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Schematics of radiative heat transfer between vertically aligned CNTs separated by a vacuum gap of d. The CNT film on each side is treated as a semi-infinite homogeneous medium at thermal equilibrium.
Dielectric functions (real part only) for ordinary and extraordinary waves with respect to angular frequency: (a) graphite whose ordinary dielectric function is scaled down by a factor of 10; (b) CNT array with f = 0.05 and x = 0.98. The shaded regions indicate hyperbolic bands (type II for graphite and type I for CNTs).
Radiative heat flux (divided by the blackbody heat flux in the far field) for d from 10 nm to 100 μm.
Comparison of the spectral heat fluxes (in nW/m2 per rad/s) for CNTs and graphite (scaled up by 10) at d = 10 nm, as well as that between blackbodies (BB scaled up by 104) in the far field. The shaded region represents the contributions to NFRHT for CNTs by the symmetrically coupled SPP and low-frequency hyperbolic modes.
Contour of the transmission coefficients for p-polarization at d = 10 nm: (a) CNTs for which the dotted line depicts the symmetrically coupled SPP branch; (b) graphite for which the dashed-dotted lines indicate the critical wavevectors separating evanescent waves (left) and propagating waves (right) inside graphite. Arrows between horizontal lines indicate the hyperbolic bands according to the shaded regions in Fig. 2 .
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