Plasmons in ultra-thin gold slabs with quantum spill-out: Fourier modal method, perturbative approach, and analytical model

TL;DR

This paper investigates the impact of quantum spill-out on plasmon modes in ultra-thin gold slabs using a novel numerical method, a perturbative approach, and analytical modeling, providing efficient tools and physical insights.

Contribution

It introduces a new nonlinear coordinate transformation for FMM convergence, a perturbative method for QSO effects, and analytical expressions for mode indices, advancing understanding of quantum effects in plasmonics.

Findings

The perturbative approach agrees well with full numerical results.

Analytical expressions accurately reproduce spill-out effects.

The methods offer efficient alternatives for studying quantum plasmonic structures.

Abstract

We numerically study the effect of the quantum spill-out (QSO) on the plasmon mode indices of an ultra-thin metallic slab, using the Fourier modal method (FMM). To improve the convergence of the FMM results, a novel nonlinear coordinate transformation is suggested and employed. Furthermore, we present a perturbative approach for incorporating the effects of QSO on the plasmon mode indices, which agrees very well with the full numerical results. The perturbative approach also provides additional physical insight, and is used to derive analytical expressions for the mode indices using a simple model for the dielectric function. The analytical expressions reproduce the results obtained from the numerically-challenging spill-out problem with much less effort and may be used for understanding the effects of QSO on other plasmonic structures.