Hyperbolic Metamaterials as an Analog of a Blackbody in the Near Field

We study the near-field heat exchange between hyperbolic materials and demonstrate that these media are able to support broadband frustrated modes which transport heat by photon tunneling with a high efficiency close to the theoretical limit. We predict that hyperbolic materials can be designed to be perfect thermal emitters at nanoscale and derive an upper limit for the heat flux due to hyperbolic modes.

Figure 1

Heat flux $\Phi$ from Eq. (1) between two semi-infinite SiC bodies over distance in units of thermal wavelength ${\lambda }_{\mathrm{th}}$. $\Phi$ is normalized to the blackbody value ${\Phi }_{\mathrm{BB}}$ for temperature $T=300\mathrm{K}$ and $\Delta T=1\mathrm{K}$. The plot also shows the contribution of the propagating and frustrated modes and the SPhP and the limit consisting of the expression in Eq. (9) plus the usual blackbody value.

Figure 2

(a) Sketch of a hyperbolic material consisting of a periodical array of nanowires. (b) Hyperbolic dispersion relation for a fixed frequency within the bands ${\Delta }_1$ and ${\Delta }_2$ in Fig. 3a. For ${\Delta }_1$ (${\Delta }_2$) we have ${ϵ}_{\parallel }>0,{ϵ}_{\perp }<0$ (${ϵ}_{\parallel }<0,{ϵ}_{\perp }>0$).

Figure 3

(a) Real part of ${ϵ}_{\parallel }$ and ${ϵ}_{\perp }$ defined in Eqs. (4, 5) with $f=0.1$. The two gray areas mark the frequency regions ${\Delta }_1$ and ${\Delta }_2$ where both permittivities have different signs, i.e., where the modes fulfill a hyperbolic dispersion relation. Vertical dashed line: frequency where $\mathrm{Re}({ϵ}_{\perp })\mathrm{Re}({ϵ}_{\parallel })=-1$. (b) Transmission coefficient ${\mathcal{T}}_p(\omega ,\kappa )$ choosing $d=100\mathrm{nm}$ for the same frequency region and the same volume filling fraction showing high transmission for regions ${\Delta }_1$ and ${\Delta }_2$. Horizontal dashed line: frequency where $\mathrm{Re}({ϵ}_{\perp })\mathrm{Re}({ϵ}_{\parallel })=-1$. For this frequency $\kappa$ has its maximum value (see Ref. 52). (c) Heat transfer coefficient for two hyperbolic materials with $f=0.1,0.2,0.3$ normalized to the value for two flat SiC half spaces ($T=300\mathrm{K}$). Inset: ${\Delta }_1$ and ${\Delta }_2$ over $f$.