The geometrical nature of optical resonances in nanoparticles

TL;DR

This paper develops a geometric theory of optical resonances in nanoparticles, extending classical models to arbitrary shapes and revealing new insights into mode behavior and excitation optimization.

Contribution

It introduces a generalized geometric framework for nanoparticle resonances, applicable to any shape, and connects these resonances to mode alignment and interference effects.

Findings

Resonances are linked to internal and scattered mode alignments.

Constructive interference of modes enhances sensing capabilities.

Modes can be bright or dark depending on excitation conditions.

Abstract

We give a geometrical theory of resonances in Maxwell's equations that generalizes Mie formulae for spheres to 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 and reveal a strong analogy between resonances in nanoparticles and excess noise in unstable macroscopic cavities. 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. We demonstrate that modes can be either bright or dark depending on the incident field and give examples of how the excitation can be optimized. Finally, we apply this theory to gold particles with shapes often used in experiments.