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

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