Perfect blackbody sheets from nano-precision microtextured elastomers for light and thermal radiation management

Microtextured polydimethylsiloxane sheets exhibit an exceptionally low reflectance of ≲0.0005 across the entire thermal infrared wavelengths while maintaining high resilience.

where ∞, n, n and n are the dielectric constant of infinite-frequency limit, the n-th resonant optical angular frequency, the corresponding damping constant, and the oscillator strength of the target material, respectively.For PDMS, the documented Lorentz's parameters PDMS of ref. 2 were used in our simulation.A geometry model of a conical spike or pit (Fig. S1a) having opening diameters d (=2r) of 2, 4 or 10 m and aspect ratio h/r of 1, 3 or 5 was built, where h denotes the height of the spike or depth of the pit.Then, normal-incidence hemispherical reflectance spectra, which includes specular and all diffusive reflectance, were calculated for mainly mid-infrared wavelengths (4-15 m).For simplicity, the simulation was conducted for a single unit cell having only one micro-cavity (spike or pit) in it but under Bloch-periodic boundary conditions (Fig. S1a).The sample thickness was assumed to be infinity, and, therefore, the effect of back reflection at an actual sample bottom was not fully considered.
For CR-39 or UV resin, the numerical simulation was not conducted, owing to the lack of reported Lorentz's parameters.Nevertheless, comparable results are expected because the averaged Fresnel reflectances of the untextured CR-39, UV resin, and PDMS were similar to each other, which means they have a similar refractive index at mid-infrared wavelengths.For the mixture of PDMS and carbon black of 5% by weight, the Lorentz's parameters of graphite G⊥ in ref. 3 were also used with an effective medium theory: mixture = (1-f)•PDMS+f•G⊥, where f denotes the concentration of the carbon black (f=0.05).
To avoid a plot error in logarithmic graphs, sub-zero reflectance data caused by the numerical instability were replaced by pseudo positive small values of 10 -8 (Fig. S1b-d).Optical characterization (see also Experimental section in main text).The measurement of ultralow reflectance requires special care; we conducted the measurement according to the guide of ref. 4 .In particular, the measurement system's (1) throughput, (2) baseline signal and (3) response linearity had to be considered in detail.
(1) Throughput.The sample reflectance (≲0.001) is significantly lower than the reference reflectance (~0.9).In this case, exchanging the sample and the reference on a single measurement port largely changes the throughput of the integrating sphere, resulting in an underestimate of the sample reflectance (factor ~0.6, at worst, in our system).To avoid this throughput fluctuation, we used an integrating sphere having two sample ports: the lowreflectance sample was set on one port, and the reference on the other port (Fig. S2a).An infrared beam introduced into the integrating sphere was flipped by the mirror and directed to each measurement port.This setup can maintain the system throughput during the measurement, preventing underestimation of the sample reflectance.
(2) Baseline signal subtraction.The flipping mirror inside the integration sphere partially scatters the incident infrared beam, causing slightly overfilled illumination onto the sample port.
Therefore, even if the sample port is empty, the non-negligible baseline signal is measured.To determine the net reflectance of the samples, we subtracted this baseline spectrum from the raw sample spectrum (Fig. S2b).In this case, the detector noise sometimes caused sub-zero reflectance data in the net reflectance spectrum.To avoid a plot error in logarithmic graphs, the sub-zero data were replaced by pseudo positive small values of 10 -8 (Fig. 2f, Fig. 3e-g, Fig. 5b and Fig. S2b (right)).Note that we made no correction on the baseline signal in terms of the system's throughput fluctuation.Regardless of whether the low reflectance sample is on the sample port or not, the system's throughput was maintained within relatively 3.5% at worst (typically <0.5%).This contribution to measurement uncertainty was estimated as relatively 2%.
In the absolute scale, at 10 m in wavelength, for example, the uncertainty was 0.00004 for the baseline signal of 0.002 reflectance-equivalent.
The light which exits the Sample port 1 is directed to the ceiling of our laboratory.There would be little risk to detect the signal from undesired back-reflection for light which exits the Sample port 1 and eventually strikes another surface.Indeed, we measured the baseline signal with a mid-infrared opaque plate (PMMA) placed at several tens of centimetres above the Sample port 1 and confirmed that the baseline signals were reproduced within the standard deviation of ~0.0003.We also measured the zero-input signal with the Sample port 1 open and confirmed no significant signal obtained.
(3) Response linearity.The system's response linearity may also affect the measurement results because the signal level for the low-reflectance sample is more than three orders of magnitude different from the reference reflectance.Mercury cadmium telluride detectors are known to show a linear response within relatively several-percent deviation over three decades of dynamic range. 5,6The nonlinear deviation is caused by detector saturation at the high signal level, and therefore, there is little risk to underestimate the signal of low reflectance level.To briefly check our system's linearity, a neutral density (ND) filter from germanium (50% or 10% nominal transmittance) was placed in the input optical path, and it was confirmed whether the resultant signal attenuation was maintained at several different signal levels.Fig. S2c shows the transmission spectra of the ND filters measured at signal levels from 0.002 to 1 reflectanceequivalent.At any signal levels, we confirmed nearly identical signal attenuation for a single fixed-transmittance ND filter, suggesting that the system had a close-linear response.The noisy deviations at shorter or longer ends of wavelength (<6 m or >10 m) are attributable to the low responsivity of the detector.The error owing to the system's linearity was conservatively estimated as relatively ~10% at worst, corresponding to the standard uncertainty of relatively 5.8%.

Measurement uncertainty and validation.
Other uncertainty factors, as follows, were also estimated according to 'Guides to the expression of uncertainty in measurement' (GUM); 7 the measurement uncertainty owing to the reference reflectance from Infragold; the system's drift; measurement repeatability were estimated as relatively ~2.6%;relatively ~5.8%; and absolutely 0.0001-0.0008reflectance-equivalent (depending on wavelength), respectively.By combining all the above uncertainty contribution, we estimated the reflectance measurement uncertainty as absolutely ~0.0005 at 95% confidence level, for the reflectance of 0.0005 at 10 m in wavelength.The uncertainty budget is summarized in Table S1, and the example of uncertainty spectrum is plotted in Fig. S2b (right).The uncertainty budget (Table S1) may not be exhaustive: we included FTIR-related sources of error, that is, the system's linearity and drift, but we did not microtextured CR-39 plate (Fig. 2b) with the uncertainty of 95% confidence level (right).c) The system's nonlinearity estimation via transmittance measurements of ND filters at several signal levels.The nominal transmittances of the ND filters were 50% (left, centre) and 10% (right).The linearity factor is defined as the ratio of the measured transmittances: a close-unity linearity factor implies that the system has a linear response.R_eq, reflectance equivalent.Examples for the reflectance of 0.0005 at 10 m in wavelength Fabrication of nickel metal replica.For nickel metal replication, electroforming was conducted by Kiyokawa Plating Industry, Co., Ltd., Japan.One of the micro-cavity templates was coated with titanium and copper of 50 nm and 300 nm in thickness as an electrode used in electroforming.Nickel electroplating was then conducted (plating thickness was 500 m), and, after that, the nickel metal replica was peeled off from the template.

Finite differential time domain
simulation.Numerical simulations of spectral reflectance were conducted by using the finite differential time domain (FDTD) software of MEEP 1 from Massachusetts Institute of Technology, USA.The MEEP software requires the dielectric function of the target material () expressed by Lorentz's model:

Fig. S1
Fig. S1 Numerical simulation of the micro-cavity blackbody performance.
Fig. S4 Testing for ultrasonic cleaning and restoring, and thermal shock.