 coherent oscillations of electron motion can be encapsulated in the dielectric constant of the material. The derivation of the electromagnetic fields which characterize bulk and surface plasmons is done below, and those interested are encouraged to work out the results. To keep things brief however, the basic form of the bulk and surface plasmon solutions are shown below, along with a plot of the dispersion relation for these modes.
The dispersion diagram relates the time-variation of the wave (given by its frequency &omega) to the spatial variation of the wave (given by its wave-vector kx). Bulk plasmons are associated with purely transverse electromagnetic waves, with the electric and magnetic fields perpendicular to the direction of propagation, and can only exist for &omega > &omegap (the plasma frequency). &omegap is the resonant frequency of free electrons in response to a perturbation (such as an electromagnetic field). For &omega < &omegap, the wave-vector for bulk plasmons becomes imaginary, giving an exponentially decaying wave instead of a propagating wave. It is for this reason that most metals are highly reflective for visible light (&omega < &omegap &asymp 10eV), but transparent for ultraviolet light (&omega > &omegap) [4, pg. 275].
Surface plasmons have an associated electromagnetic wave with both transverse and longitudinal field components. Such waves can only be excited at the interface between a conductor and dielectric, and are tightly bound to the surface. The fields reach their maximum at the interface (z=0), and exponentially decay away from the surface. The wave-vector of the surface plasmon mode (kspp) always lies to the right of the free space wave-vector (ko), such that &lambdaspp < &lambdao, where &lambdaspp is the wavelength of the surface plasmon and &lambdao is the wavelength of light in free space (vacuum). Additionally, this makes it impossible to directly launch a surface plasmon wave by illumination with free-space radiation: the free-space photons simply do not have enough mom