## 2 Development of Thin Film Blackbody Radiation Source  
The thermal radiation of a blackbody can be a photon source at any frequency. According to the Planck equation for radiation power in a single frequency band and one spatial mode, the power is  
\[P_{bb}(f)=\frac{hf}{exp\left(\frac{hf}{kT_{bb}}\right)-1} \tag{1}\]  
This equation approaches the Nyquist formula, with \(P_{N}=kT\) at low and high frequencies, while taking into account quantum corrections using the Callen-Welton formula  
\[P_{CW}(f)=\frac{hf}{2}+\frac{hf}{exp\left(\frac{hf}{kT}\right)-1} \tag{2}\]  
where the first term describes zero fluctuations. The radiation power can be transferred to another matched load only by the second term. The blackbody radiation can be easily controlled by changing its electron temperature; in this case, a thin film resistor can be used as a source of radiation of hot photons. It seems reasonable to create such a blackbody as a thin metal film with resistance on the order of that of free space (\(Z_{0}=377\)\(\Omega\)). It is important to keep in mind that the thickness of such a film is small compared to wavelength and skin depth. In the case of different dielectrics with refractive indexes n\({}_{1}\) and n\({}_{2}\) adjacent to film, film conductivity per square is \(\sigma=1/R\), the transfer matrix element is \(T_{12}=0.5\) (\(1+n_{1}/n_{2}+\sigma Z_{0}/n_{2}\)), and the absorption coefficient is \(A=4\)\(Z_{0}\sigma/(n_{1}+n_{2}+\sigma Z_{0})^{2}\). In the case of vacuum on both sides of the film with a refractive index \(n=1\), the coefficient of absorbance for a normally incident wave is \(A=4\)\(\sigma Z_{0}/(2+\sigma Z_{0})^{2}\). The maximum value of the absorption coefficient that can be achieved is \(A_{max}=0.5\) with resistance per square \(1/\sigma=R\) = \(Z_{0}/2=188\)\(\Omega\). For an arbitrary value of the refractive index of the second material \(n_{2}\), the absorption coefficient will be \(A=4\)\(\sigma Z_{0}/(1+n_{2}+\sigma Z_{0})^{2}\). It approaches the maximum value of \(A_{max}=1/(n_{2}+1)\) if the resistance of the film is \(R\) = \(Z_{0}/(n_{2}+1)\). For thick silicon substrate, the optimal value is \(R\) = 84 \(\Omega\) and \(A_{max}=0.2\). This is one of the important conclusions of our research. At first glance, it seems that square resistance should be equal to \(Z_{0}\) for perfect matching. However, such a film is very thin compared to the skin depth, it is semitransparent, and increasing resistance towards \(Z_{0}\) will just increase transmission and reduce absorption. On the other hand, reducing resistance leads to increasing reflection that, again, reduces absorption. To model the absorption coefficient of thin film, CST Studio Suite was used. A schematic image of the project is presented in Figure 1a. Thin film on a substrate of the chosen material was placed inside the wave guiding structure (circular waveguide), and the two waveguide ports (377 \(\Omega\)) were placed on both sides of the guiding structure to generate/receive the signal and determine S-parameters. The main feature of modelling such projects in CST is that when considering the film's characteristics (skin depth and film thickness), the material of the metallic film must be determined as a \"thin panel\", and the TLM module (in T-solver) is used for calculation. In the opposite case, the thin film will be treated as a \"thick\" metal surface, and regardless of the thickness (even zero), the transmittance coefficient will be zero. The absorption coefficient is calculated from S-parameters by the following formulas:  
\[A_{1}=1-S_{11}^{2}-S_{21}^{2}\text{ and }A_{2}=1-S_{22}^{2}-S_{12}^{2} \tag{3}\]  
where \(A_{1}\) and \(A_{2}\) are the absorption coefficients in case of irradiation from the film side and the substrate side, respectively. The guiding structure is required because the waveguide port positioning should be used for calculation in this module.