical and nonspherical shape. In fact, the accuracy of the numerical solution, especially in the near zone, is of great importance in the analysis and design of plasmonic nanostructures, whose operation critically depends on the manipulation of electromagnetic hot spots. Four formulation types are considered: the N-combined region integral equations, the T-combined region integral equations, the combined field integral equations and the null field integral equations. A detailed comparison between their numerical solutions obtained for several nanoparticle shapes is performed by examining convergence rate and accuracy in both the far and near zone of the scatterer as a function of the number of degrees of freedom. A rigorous analysis of SIE formulations and their limitations can have a high impact on the engineering of numerous nano-scale optical devices such as plasmon-enhanced light emitters, biosensors, photodetectors, and nanoantennas.
基于表面积分方程（SIEs）的数值公式为频域中三维等离子体纳米结构的电磁散射问题求解提供了一个准确且高效的框架。在本文中，我们给出了具有奇异和非奇异核的SIE公式的统一描述，并研究了它们在求解球形和非球形金属纳米颗粒散射问题时的精度。事实上，数值解的精度，尤其是在近场区域，在等离子体纳米结构的分析和设计中非常重要，其运行关键取决于对电磁热点的操控。考虑了四种公式类型：N组合区域积分方程、T组合区域积分方程、组合场积分方程和零场积分方程。通过检查散射体远场和近场中作为自由度数量函数的收敛速率和精度，对几种纳米颗粒形状的数值解进行了详细比较。对SIE公式及其局限性的严格分析可能会对众多纳米级光学器件的工程设计产生重大影响，如等离子体增强发光器、生物传感器、光电探测器和纳米天线。
