An introduction to surface plasmons

Surface plasmon resonances are free oscillations of the conduction electrons at a metal surface. The conduction electrons are free to roam within the metal and can be thought of as a gas of charged particles - a plasma. If we could displace some of the electron plasma away from the metal surface and release it again, it would create a charge density pulse sending waves over the metal surface - much like ripples in a pond. This surface charge wave is the surface plasmon. The charges in the wave create an electric field that extends into the dielectric material (such as air) above the metal surface. The electric field polarizes the dielectric and this polarization also has the characteristics of a wave. It is known as a polariton. Because the polariton is coupled to the charge wave, the surface plasmon is often referred to as a surface plasmon polariton. Strictly, the name "plasmon" refers to a quantum of this surface charge wave. However, the properties of the surface plasmon can be described classically, using Maxwell's equations, and we generally think of it as the surface-charge wave.

The simulation on the right shows a surface plasmon propagating as a wave over the surface of a thick gold film. This simulation is based on a solution of Maxwell's equations. In the simulation, blue represents an electric field vector pointing upwards and red represents the field vector pointing down (the horizontal components are not shown). As can be seen, the surface plasmon propagates as a wave and it does not radiate energy back into space - that is, the electric fields are evanescent and fall off exponentially with vertical distance. Surface plasmons can also exist on thin metal films where the electric field appears on both sides of the film.

Under special conditions the surface plasmons can be excited by light. The surface plasmon charges oscillate at extremely high frequencies, typically around 500 THz which is the frequency of visible light. Moreover they have very short wavelengths - they provide a means by which light energy can be captured and manipulated at size scales much smaller than the wavelength of the light. The surface plasmons are characterised by strong electric fields that are confined to the metal surface. The electric fields are evanescent and decay with distance away from the metal. This means that the surface plasmon will not radiate light. Conversely the surface plasmons are not easily excited by light. Since the surface plasmon arises from the motion of the electric charges in the metal, as they propagate they lose energy as heat, largely due to Ohmic losses in the metal.

The problem with exciting surface plasmons is related to their phase velocity compared with that of light. The equation on the right comes from the solution to Maxwell's equations of a surface plasmon on a thick metal film. The wavenumber of the surface plasmon is related to that of the incident light by the electric permittivities of the metal (epsilon with subscript m) and that of the medium above the film surface (epsilon with a subscript b). The permittivity of the metal is usually large and negative.

From this equation we find that the wavenumber of the surface plasmon is always larger than the wavenumber of light with the same frequency. This means that it cannot radiate into space from the metal surface unless there is some perturbation such as a defect in the surface or some boundary.

There are a number of methods that can be used to excite surface plasmons which are discussed on the next page.

Copyright Tim Davis 2012