Gallinet Benjamin, Kern Andreas M, Martin Olivier J F
Nanophotonics and Metrology Laboratory, Swiss Federal Institute of Technology Lausanne, 1015 Lausanne, Switzerland.
J Opt Soc Am A Opt Image Sci Vis. 2010 Oct 1;27(10):2261-71. doi: 10.1364/JOSAA.27.002261.
A surface integral formulation for light scattering on periodic structures is presented. Electric and magnetic field equations are derived on the scatterers' surfaces in the unit cell with periodic boundary conditions. The solution is calculated with the method of moments and relies on the evaluation of the periodic Green's function performed with Ewald's method. The accuracy of this approach is assessed in detail. With this versatile boundary element formulation, a very large variety of geometries can be simulated, including doubly periodic structures on substrates and in multilayered media. The surface discretization shows a high flexibility, allowing the investigation of irregular shapes including fabrication accuracy. Deep insights into the extreme near-field of the scatterers as well as in the corresponding far-field are revealed. This method will find numerous applications for the design of realistic photonic nanostructures, in which light propagation is tailored to produce novel optical effects.
提出了一种用于周期性结构光散射的表面积分公式。在具有周期性边界条件的单位晶胞中的散射体表面上推导了电场和磁场方程。采用矩量法计算解，并依赖于用埃瓦尔德方法对周期性格林函数的评估。详细评估了这种方法的精度。通过这种通用的边界元公式，可以模拟非常多种几何形状，包括衬底上和多层介质中的双周期结构。表面离散化具有很高的灵活性，允许研究包括制造精度在内的不规则形状。揭示了对散射体的极近场以及相应远场的深入洞察。这种方法将在实际光子纳米结构的设计中找到许多应用，其中光传播被定制以产生新颖的光学效应。
