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As part of a project work I had to derive the absorption of a thin-film stack. It was a semiconductor between two oxides on a metallic back reflector. I used Fresnel equations and optimized the absorption by adjusting the thickness. After fabricating the device, it looked quite black, which was exactly what was the goal. Therefore my calculations seem to be successful and match the problem.

I am now putting everything in my thesis, but there is one open question for me. As a body that is absorbing is also emitting, I would expect the semiconductor material and back reflector to emit as well (as they have complex refractive indices). My question is, how the Fresnel equations could possibly already account for this problem (I don't think that they'll do)? Emission in my opinion can occur at any depth of the material, so if I would consider it, I would get all kinds of different phase shifts, intimating a very messy calculation. Nevertheless it seems, that emission is only a minor problem, because otherwise my structure would be far from being a good absober, thus far from being black. Any ideas, why that is the case?

Thanks for any help!

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The Fresnel equations describe the response to an external field. Your structure will also emit black body radiation, depending on temperature, and its intensity is modified by the emissivity. For example, at a frequency for which a material is transparent the emissivity is zero and it will not emit any black body radiation.

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  • $\begingroup$ Thank you for your answer. I get what you mean, but still don't know how you would model such a thing. In the supplementary information of "Engineering Light Outcoupling in 2D Materials" by Lien et al., they calculate the amplitudes of absorption and emission at a certain depth and then they just put the product of those two amplitudes in an integral and square it. First, if you multiply two electric field vectors you already have something like an intensity. They still square again. Also they have some mistakes in there, and that's why I don't trust that model completely. $\endgroup$ – Singularity Sep 20 '18 at 5:31

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