Surface plasmon polaritons (SPPs) are electromagnetic waves that travel along a metal–dielectric or metal–air interface, practically in the infrared or visible-frequency. The term "surface plasmon polariton" explains that the wave involves both charge motion in the metal ("surface plasmon") and electromagnetic waves in the air or dielectric ("polariton").
They are a type of surface wave, guided along the interface in much the same way that light can be guided by an optical fiber. SPPs have a shorter wavelength than light in vacuum at the same frequency (photons). Hence, SPPs can have a higher momentum and local field intensity. Perpendicular to the interface, they have subwavelength-scale confinement. An SPP will propagate along the interface until its energy is lost either to absorption in the metal or scattering into other directions (such as into free space).
Application of SPPs enables subwavelength optics in microscopy and photolithography beyond the diffraction limit. It also enables the first steady-state micro-mechanical measurement of a fundamental property of light itself: the momentum of a photon in a dielectric medium. Other applications are photonic data storage, light generation, and bio-photonics.
Excitation
SPPs can be excited by both electrons and photons. Excitation by electrons is created by firing electrons into the bulk of a metal. As the electrons scatter, energy is transferred into the bulk plasma. The component of the scattering vector parallel to the surface results in the formation of a surface plasmon polariton.
For a photon to excite an SPP, both must have the same frequency and momentum. However, for a given frequency, a free-space photon has less momentum than an SPP because the two have different dispersion relations (see below). This momentum mismatch is the reason that a free-space photon from air cannot couple directly to an SPP. For the same reason, an SPP on a smooth metal surface cannot emit energy as a free-space photon into the dielectric (if the dielectric is uniform). This incompatibility is analogous to the lack of transmission that occurs during total internal reflection.
Nevertheless, coupling of photons into SPPs can be achieved using a coupling medium such as a prism or grating to match the photon and SPP wave vectors (and thus match their momenta). A prism can be positioned against a thin metal film in the Kretschmann configuration or very close to a metal surface in the Otto configuration (Figure 1). A grating coupler matches the wave vectors by increasing the parallel wave vector component by an amount related to the grating period (Figure 2). This method, while less frequently utilized, is critical to the theoretical understanding of the effect of surface roughness. Moreover, simple isolated surface defects such as a groove, a slit or a corrugation on an otherwise planar surface provide a mechanism by which free-space radiation and SPs can exchange energy and hence couple.
Fields and dispersion relation
The properties of an SPP can be derived from Maxwell's equations. We use a coordinate system where the metal–dielectric interface is the plane, with the metal at and dielectric at . The electric and magnetic fields as a function of position and time t are as follows:
where
n indicates the material (1 for the metal at or 2 for the dielectric at ); ω is the angular frequency of the waves; the is + for the metal, − for the dielectric. are the x- and z-components of the electric field vector, is the y-component of the magnetic field vector, and the other components () are zero. In other words, SPPs are always TM (transverse magnetic) waves. k is the wave vector; it is a complex vector, and in the case of a lossless SPP, it turns out that the x components are real and the z components are imaginary—the wave oscillates along the x direction and exponentially decays along the z direction. is always the same for both materials, but is generally different from , where is the permittivity of material 1 (the metal), and c is the speed of light in vacuum. As discussed below, this can also be written.
A wave of this form satisfies Maxwell's equations only on condition that the following equations also hold:
and
Solving these two equations, the dispersion relation for a wave propagating on the surface is
In the free electron model of an electron gas, which neglects attenuation, the metallic dielectric function is