论文标题
晶格总结了在两个维度和三个维度的赫尔姆霍兹方程解决方案的多个sublattices
Lattice Sums Accommodating Multiple Sublattices for Solutions of the Helmholtz Equation in Two and Three Dimensions
论文作者
论文摘要
评估在晶格上排列的对象之间的相互作用需要计算晶格总和。经常遇到的方案是由helmholtz方程在形成超材料，跨表面或光子晶体的一系列颗粒中的螺丝散射的背景下控制的。虽然众所周知，虽然直接晶格总和的收敛性是缓慢的，但Ewald方法的应用将直接总和转换为指数收敛的序列。我们提出了Helmholtz方程的2D和3D溶液（即球形和圆柱溶液）的衍生。与先前的研究相比，我们的新表达式尤其旨在计算1D晶格（链），2D晶格（光栅）和3D晶格中几个相互作用的sublattices的晶格总和。我们通过与晶格总和的直接计算进行比较来验证结果。
The evaluation of the interaction between objects arranged on a lattice requires the computation of lattice sums. A scenario frequently encountered are systems governed by the Helmholtz equation in the context of electromagnetic scattering in an array of particles forming a metamaterial, a metasurface, or a photonic crystal. While the convergence of direct lattice sums for such translation coefficients is notoriously slow, the application of Ewald's method converts the direct sums into exponentially convergent series. We present a derivation of such series for the 2D and 3D solutions of the Helmholtz equation, namely spherical and cylindrical solutions. When compared to prior research, our novel expressions are especially aimed at computing the lattice sums for several interacting sublattices in 1D lattices (chains), 2D lattices (gratings), and 3D lattices. We verify our results by comparison with the direct computation of the lattice sums.
