Near-field thermal radiative transfer between two coated spheres

In this work, we present an expression for the near-field thermal radiative transfer between two spheres with an arbitrary numbers of coatings. We numerically demonstrate that the spectrum of heat transfer between layered spheres exhibits novel features due to the newly introduced interfaces between coatings and cores. These features include broad super-Planckian peaks at nonresonant frequencies and near-field selective emission between metallic spheres with polar material coatings. Spheres with cores and coatings of two different polar materials are also shown to exceed the total conductance of homogeneous spheres in some cases.

Figure 1

Geometry of two-sphere problem: (a) exterior view of two sphere configuration and (b) interior view of sphere A. Sphere B is similar, but with ${\displaystyle M}$ layers and outer radius ${\displaystyle b}$.

Figure 2

(a) Spectral conductance between sets of identical coated spheres with varying core/coating interface positions (normalized by that of two blackbody spheres). Spheres have a silver core and silica layer with outer radii of 10 ${\displaystyle \mu \mathrm{m}}$ and minimum separation gap of 1 ${\displaystyle \mu \mathrm{m}}$. Surface phonon polariton (SPhP), Fabry-Perot (FP), and epsilon near zero (ENZ) peaks are labeled. Legend appearing in (c) also applies to curves appearing in (a). (b) Real (${\displaystyle n}$) and imaginary (${\displaystyle \kappa }$) components and magnitude (${\displaystyle |n+i\kappa |}$) of the complex refractive index of silica. (c) Cumulative spectral contribution to conductance for the curves depicted in (a). Select data points may be found in tabular form in the Supplemental Material [56].

Figure 3

Distance dependence of total conductance between two identical coated spheres. Spheres have a silver core and silica layer with outer radii of 5 ${\displaystyle \mu \mathrm{m}}$. Total conductance is normalized by that of two blackbodies, and a minimum separation gap is normalized by the outer radii of the spheres. Data points may be found in tabular form in the Supplemental Material [56].

Figure 4

(a) Total conductance between two identical coated spheres (normalized by that of two blackbody spheres) as a function of the core/coating interface position. Spheres have a beryllia core and an alumina coating, or vice versa. The spheres have outer radii of 5 ${\displaystyle \mu \mathrm{m}}$ and a minimum separation gap of 100 nm. Dashed lines represent the total conductance of homogeneous beryllia and alumina spheres of the same geometry. Surface phonon polaritonic peaks (SPhP) for the homogeneous spheres are labeled. (b) Spectral conductance of spheres from (a) for homogeneous beryllia, homogeneous alumina, and the coated sphere with the maximum total conductance (alumina coating and beryllia core with ${\displaystyle t/R=0.05}$). All spectral conductances are normalized by that of two blackbody spheres. Select data points may be found in tabular form in the Supplemental Material [56].