Surface plasmon polaritons are collective longitudinal oscillations of electrons near a material surface, strongly coupled to an electromagnetic wave. The existence of coherent electron oscillations bound to the surface of a conductor were first predicted by Ritchie in 1957 and demonstrated by Powell and Swan[2,3] in 1959, but have recently experienced an explosion of interest due to their ability to efficiently manipulate light on a deep sub-wavelength scale. Because the electromagnetic wave is coupled to the motion of conduction band electrons bound to the material surface, the fields are strongly localized to the surface, opening up possibilities of sub-wavelength optical detectors and waveguides; compact, sensitive chemical detectors; and enhanced light-matter interaction.
|Fig. 1: Dispersion relation for bulk plasmons, free-space electromagnetic waves, and surface plasmons.|
Both bulk and surface plasmons have associated electromagnetic waves, and can consequently be described by Maxwell's equations. The 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 momentum to excite the surface plasmon. As &omega increases, kspp gets larger and larger, moving further away from ko. As kspp increases, the surface plasmon wavelngth decreases and the wave is more tightly bound to the surface. This process has an upper limit of &omegasp, the surface plasmon resonant frequency, which occurs when the dielectric constant of the metal and the dielectric have the same magnitude but opposite signs.
|Fig. 2: Schematic of a Kretschmann coupling setup for launching surface plasmons optically.|
Surface plasmons were first predicted by Ritchie in 1957, and were experimentally verified by Powell and Swan[2,3] in 1959 with electron energy loss spectroscopy measurements. In these measurements, high energy electrons were used to bombard a thin metallic film and launch surface plasmons. The charge of the high energy electrons couples to the plasma oscillations of electrons in the metal; by tuning the energy and angle of incidence of the electrons, the wave-vector can be tuned and surface plas