Perturbation theory for plasmonic eigenvalues

TL;DR

This paper introduces a perturbative method to efficiently compute shifts in plasmonic eigenvalues caused by shape deformations of dielectric nanostructures within the quasistatic approximation.

Contribution

It develops a novel perturbation theory converting the eigenvalue problem into an inhomogeneous system, enabling quick analysis of shape fluctuations in plasmonic resonances.

Findings

Derived a general expression for first-order eigenvalue shifts

Verified the approach with solvable cases and a deformed nanosphere example

Facilitates rapid scanning of shape fluctuation effects on plasmonic properties

Abstract

We develop a perturbative approach for calculating, within the quasistatic approximation, the shift of surface resonances in response to a deformation of a dielectric volume. Our strategy is based on the conversion of the homogeneous system for the potential which determines the plasmonic eigenvalues into an inhomogeneous system for the potential's derivative with respect to the deformation strength, and on the exploitation of the corresponding compatibility condition. The resulting general expression for the first-order shift is verified for two explicitly solvable cases, and for a realistic example of a deformed nanosphere. It can be used for scanning the huge parameter space of possible shape fluctuations with only quite small computational effort.