Fundamental Limits to Radiative Heat Transfer: The Limited Role of Nanostructuring in the Near-Field

In a previous Letter, we derived fundamental limits to radiative heat transfer applicable in near- through far-field regimes, based on the choice of material susceptibilities and bounding surfaces enclosing arbitrarily shaped objects; the limits exploit algebraic properties of Maxwell’s equations and fundamental principles such as electromagnetic reciprocity and passivity. In this Letter, we apply these bounds to two different geometric configurations of interest, namely dipolar particles or extended structures of infinite area in the near field of one another. We find that while near-field radiative heat transfer between dipolar particles can saturate purely geometric “Landauer” limits, bounds on extended structures cannot, instead growing very slowly with respect to a material response figure of merit (an “inverse resistivity” for metals) due to the deleterious effects of multiple scattering between bodies. While nanostructuring can produce infrared resonances, it is generally unable to further enhance the resonant energy transfer spectrum beyond what is practically achieved by planar media at the surface polariton condition.

Figure 1

Comparison of ${\mathrm{\Phi }}_{\text{opt}}$ (orange) to ${\mathrm{\Phi }}_{\mathrm{qs}}$ (purple) for (a) two dipolar bodies of volumes $V_{A,B}$ (thin lines, $\kappa =V_A{V}_B/d^6$) or a dipolar of volume $V$ body and an extended structure (thick lines, $\kappa =V/d^3$), (b) two extended structures of infinite thickness and area $A$, or (c) or two extended structures of finite thickness $h$. ${\mathrm{\Phi }}_L$ is also shown in (a). Note that bounds between two extended structures are normalized by $A/d^2$.

Figure 2

Comparison of ${\mathrm{\Phi }}_{\mathrm{qs}}(\omega )$ (purple) and ${\mathrm{\Phi }}_{\text{opt}}(\omega )$ (orange) for extended bodies to planar heat transfer ${\mathrm{\Phi }}_{\text{planar}}(\omega )$ (black) at frequencies $\omega$ relevant to the Planck function at typical experimental temperatures, corresponding to Au (dot-dashed), doped Si (dashed), and SiC (black). Also shown with labeled dots are the maximum $\mathrm{\Phi }$ of representative nanostructured Au [18] and doped Si [7] surfaces. ${\mathrm{\Phi }}_{\mathrm{qs}}$ for Au is several orders of magnitude above the plotted range.