Figure 2(a) shows a computed 3D temperature map of our W-PC sample under heating. The computation was performed for a 70 × 70 μm2 area using COMSOL software, with the silicon substrate temperature maintained at T = 600K. As shown, the temperature is uniform in the x-y plane, and the maximum temperature difference across the z-direction is less than 0.1K. Figure 2(b) shows the same computation for the W-PC sample when a piece of black-CNT is mounted on top of it. It is noted that the temperature difference between the CNT- and the DBR-surfaces is less than 0.1K. To simulate the heating filament and the silicon substrate (with a larger sample area of 8 × 8 mm2), a separate computation is performed using the Joule heating module in the COMSOL software. The COMSOL calculation is discussed in detail in the Method Section of the Supplementary Information. The inset of Fig. 2(c) shows the computed temperature profile of the heating filament and the silicon substrate at a filament input power of P input = 4W. The center portion of the filament is approximately 40K hotter than the silicon’s top surface and its significance will be taken up in the later section. Figure 2(c) shows the computed temperature along a dashed line at the silicon top surface for P input = 4, 5, 6, 7 and 8W. The temperature difference across the sample surface without the CNT is uniform to within 2K at P input = 4–5W and within 4K at P input = 6–8W.

Figure 2 (a) Shows a computed temperature profile of our W-PC sample under heating. The silicon substrate is kept at T = 600K. (b) shows a computed temperature profile of our heated W-PC when a piece of black-CNT is coated at the center region of its DBR top surface. The silicon substrate is kept at T = 600K. (c) shows the computed temperature along the dashed line of the silicon top surface. The filament’s input powers are P input = 4, 5, 6, 7 and 8W, respectively. Inset: A computed temperature distribution profile of the silicon substrate at P input = 4 Watts. (The computation is performed using COMSOL version 5.4 software. Its URL is https://www.comsol.com/release/5.4). Full size image

Figure 3 shows the measured radiation spectra of the heated PC sample at T = 575K along the surface normal. The data were taken for a series of aperture positions, from pos. −0 to pos. −5. At Pos. −0, the aperture is aligned with the black-CNT area and the radiation shows a smooth λ-dependence. This data serves as the blackbody radiation reference. The slight dip at λ~2.7 μm is an artifact due to absorption by the interferometer’s quartz beam-splitter. At pos. −1, the aperture is moved away from the CNT area along the x-direction and into the PC area, and a small radiation peak appears at λ = 1.7 μm. This radiation peak gradually becomes more distinct as the aperture continues through pos. −2 to pos. −4. Finally, at pos. −5, when the aperture is completely out of the CNT area and aligned only with the PC area, the peak intensity reaches its maximum value. This maximum intensity is found to be 8.3 times greater than the blackbody reference taken at pos. −0. The evolution and systematic increase of the observed peak intensity suggests the co-existence of two different types of light emission: One represents the usual blackbody radiation, and the other, a new type of light emission. From a 3D thermal flow analysis using COMSOL, we note the sample’s surface temperature between pos-0 and pos-5 is approximately constant within 2K. Therefore, this observation offers direct evidence of super-Planckian thermal radiation being emitted at λ = 1.7 μm from a heated 3D tungsten PC in the far-field.

Figure 3 Measured radiation spectra of the W-PC sample heated to T = 575K. The data were taken for a series of aperture positions, from pos. −0 to pos. −5. At Pos. −0, the aperture is aligned with the black-CNT area and the emission shows a smooth λ-dependence. At pos. −1, the aperture is moved away from the CNT area and into the PC-cavity area, a small emission peak occurs at λ = 1.7 μm. As the aperture is moved from pos. −2 to pos. −4, the emission peak at λ = 1.7 μm becomes more distinct. At pos. −5, when the aperture is completely out of the CNT area and aligned only with the W-PC area, the peak intensity reaches its maximum. This peak intensity is 8.3 times above the blackbody reference taken at pos. −0. Full size image

Figure 4(a–c) shows a comparison of the PC radiation spectra (the red curve) with that of the black-CNT (the blue curve) for T = 575, 630 and 690K, respectively. In all three cases, the PC radiation intensity exceeds the blackbody’s at λ = 1.7 μm. Emission enhancement was also observed at the DBR band-edge resonances of λ = 1.15 and ~3 μm. Quantitatively, an exceeding factor (η) may be defined as the ratio of the PC to the black-CNT radiation intensity. A PC emission with η = 1 thus corresponds to the standard blackbody radiation limit. At λ = 1.7 μm, η is found to be 8.3, 7 and 5.5 for T = 575, 630 and 690K, respectively. Figure 4(d) summarizes the λ-dependence of η for all three temperatures. In the resonant wavelength range, η(λ) is found to be greater than one. In sharp contrast, away from the resonant regime, η(λ) drops to be less than one. Note that η(λ = 1.15 μm) > η(λ = 1.7 μm) > η(λ~3 μm). The highest η-value occurs at the shortest wavelength, i.e. λ = 1.15 μm. The data at λ~1.15 μm contains significant noise because the blackbody radiation is relatively weaker when photon energy (E = 1.1 eV) is much greater than thermal energy (k b T = 0.05–0.06 eV) at T = 575–690K. The inset of Fig. 4(d) summarizes the T-dependence of η(Τ) at λ = 1.7 μm. The exceeding factor is found to be η = 16 at T = 450K. The blue line is a guide to the eye showing a decreasing η as the sample temperature is increased. The temperature dependence of the enhancement factor at 1.7 microns as seen in Fig. 4(d) is likely due to losses in the tungsten (arising from the electronic scattering rate) that increase with temperature, as modeled in reference-10. In this model, output intensity is diminished by temperature-dependent resistivity in the metal.

Figure 4 (a–c) A comparison of radiation spectra of a W-PC sample (the red curve) to that of a black-CNT (the blue curve) for T = 575, 630 and 690K, respectively. For all three Ts, the W-PC radiation intensity at λ = 1.7 μm far exceeds the usual blackbody radiation. (d) A summary plot of the exceeding factor η vs. wavelength for T = 575, 630 and 690K, respectively. The black dashed line is for η = 1, which indicates the blackbody limit. At resonances, η is greater than one. η is less than one when off resonances. Inset: a plot of the T-dependence of η at λ = 1.7 μm. The blue line is only a guide for the eyes. Full size image