# Computation of scattering resonances in absorptive and dispersive media with applications to metal-dielectric nano-structures

## TL;DR

This paper introduces an advanced $hp$-FEM computational method for accurately and efficiently calculating scattering resonances in complex, lossy, and dispersive media like metal-dielectric nano-structures, with improved convergence and performance.

## Contribution

It combines a novel $hp$-FEM approach with a fast nonlinear eigenvalue solver, significantly reducing pre-asymptotic errors and enhancing efficiency for high-contrast nano-structures.

## Key findings

- Reduced pre-asymptotic phase compared to standard methods
- Efficiency increases with refractive index contrast
- Achieves high accuracy with short runtimes on parallel platforms

## Abstract

In this paper we consider scattering resonance computations in optics when the resonators consist of frequency dependent and lossy materials, such as metals at optical frequencies. The proposed computational approach combines a novel $hp$-FEM strategy, based on dispersion analysis for complex frequencies, with a fast implementation of the nonlinear eigenvalue solver NLEIGS. Numerical computations illustrate that the pre-asymptotic phase is significantly reduced compared to standard uniform $h$ and $p$ strategies. Moreover, the efficiency grows with the refractive index contrast, which makes the new strategy highly attractive for metal-dielectric structures. The $hp$-refinement strategy together with the efficient parallel code result in highly accurate approximations and short runtimes on multi processor platforms.