Resonant Polariton Thermal Transport Along a Vacuum Gap

The in-plane thermal conductance of a vacuum gap supporting the propagation of hybridized guided modes along its interfaces with two polar ${\mathrm{SiO}}_2$ materials is quantified and analyzed as a function of the gap distance and temperature. In contrast to the well-known cross-plane thermal conductance, we show that the in-plane one increases with the gap distance up to 1 cm, in which it takes its maxima that increase with temperature. A maximum thermal conductance per unit width of $103{\text{mW~m}}^{-1}{\mathrm{K}}^{-1}$ is found at 500 K, which is more than 6 (3) orders of magnitude higher than the corresponding one found in the near-field (far-field) regime. This top polariton thermal conductance along the cavity is pretty much equal to the radiative one predicted by Planck's theory and therefore it could be useful to amplify or evacuate heat currents along macroscale gaps.

Figure 1

Scheme of a vacuum gap between two identical semi-infinite polar materials of relative permittivity ${\epsilon }_1$. The gap supports the propagation of HGMs via symmetric (even) and antisymmetric (odd) modes.

Figure 2

Spectra of the (a) dispersion relation and (b) in-plane propagation length of HGMs propagating along a 1-cm-thick gap surrounded by ${\mathrm{SiO}}_2$, in comparison with the corresponding ones (black lines) obtained for a single interface ($d\to \mathrm{\infty }$). Calculations are done for 5 representative branches of the first 200 of the symmetric mode.

Figure 3

Spectra of the cross-plane (a) propagation length and (b) wavelength of HGMs propagating along a 1-cm-thick gap surrounded by ${\mathrm{SiO}}_2$, in comparison with the corresponding ones (black lines) found for an infinitely thick cavity ($d\to \mathrm{\infty }$).

Figure 4

Spectrum of the HGM thermal conductance for a 1-cm-thick gap surrounded by ${\mathrm{SiO}}_2$, in comparison with the corresponding one (black line) for a thick gap ($d\to \mathrm{\infty }$). Calculations are done for $T=500\mathrm{K}$.

Figure 5

HGM thermal conductance per unit width of a vacuum gap, as a function of its distance. (a) Contribution of the even and odd modes at 500 K and (b) the total values for three representative temperatures. The green line in (a) represents the ratio between the odd and even mode contributions, while the dashed lines in (b) represent the predictions of Planck’s theory [31], as detailed in the SM [29]. Calculations are done by summing up the contributions of the first 800 branches of each of the even and odd modes, for $a=l=1\mathrm{mm}$ and $\delta T=10\mathrm{K}$.