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I have analysed a thin-film sample on a reflective setup, using a setup similar to the one represented in the figure below. I also know the thickness of the sample d to be considerably smaller than the wavelength of the signal used.

How can I obtain the refractive index of such a sample?

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  • I thought of calculating the sample-to-reference ratio in terms of the Fresnel coefficient of the air-sample, and sample-air interfaces, but because we have air on both sides, this would result in simply 1, and thus not work.
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  • $\begingroup$ This may help - Fresnel Equations. If not, there are links to plenty more information. $\endgroup$
    – mmesser314
    Commented Oct 26, 2022 at 13:46

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The answer depends on how thin your thin sample is. Since you are talking some detectable reflection intensity, I will assume that the sample is at least a few wave-lengths thick. In this case you can measure the reflected signal as a function of incident angle. Then you apply Fresnel formulae to determine the complex reflection coefficient for the both reflected beams (from the inner and the outer surfaces) and deduce the refractive index by fitting your data to the formula as obtained via Fresnel. In particular you may notice that at certain angles the two reflected beams will interfere destructively, knowing these angles (and sample thickness) will give you the phase refractive of the sample material (don't forget the phase shift upon reflection).

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  • $\begingroup$ +1, but "a few wavelengths thick" is thicker than usual. For example, an anti-reflection coating would be $1/4$ wave thick, so the wave traveling to the rear surface and back travels an extra $1/2$ wavelength and destructively interferes with the front wave. $\endgroup$
    – mmesser314
    Commented Oct 26, 2022 at 13:50
  • $\begingroup$ The sample is thinner than the wavelength, as the wavelength of the signal is around 100 $\mu$m and the sample is around 6 $\mu$m thick. Doesn't this have an effect on the mathematical approach? $\endgroup$
    – user7077252
    Commented Oct 26, 2022 at 14:04

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