Giant resonant radiative heat transfer between nanoparticles

Near-field radiative heat transfer exhibits various effects, such as amplification due to the geometry of the system. In this work, we construct a periodic layered structure which consists of multiple layers of alternating materials. Radiative heat transfer (RHT) between nanoparticles placed on each side of an intermediate structure is studied. Thermal energy exchange between nanoparticles is assisted by transmitted evanescent fields, which is theoretically included in the system's Green's function. We show that the resulting heat transfer with the assistance of a multilayered structure is more than five orders of magnitude higher than that in the absence of the multilayered structure at the same interparticle distance. This increase is observed over a broad range of distances ranging from near to far field. This is due to the fact that the intermediate multilayered structure supports hyperbolic phonon polaritons, where the edge frequencies of the type-I and type-II reststrahlen bands coincide at a value that is approximately equal to the nanoparticle resonance. This allows high-$k$ evanescent modes to resonate with the nanoparticles. The effects of the number of layers and fill factor in the multilayered structure on RHT are examined. Finally, we show that when there is a lateral distance between the two particles assisted by the interference of surface waves, RHT conductance exhibits an oscillating and nonmonotonic behavior with respect to the lateral distance between nanoparticles. These results illustrate a powerful method for regulating energy transport in particle systems and can be relevant for effective energy management at nano-micro scales.

Figure 1

Schematic of RHT between two nanoparticles in the presence of a multilayered slab. The nanoparticles lie on opposite sides of the intermediate structure with thickness $h$. The top surface of the slab coincides with the origin. The periodic multilayered slab consists of multiple layers of alternating materials.

Figure 2

Optical properties of the multilayered structure. (a) Dielectric functions of SiC and NaBr. (b) Real parts of the in-plane and out-of-plane permittivities of the multilayered structure predicted using EMA. (c) Type-I and type-II reststrahlen bands near the SiC reststrahlen band, which are shaded in blue and yellow, respectively. The resonance of the SiC nanoparticle ${\omega }_{np}$ is shown in panel (c).

Figure 3

The 2D distributions of the imaginary part of the transmission coefficient $\mathrm{Im}\left(t_p\right)$ of the multilayered structure obtained with (a) EMA and (b) the exact model. Note that $h=1\mu \mathrm{m}$. The purple and blue lines mark the dispersion relations for type-I and type-II hPhPs, respectively. Integers 0–5 denote the order of an hPhP resonance. The frequency limits for the hPhPs are identified in panel (a).

Figure 4

Simulated resonances in the multilayered structure with $h=1\mu \mathrm{m}$ excited in the Otto geometry. (a) Scheme of the Otto geometry using KRS5 as a highly refractive coupling medium ($n\approx 2.4$). The absolute ${\vec{E}}_x$-field amplitudes from the (b) EMA model and (c) exact model are shown as a function of frequency and $z$ position at $\theta ={80}^{\circ }$ and the corresponding critical gap of $d_{\mathrm{gap}}=500\mathrm{nm}$.

Figure 5

(a) RHT conductance Φ between the two particles as a function of interparticle distance $L$. (b) The factor $R$ between Φ and the conductance in the absence of the structure ${\mathrm{\Phi }}_0$. The temperature is $T=300\mathrm{K}$. The particles are separated from the surface by a distance $d=50\mathrm{nm}$. $h$ is varied from 100 nm to 100 μm. Point A in panel (a) denotes the conductance at 2 μm, which is equal to that at 0.2 μm in the absence of the intermediate structure. All slabs are of equal thickness. The symbols/colors in panel (a) mean the same as those in panel (b).

Figure 6

(a) Spectral conductance ${\mathrm{\Phi }}_{\omega }$. (b) Trace of the GF and polarizability of the SiC particles. The absolute square of the $zz$ element $|G_{zz}{|}^2$ of (c) the reflection GF at the two positions separated at $L=2.05\mu \mathrm{m}$ above the SiC bulk, and the transmission GF at the two positions separated by the multilayer structure with (d) $N=1$ and (e) $N=21$ layers. $h=1.95\mu \mathrm{m}$ for the transmission model and $d=50\mathrm{nm}$. The three vertical yellow dotted lines in panels (a) ,(b) mark the three resonances at ${\omega }_h, {\omega }_{np}$, and ${\omega }_s$, respectively. These are shown using horizontal white, blue, and pink dotted lines in panels (c)–(e).

Figure 7

(a) Φ obtained using EMA with respect to $L$ in the presence of the multilayer structure with different $f$ values. The absolute square of the $zz$ element in the transmission GF $|G_{zz}{|}^2$ obtained with EMA for (b) $f=0.3$ and (c) $f=0.7$. In panels (b), (c), the configuration parameters are set to $d=50\mathrm{nm}$ and $h=1.95\mu \mathrm{m}$, and the horizontal blue line marks the resonance at ${\omega }_{np}$.

Figure 8

(a) Dielectric function of the multilayered structure with $f=0.3$ and 0.7. (b) Plots of $|{\varepsilon }_{\left|\right|}|/|{\varepsilon }_{\perp }|$ with $f=0.3$, 0.5, and 0.7. Type-I and type-II reststrahlen bands are shaded in blue and yellow, respectively.

Figure 9

(a) RHT conductance with respect to the interparticle distance in the multilayered structure with 1, 3, and 21 layers when the lateral distance $d_x$ is varied from 100 nm to 80 μm. The particle-surface distance $d=50\mathrm{nm}$ and the total thickness is $h=1\mu \mathrm{m}$. (b) Partially magnified view of panel (a). (c) RHT conductance spectrum between the two particles in the presence of multilayered SiC/NaBr with $N=21$. The red line in panel (c) denotes the nanoparticle resonance.

Figure 10

$|G_{zz}{|}^2$ in the transmission GF for (a) $L=1.1\mu \mathrm{m}$ ($d_x=0$), (b) $L=3\mu \mathrm{m}$ ($d_x=2.791\mu \mathrm{m}$), and (c) $L=40\mu \mathrm{m}$ ($d_x=39.985\mu \mathrm{m}$). $h=1\mu \mathrm{m}$ and $N=21$.

Figure 11

RHT conductance with respect to $d_x$ for a multilayered structure with $N=1$ or 21, $d=50\mathrm{nm}$, and $h=5$ and 10 μm.