Fall Mandiaye, Boutami Salim, Glière Alain, Stout Brian, Hazart Jerome
J Opt Soc Am A Opt Image Sci Vis. 2013 Jun 1;30(6):1273-80. doi: 10.1364/JOSAA.30.001273.
A combination of the multilevel fast multipole method (MLFMM) and boundary element method (BEM) can solve large scale photonics problems of arbitrary geometry. Here, MLFMM-BEM algorithm based on a scalar and vector potential formulation, instead of the more conventional electric and magnetic field formulations, is described. The method can deal with multiple lossy or lossless dielectric objects of arbitrary geometry, be they nested, in contact, or dispersed. Several examples are used to demonstrate that this method is able to efficiently handle 3D photonic scatterers involving large numbers of unknowns. Absorption, scattering, and extinction efficiencies of gold nanoparticle spheres, calculated by the MLFMM, are compared with Mie's theory. MLFMM calculations of the bistatic radar cross section (RCS) of a gold sphere near the plasmon resonance and of a silica coated gold sphere are also compared with Mie theory predictions. Finally, the bistatic RCS of a nanoparticle gold-silver heterodimer calculated with MLFMM is compared with unmodified BEM calculations.
多级快速多极子方法（MLFMM）和边界元方法（BEM）相结合可以解决任意几何形状的大规模光子学问题。在此，描述了基于标量和矢量势公式而非更传统的电场和磁场公式的MLFMM-BEM算法。该方法可以处理任意几何形状的多个有损或无损介质物体，无论它们是嵌套的、接触的还是分散的。通过几个例子证明了该方法能够有效地处理涉及大量未知数的三维光子散射体。将通过MLFMM计算的金纳米颗粒球的吸收、散射和消光效率与米氏理论进行了比较。还将MLFMM计算的等离子体共振附近金球体和二氧化硅包覆金球体的双站雷达散射截面（RCS）与米氏理论预测进行了比较。最后，将用MLFMM计算的纳米颗粒金银异质二聚体的双站RCS与未修改的BEM计算结果进行了比较。
