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 plasmons of a whole range of wavelengths can be excited. However, due to the high energy of the electrons, they have a very large momentum and it is difficult to precisely control the coupling: even a slight spread in energy or angle will result in a very broad range of surface plasmon wavelengths being excited. Additionally, only surface plasmons far along the dispersion curve, where kspp is largest, are generally excited. A more precise method to launch surface plasmons is through coupling with an incident electromagnetic wave (photon).
As mentioned previously, direct excitation of surface plasmons by free-space photons is not achievable because kspp is always greater than ko; this can be seen in figure 1, where the surface plasmon dispersion relation always lies to the right of the free space dispersion curve.
This can be overcome by back-side illumination through a material with a higher index of refraction (n), where the far-field radiation has a larger wave-vector (k=nko). This type of coupling geometry is shown in figure 2, and is known as a Kretschmann-Raether coupler. A surface plasmon will be efficiently excited when k|| = nkosin(&theta) = kspp. Kretschmann couplers are commonly used in experiments, but are limited to very thin films such that the high-k photon is able to tunnel through the film and couple to a surface plasmon on the lower-index surface.
A more general approach to launching surface plasmons with light is the use of structured surfaces that are able to impart momentum on the photon, enabling it to couple to the surface plasmon mode. Anything from a single sub-wavelength disk or slit, to rectangular or sinusoidal diffraction gratings are used for this type of coupling. A thorough overview of surface plasmon coupling and patterned and rough surfaces is given by Raether.
Surface plasmons have many interesting applications such as optical measurements of films, chemicals, and biological agents bound to a metallic surface; confinement and guiding of light below the classical diffraction limit; an