Event № 384
Metallic nanoparticles are optically extraordinary in that they support resonances at wavelengths that greatly exceed their own size. These “surface-plasmon” resonances are normally in the visible range, the (roughly scale-invariant) “colours” sensitively depending on material and shape. In creating the dichroic glass of the Lycurgus cup, the ancient Romans had exploited the phenomenon, probably unknowingly, already in the 4th Century. Nowadays, surface-plasmon resonance is fundamental to the field of nanophotonics, where the goal is to manipulate light on small scales below the so-called diffraction limit. Numerous emerging applications rely on the ability to design and realise compound nanostructures that support tunable and strongly localised resonances.
In this talk I will focus on the misleadingly simple-looking eigenvalue problem governing the colours of plasmonic nanostructures. I’ll present new asymptotic solutions that describe the resonances of the multiple-scale structures ubiquitous in applications: dimers of nearly touching nanowires (2D) and spheres (3D), elongated nano-rods, particles nearly touching a mirror etc. The plasmonic spectrum of these structures can be quite rich. For example, the spectrum of a sphere dimer is compound of three families of modes, each behaving differently in the near-contact limit; moreover, these asymptotic trends mutate at moderately high mode numbers (and again at yet larger mode numbers). This non-commutativity of limits will lead me to a discussion of the convergence in 2D and 3D of the spectrum to a universal accumulation point (the “surface-plasmon frequency”) as the mode number tends to infinity. Time permitting, I will also discuss the asymptotic renormalisation of the singular eigenvalues of closely separated dimer configurations owing to “nonlocal” effects (with Richard V. Craster, Vincenzo Giannini and Stefan A. Maier).