Electromagnetic Surface Modes at Low Frequencies

Abstract

We have seen in previous chapters that surface plasmon polaritons can con- fine electromagnetic fields to the interface between a dielectric and a conductor over length scales significantly smaller than the wavelength. This high field localization occurs as long as the fields oscillate at frequencies close to the in- trinsic plasma frequency of the conductor. The most promising applications of plasmonics based on metals, such as highly localized waveguiding and optical sensing with unprecedented sensitivity (which will be discussed in part II of this book), have therefore been limited to the visible or near-infrared part of the spectrum. At lower frequencies, a brief look at the SPP dispersion relation reveals that the confinement to the interface breaks down as the propagation constant rapidly decreases towards the wave vector in the dielectric. Therefore, for typical metals such as gold or silver, SPPs evolve into graz- ing incidence light fields as the frequency is lowered, extending over a great number of wavelengths into the dielectric space above the interface. The un- derlying physics of this evolution from a highly confined surface excitation to an essentially homogeneous light field in the dielectric, propagating along the interface with the same phase velocity as unbound radiation, is the decrease in field penetration into the conductor at lower frequencies, due to the large (neg- ative) real and (positive) imaginary parts of the permittivity. Since an appre- ciable field amplitude inside the metal is essential for providing the non-zero component of the electric field parallel to the surface necessary for the estab- lishment of an oscillating spatial charge distribution, SPPs vanish in the limit of a perfect electrical conductor. Highly doped semiconductors however can exhibit plasma frequencies at mid- and far-infrared frequencies, and thus allow SPP propagation akin to metals at visible frequencies, albeit with high losses.