Scattering Theory in Fluctuational Electromagnetics at the Nanoscale: From Numerical Methods to Fundamental Limits

Abstract

Fluctuational electromagnetic (EM) phenomena, including van der Waals/Casimir interactions as well as thermal radiation, are of great interest to material characterization and engineering at the nanoscale. They affect the stability and mechanical properties of materials, and can be tailored to design a variety of devices including new sensors, microscopes, adhesive or self-assembling materials, microchips avoiding sticking or overheating, and thermophotovoltaic devices. Accurate characterization of these phenomena, particularly once atom-scale effects become relevant, and of limits to relevant figures of merit are of paramount importance to such design problems.

We present a new framework for computing these fluctuational EM phenomena, particularly vdW interactions and thermal radiation, using the language of EM scattering theory; this encompasses material effects at many different length scales, from small molecules and low-dimensional materials to larger nanostructured bulk media. This framework yields predictions of unusual distance dependence of such phenomena due to the complicated conjunction of delocalized response due to phonons along with multiscale many-body EM and geometric effects. Furthermore, at atom-scale separations, conduction as well as radiation contribute to heat transfer between bodies, so we broaden our formalism to account for more general means of heat transport, clarify analogies between conductive and radiative processes, and predict novel distance dependence of heat transfer in molecular systems due to the interplay of conductive and radiative effects.

We also exploit EM scattering theory to derive new limits on thermal emission, radiative heat transfer, and Casimir-Polder forces. Our bounds on thermal emission generalize Planck’s blackbody law to wavelength-scale and smaller regimes, where complicated wave and material effects have hampered assessment of possible device performance. Our bounds on radiative heat transfer and attractive Casimir-Polder forces are nearly saturated by simple planar media, but bounds on repulsive Casimir-Polder forces are still orders of magnitude larger than predictions for systems proposed to exhibit repulsion in vacuum. Furthermore, we generalize these bounds on thermal radiation to other forms of heat transport, and in turn show how bounds on phonon conduction in realistic nanoscale systems can be much tighter than previously predicted.