The geometrical nature of optical resonances in nanoparticles

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.

4 pages, 3 figures

References in corpus (2)

• Observation of Strong Coupling between One Atom and a Monolithic Microresonator
• Angles Between Infinite Dimensional Subspaces with Applications to the Rayleigh-Ritz and Alternating Projectors Methods

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• Optical LC-like resonances in high-index particles