Travelling Surface Plasmons with Interference Envelope and A Vision for Time Crystals

TL;DR

This paper investigates how film thickness and substrate refractive index influence surface plasmon polaritons (SPPs), revealing interference patterns and the transition to volume plasmons, with implications for designing plasmonic nanostructures.

Contribution

It provides new insights into the propagation mechanisms of SPPs and volume plasmons in thin metallic films, highlighting the effects of substrate and film thickness on surface wave behavior.

Findings

Superposition of SPP waves creates interference envelopes dependent on frequency and dielectric properties.

Reduced film thickness leads to dominance of volume plasmons within the film.

Interference patterns can be controlled by adjusting substrate and film parameters.

Abstract

The influence of the film thickness and the substrate's refractive index on the surface mode at the superstrate is an important study step that may help clearing some of the misunderstandings surrounding their propagation mechanism. A single sub-wavelength slit perforating a thin metallic film is among the simplest nanostructure capable of launching Surface Plasmon Polaritons on its surrounding surface when excited by an incident field. Here, the impact of the substrate and the film thickness on surface waves is investigated. When the thickness of the film is comparable to its skin depth, SPP waves from the substrate penetrate the film and emerge from the superstrate, creating a superposition of two SPP waves, that leads to a beat interference envelope with well-defined loci which are the function of both the drive frequency and the dielectric constant of the substrate/superstrate. As the film thickness is reduced to the SPP's penetration depth, surface waves from optically denser dielectric/metal interface would dominate, leading to volume plasmons that propagate inside the film at optical frequencies. Interference of periodic volume charge density with the incident field over the film creates charge bundles that are periodic in space and time.