Thermal radiation dynamics in two parallel plates: The role of near field

The temperature dynamics of the radiative heat propagation in a multilayer structure is theoretically treated with a formalism combining the scattering matrix and Green's-functions methods. The time evolution of the temperature of parallel plates of silicon carbide in vacuum is simulated for different interplate distances and thicknesses of plates. The characteristic radiative heat exchange time and temperature of the plates at stationary state are determined from the time evolutions. The threshold interplate distance which separates heating and cooling regimes for the sink plate is found. We show that the variation of the interplate distance allows us to control the relaxation processes in the system of absorber and emitter.

Figure 1

Intensity of the heat transfer from one SiC plate to another as a function of the distance between plates, $d$, calculated for different thicknesses of plates, $h$. Inset: Sketch of the structure.

Figure 2

Intensity of the heat transfer from one SiC plate to another as a function of the thickness of plates, $h$, calculated for different distances between plates, $d$.

Figure 3

Spatial distributions of the $x$ component of the electric field of a plane of vertically oriented oscillating dipoles located in the middle of the bottom SiC plate (dotted line). SiC plates are separated by a (a) 100-nm or (b) 300-nm vacuum gap. Parameters of calculation are the following: $\omega =179.5$ THz; $k_x=27.5k_0$, where $k_0$ is the wave vector in vacuum; and $p$ polarization. Interfaces between layers are shown by dashed lines. The color scale on the right shows the calculated electric-field strength in arbitrary units.

Figure 4

(a) Sketch of the two-plates structure and (b) thermal radiation fluxes from the top and bottom plates.

Figure 5

Time evolutions of the temperature of plate 2 calculated for different distances between plates. The thickness of the plates is $h=$100 nm. The initial temperature of plate 2 is 273 K. $T_1=300$ K.

Figure 6

Time evolutions of the temperature of plate 2 calculated for distances between plates $d=100$ nm and 100 $\mu$m and different initial conditions $T_2\left(0\right)$. The thickness of the plates is $h=$100 nm. $T_1$ = 400 K.

Figure 7

Time it takes for plate 2 to reach stationary state, ${\tau }_{\text{SS}}$, and temperature of plate 2 at stationary state, $T_2^{\text{SS}}$, as a function of the distance between plates. The thickness of the plates is $h=100$ nm. $T_1=300K.$

Figure 8

Temperature of plate 2 at stationary state as a two-dimensional function of the distance between plates, $d$, and thickness of the plates, $h$. The near-field and far-field regimes are separated by black dashed lines. The color scale on the right shows the calculated values of parameter $T_2^{\text{SS}}$. The solid line is a contour line at $T_2^{\text{SS}}=273$ K and separates heating and cooling regimes in the assumption that $T_2\left(0\right)=273$ K. $T_1=300$ K.

Figure 9

Time it takes for plate 2 to reach stationary state as a two-dimensional function of the distance between plates, $d$, and thickness of the plates, $h$. The contour lines are shown by black solid lines. The near-field and far-field regimes are separated by black dashed lines. The color scale on the right shows the calculated values of the parameter $\tau$ in seconds.

Figure 10

(a) Sketch of the layered structure and (b) amplitudes of forward and backward traveling plane waves in the layered structure.

Figure 11

Sketch of the layered structure with a plane of oscillating dipoles for the case (a) $z_c>z_s$ and (b) $z_c<z_s$. The plane of oscillating dipoles is denoted by the dash-dotted line.

Figure 12

Layered structures with a source layer (pink) and receiver layer (blue). Arrows show the complex amplitudes of forward and backward traveling plane waves taken at specific coordinates. Amplitudes $P^{+}(z^{\prime }-0)$ and $P^{-}(z^{\prime }+0)$ in panel (a) are shown by dots in order to avoid overlapping with arrows labeled as $P^{+}(z^{\prime }+0)$ and $P^{-}(z^{\prime }-0)$.

Figure 13

Layered structures with a source layer (pink) and receiver layer (blue). Arrows show the complex amplitudes of forward and backward traveling plane waves taken at specific coordinates. Amplitudes $A(z^{\prime }-0)$ and $B(z^{\prime }+0)$ in panel (a) are shown by dots in order to avoid overlapping with arrows labeled as $A(z^{\prime }+0)$ and $B(z^{\prime }-0)$.