Surface Plasmons-Polaritons, Surface Waves, and Zenneck Waves: Clarification of the terms and a description of the concepts and their evolution

Abstract

The first objective of this article is to explain what surface plasmons and surface plasmon polaritons are. The term surface plasmons (SPs) was first coined in the middle of the 20th century to study the response of thin metal foils at petahertz frequencies when subjected to fast electron bombardment. SPs are coherent electron oscillations that exist at the interface between two materials where the real part of the permittivity changes sign across the interface. When an SP couples with a photon, the resulting hybrid excitation is called a surface plasmon polariton (SPP). SP refers to the charge oscillations alone, while SPP refers to the entire excitation of the charge oscillations and the electromagnetic (EM) wave. Under the right conditions, the photon can excite a longitudinal wave of electrons in the metal. The second objective is to describe the evolution of these concepts over the years and illustrate their relation to a surface wave and not to a Zenneck wave. Both Zenneck and surface waves are transverse magnetic (TM) waves. The surface waves thus cannot be excited by transverse EM (TEM) waves but rather by an electron beam that can be effectively generated by a source of electrons or a quasiparticle such as an evanescent wave, which can tunnel through the medium and thus excite the electrons. This electron wave produces its own EM wave, and this plasmonic wave is confined to a very small region near the interface. Hence, SPP is a surface wave with a longitudinal field component that propagates at the interface between a metal and a dielectric at petahertz when the conditions are right and can propagate along the metal-dielectric interface at a wavelength that is shorter than that of incident light until its energy is lost either via absorption in the conductivity of the metal or through radiation in free space. The longitudinal surface wave of an SPP is sometimes wrongly associated with a Zenneck wave. Zenneck wave is produced at the zero of the reflection coefficient of a plane incident TM wave (at the Brewster angle of incidence) on an air-dielectric interface, whereas surface waves are produced when the TM reflection coefficient is infinite. Both the Zenneck wave and the surface wave are TM waves and are nonradiating, as they have, in general, exponentially decaying fields with distance. For the Zenneck wave, the evanescent transverse field components do not change appreciably with frequency (because the phenomenon of Brewster angle is independent of frequency), whereas for a surface wave, with an increase of the frequency the wave is more closely coupled to the surface. This property makes it possible to distinguish between these two evanescent waves. SPP is generally coupled with Raman scattering and not with Rayleigh scattering. These points are illustrated in the remainder of the article. Hence, surface plasmons/polaritrons are surface waves that are the solution of Maxwell's equations unless perhaps there is a resonant Raman scattering, which is equivalent to exciting the structure with an incident frequency corresponding to the electronic absorption bands, as illustrated in A Survey of the Various Natures of Light Scattering.