### Asymptotic solutions of the plasmonic eigenvalue problem and applications

Fluids and Materials Seminar

30th November 2017, 2:00 pm – 3:00 pm

Main Maths Building, SM3

The unique optical properties of metals at visible frequencies enable guiding, localisation and enhancement of light on nanometric scales, below the so-called diffraction limit, with applications emerging in bio-sensing, photovoltaics, medical treatment, optical circuitry, metamaterial, nonlinear optics and fundamental solid-state physics. Most of these applications rely on the excitation of localised-surface-plasmon resonances of metallic nanoparticles (and structures), namely collective standing-wave oscillations of the electron-charge density at the metal-dielectric boundary and the concomitant electric field.

I will present asymptotic solutions of the (purely geometric) “plasmonic eigenvalue problem” governing these resonances, in singular limits inherent to applications yet unexploited by existing methods.I will first discuss metallic nanostructures characterised by disparate length scales, namely closely spaced particles and slender bodies, which are crucial and ubiquitous in applications as they enable strong confinement, field enhancements and frequency tuneability. I will then discuss the generic limit of high-order (high-wavenumber) modes living close to the spectral accumulation point, known as the surface-plasmon frequency. Specifically, I will show how a surface-plasmon geometric ray-diffraction theory can be generated, yielding a quantisation rule for smooth bodies of revolution of otherwise arbitrary shape (not necessarily slender). Time permitting, I will point out challenging open problems, direct relations to other spectral problems in the theory of partial differential equations and composite-media theory, and generalisations of the results to account for hydrodynamic nonlocality of the metal’s electron gas.

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