Modeling near-field radiative heat transfer from sharp objects using a general three-dimensional numerical scattering technique

We develop a general numerical method to calculate the nonequilibrium radiative heat transfer between a plate and compact objects of arbitrary shapes, making the first accurate theoretical predictions for the total heat transfer and the spatial heat flux profile for three-dimensional compact objects including corners or tips. In contrast to the known sphere-plate heat transfer, we find qualitatively different scaling laws for cylinders and cones at small separations, and, in contrast to a flat or slightly curved object, a sharp cone exhibits a local minimum in the spatially resolved heat flux directly below the tip. Our results may have important implications for near-field thermal writing and surface roughness.

Figure 1

Total thermal transfer between a silica plate and doped silicon objects of various shapes. The plate is semi-infinite, and the objects all have heights equal to $1\mu \mathrm{m}$ in the $z$ direction. The plate/environment temperature is $T_P=300\mathrm{K}$ and the objects are at temperature $T_A=600\mathrm{K}$. Red dots denote results with the sphere scattering matrix determined analytically, the only case in which we have an analytic solution for the scattering matrix.

Figure 2

Poynting flux at the origin for the geometries of Fig. 1 with plate/environment temperature $T_P=300\mathrm{K}$ and object temperature $T_A=600\mathrm{K}$, using the single polarization approximation (SPA) for the sphere and cylinders. The light pink line denotes the sphere-plate without the SPA, and the horizontal dashed line denotes the threshold used for the cross-sectional flux profiles of Fig. 3.

Figure 3

Spatially resolved heat flux profiles at the substrate surface. $z$ is chosen to fix the Poynting flux at $x=0$ at ${10}^{-3}{\left(2\pi \right)}^{2}hc/\mu {\mathrm{m}}^4$.

Figure 4

Spatially resolved heat flux profiles (arbitrary units) at the substrate surface for all three cones at $z=70\mathrm{nm}$. The profiles are normalized so that their maximal value is equal to one. For comparison, the profile for a cylinder of radius $d=200\mathrm{nm}$ (using the SPA) is shown as well.