Electromagnetic energy density in dispersive and dissipative media

Abstract

The description of the energy density associated with an electromagnetic field propagating through matter must treat two different phenomena: dispersion, the variation of the refractive index with frequency, and dissipation, the loss of field energy by absorption. In many cases, as in common dielectrics, the dispersive medium is essentially transparent, so dissipation can be neglected. For metals, however, both dispersion and dissipation must be taken into account, and their respective contributions vary significantly with the frequency of the electromagnetic field. Plasmonic structures such as slits, holes, and channel waveguides always involve surfaces between dielectrics and metals, and the energy density in the vicinity of the interface figures importantly in the dynamic response of these structures to light excitation in the visible and near-infrared spectral regions. Here we consider the electromagnetic energy density propagated on and dissipated at real metal–dielectric surfaces, including the important surface plasmon polariton, the wave guided by the interface. We show how the “stored energy” oscillates over an optical cycle between the plasmonic structure and the propagating surface mode, while the dissipated energy continues to accumulate over the same period. We calculate these energy densities for the case of the silver–air interface (using two datasets for silver permittivity commonly cited in the research literature) over a range of frequencies corresponding to the range of wavelengths from 200 to 2000 nm.