d transport information, analogous to electronics and photonics. Photonics has nearly unlimited bandwidth and almost no loss or dispersion, making it invaluable for high-throughput long-haul information networks. However, photonics components are diffraction-limited to micron-scale sizes, ruling out dense integration with nanoscale electronics. Plasmonics is potentially poised to bridge the tens of nanometer scale of modern electronics to the micron scale world of photonics. Many interesting devices, such as a 50nm metal-insulator-metal (MIM) surface plasmon waveguide capable of guiding 1.5um light even around 90o corners, have been proposed and are being actively investigated. Such devices have great promise, but also must overcome the limits imposed by the lossy propagation of surface plasmons in metals. The propagation lengths of surface plasmon waves in the visible and near infrared regimes are typically on the order of hundreds of microns on unpatterned surfaces, but drop to under thirty microns in sub-wavelength MIM waveguides. The propagation length in a modern optical fiber is drastically larger, on the order of kilometers. The small propagation lengths of surface plasmons are a significant hurdle in the practical implementation of plasmonics; however, researchers throughout the world are actively pursuing geometries which take account for this loss and new designs to limit the loss as much as possible.
Surface plasmons have many exciting potential applications and rich underlying physics drawing heavily from solid-state physics and electrodynamics. Although known for over 50 years, there are still many unsolved theoretical and experimental problems in the field of surface plasmons. Additionally, with the use of modern nanofabrication techniques, a whole range of new plasmonic devices have become possible. Although not without their drawbacks, surface plasmon based devices have a plethora of laboratory and commercial applications--including the potential to revolutionize photonic-electronic integration with the burgeouning field of plasmonics.
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. A simple model for the motion of an electron in a conductor is a free electron driven by the field of the electromagnetic wave.
This electron motion can then be converted into a dielectric constant by using the definitions of the dipole moment, electric susceptibility, and dielectric constant:
|Fig. A-1: Dispersion relation for bulk plasmons and free-space electromagnetic waves.|
&omegap is known as the plasma frequency. This dielectric constant can then be inserted into the standard electromagnetic wave equation
The wave equation allows for the standard propagating wave solution, given by
This is a valid solution provided that
This is the dispersion relation of bulk plasmon polaritons propagating in a metallic film. The dispersion relation gives the correspondence between the time-dependence of the electromagnetic wave (&omega), and the spatial variation (k);
the wavelength of the wave is given by &lambda=2&pi/k. Figure A-1 shows a plot of the bulk plasmon dispersion relation (solid line), along with the free space dispersion relation (&omega = ck). For frequencies above the plasma frequency &omegap, the metal supports propagating modes. For frequencies below &omegap, k becomes imaginary and the fields exponentially decay inside the metal. For typical metals, h&omegap/2&pi &asymp 10eV (in the ultra-violet); for semiconductors, h&omegap/2&pi < 0.5eV (in the terahertz regime). Although bulk plasmons, which can exist even deep inside a metal, do not exist for &omega < &omegap, there is an additional solution to Maxwell's equations for these frequencies: surface plasmons.
Surface plasmons are propagating waves bound to plasmon oscillations of electrons at a metal-dielectric interface. The field intensity of the wave is at a maximum at the inter