Near-field radiative heat transfer between metasurfaces: A full-wave study based on two-dimensional grooved metal plates

Metamaterials possess artificial bulk and surface electromagnetic states. Tamed dispersion properties of surface waves allow one to achieve a controllable super-Planckian radiative heat transfer (RHT) process between two closely spaced objects. We numerically demonstrate enhanced RHT between two two-dimensional grooved metal plates by a full-wave scattering approach. The enhancement originates from both transverse-magnetic spoof surface-plasmon polaritons and a series of transverse-electric bonding- and anti-bonding-waveguide modes at surfaces. The RHT spectrum is frequency selective and highly geometrically tailorable. Our simulation also reveals thermally excited nonresonant surface waves in constituent metallic materials may play a prevailing role for RHT at an extremely small separation between two metal plates, rendering metamaterial modes insignificant for the energy-transfer process.

Figure 1

Schematic of the proposed two 2D grooved metal metasurfaces with a square lattice with a period of $a=1\mu \mathrm{m}$ separated by vacuum gap of $g$. The thickness of the homogeneous gold substrate is $h_1=1\mu \mathrm{m}$. The groove depth and groove width are $h_2=5\mu \mathrm{m}$ and $b=200\mathrm{nm}$, respectively. The temperatures of the bottom (hot) and top (cold) plates are $T_1=301$ and $T_2=300\mathrm{K}$, respectively.

Figure 2

Transmission factors $\mathrm{\Phi }(\omega ,k_x,0)$ between two grooved metal metasurfaces with an in-plane wave vector along the $\mathrm{\Gamma }\text{−}X$ direction as a function of angular frequency $\omega$ and $k_x$ for gap sizes of (a) $g=3000\mathrm{nm}$, (b) $g=1000\mathrm{nm}$, and (c) $g=50\mathrm{nm}$. (d) Transmission factor at frequency $\omega =0.1306[2\pi c/a]$ for the same structure as in (b) but for surface-parallel vector directions ranging from $0^{\circ }$ to ${360}^{\circ }$ with respect to the $+x$ axis. The dashed white line denotes the light line in vacuum, and the solid white line denotes the normalized $\mathrm{\Theta }(\omega ,301\mathrm{K})-\mathrm{\Theta }(\omega ,300\mathrm{K})$.

Figure 3

The relationship between the real part of the complex wave-vector $k_x$ and the angular frequency for two 2D GMPs separated by a vacuum gap of $g=1000\mathrm{nm}$. The solid red curve denotes the TM modes, and the dashed lines denote the bonding (blue) and antibonding (green) TE modes. The black dashed line indicates the light line in vacuum. The markers denote the mode positions on the band diagram, whose corresponding field distributions are mapped on the right.

Figure 4

Spectral heat flux between two 2D grooved metal plates with an exact solution using a scattering approach (solid red line) and PA (dashed red line), two 1D grooved metal metasurfaces, and two $5.7\text{−}\mu \mathrm{m}$ gold plates for gap sizes of (a) $g=400\mathrm{nm}$, (b) $g=100\mathrm{nm}$, and (c) $g=50\mathrm{nm}$. (d) The integrated heat flux as a function of gap size for these four configurations. The black dashed line denotes the heat transfer between two blackbodies.