Abstract
Abstract. In the calculation of eigenfrequencies of 3-D metallic nanostructures occurs the challenge that the material parameters depend on the desired eigenfrequency. We propose a formulation where this leads to a polynomial eigenvalue problem which can be tackled by different solving strategies. A comparison between a Newton-type method and a Jacobi-Davidson algorithm is given.
Highlights
The focus of our analysis is on nanostructures which include a metallic substructure
In the calculation of eigenfrequencies of 3-D metallic nanostructures occurs the challenge that the material parameters depend on the desired eigenfrequency
We propose a formulation where this leads to a polynomial eigenvalue problem which can be tackled by different solving strategies
Summary
The focus of our analysis is on nanostructures which include a metallic substructure. The nanostructures are supposed to operate at optical frequencies, the finite conductivity of the metallic parts and their frequency dependence must not be neglected. Since we are interested in the computation of eigensolutions of such nanostructures, there is the challenge that the operating frequency (the eigenvalue) is not a-priori known. The material dispersion leads to a nonlinear eigenvalue formulation. The rest of the paper is organized as follows: Sect. briefly reviews the material behavior of metals at optical frequencies. we derive in the first part a continuous eigenvalue representation which is able to take the dispersion into account. A numerical example is presented in Sect.
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