Papoff F, Hourahine B
SUPA, Department of Physics, University of Strathclyde, Glasgow, G4 0NG, UK.
Opt Express. 2011 Oct 24;19(22):21432-44. doi: 10.1364/OE.19.021432.
We give a geometrical theory of resonances in Maxwell's equations that generalizes the Mie formulae for spheres to all scattering channels of any dielectric or metallic particle without sharp edges. We show that the electromagnetic response of a particle is given by a set of modes of internal and scattered fields that are coupled pairwise on the surface of the particle and reveal that resonances in nanoparticles and excess noise in macroscopic cavities have the same origin. We give examples of two types of optical resonances: those in which a single pair of internal and scattered modes become strongly aligned in the sense defined in this paper, and those resulting from constructive interference of many pairs of weakly aligned modes, an effect relevant for sensing. This approach calculates resonances for every significant mode of particles, demonstrating that modes can be either bright or dark depending on the incident field. Using this extra mode information we then outline how excitation can be optimized. Finally, we apply this theory to gold particles with shapes often used in experiments, demonstrating effects including a Fano-like resonance.
我们给出了麦克斯韦方程组中共振的几何理论，该理论将球体的米氏公式推广到任何无尖锐边缘的电介质或金属粒子的所有散射通道。我们表明，粒子的电磁响应由一组内部场和散射场模式给出，这些模式在粒子表面成对耦合，并揭示了纳米粒子中的共振和宏观腔中的过量噪声具有相同的起源。我们给出了两种光学共振的例子：一种是在本文所定义的意义上，一对内部模式和散射模式强烈对齐的共振；另一种是由许多对弱对齐模式的相长干涉产生的共振，这种效应与传感相关。这种方法计算了粒子每个重要模式的共振，表明模式根据入射场可以是亮的或暗的。利用这些额外的模式信息，我们接着概述了如何优化激发。最后，我们将该理论应用于实验中常用形状的金粒子，展示了包括类法诺共振在内的效应。
