Energy and momentum of the surface plasmon-polariton supported by a thin metal film

TL;DR

This paper analyzes the energy and momentum characteristics of surface plasmon-polaritons in a symmetric insulator-metal-insulator structure, comparing phenomenological and microscopic models, and classifying various energy and momentum contributions.

Contribution

It provides explicit representations and numerical analysis of energy and momentum constituents in SPPs, including quantum effects and mode comparisons, advancing understanding of plasmonic systems.

Findings

Explicit formulas for energy and momentum in SPPs derived.

Quantum hydrodynamic model incorporated for metal electron gas.

Distinct characteristics identified for symmetric and antisymmetric modes.

Abstract

We study the energy and momentum of the surface plasmon-polariton (SPP) excited in a symmetric 3-layer "insulator-metal-insulator" structure, which is known to support the symmetric (S) mode with the negative group velocity as well as the antisymmetric (AS) mode with only positive energy flow. The electric and magnetic field vectors are calculated via both the phenomenological and the microscopic approach; the latter involves the hydrodynamic model accounting for the quantum statistical effects for the electron gas in metal. Explicit representation for the energy and momentum constituents in the dielectric and in the metal film are obtained, and the wavenumber dependences of the energy and momentum contributions for the whole SPP are analyzed numerically. The various energy and momentum constituents are classified with respect to their origin: "field" or "material", and the physical nature: orbital (canonical) and spin (Belinfante) momentum contributions. The pictures characteristic for the S and AS modes are systematically compared. The results can be useful for the studies and applications of the SPP-induced thin-film effects, in particular, for the charge and spin dynamics in thin-film plasmonic systems.