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Nick89

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I am trying to understand the reflectivity from metal surfaces, but I'm stuck... I am finding contradicting results and I can't figure out where I'm going wrong.

I am reading a paper [1] about IRAS (Infrared reflection absorption spetroscopy) where an IR beam is reflected from a metal with a thin film of adsorbed material. The author first mentions the reflectivities [itex]R_s[/itex] and [itex]R_p[/itex] of the s- and p-polarized light respectively. Now, unless I am already really mistaken here, the s-polarized light is where the electric field is perpendicular to the plane of incidence, and the p-light is where the electric field is parallel to the plane of incidence.

He quotes the reflectivities from a clean metal surface (assuming [itex]n^2+k^2 \gg 1[/itex] which should be true for IR light) as:

[tex]R_s = \frac{\left( n - \sec \phi \right)^2 + k^2}{\left( n + \sec \phi \right)^2 + k^2}[/tex]

[tex]R_p = \frac{\left( n - \cos \phi \right)^2 + k^2}{\left( n + \cos \phi \right)^2 + k^2}[/tex]

where [itex]\phi[/itex] is the angle of incidence (measured from the surface normal as usual) and of course the refractive index is [itex]n + ik[/itex].

This seems fine to me.

The author then goes on to calculate the change in reflectivity resulting from the thin film of adsorbed material and finds a quite complex equation, that's not really relevant.

When he plots these changes in reflectivity however, he also plots the reflectivity of the clean metal surface. Example:

The R* (top graph) should be the reflectivity from a clean surface, ignore the others.

He does not state whether he is talking about [itex]R_s[/itex] or [itex]R_p[/itex], but I have assumed [itex]R_p[/itex] due to two reasons:

1. The paper is about IRAS on metals. In this case one uses a very large angle of incidence. The incoming and reflected light interfere in this case and the s-polarized light very nearly cancels out (due to a 180 degree phase shift). The idea of IRAS is to ignore s-light and use only p-light, so it wouldn't make sense that he would be talking about Rs...

2. A few lines later he mentions:

Equation 2.2 is the equation for [itex]R_p[/itex].So it seems the reflectivity for p-light ([itex]R_p[/itex]) has a 'dip' so it has a minimum at a certain high angle of incidence. So far so good... Until I tried to plot the function myself.When I plot Rs and Rp using Maple, I get the dip for [itex]R_s[/itex] and certainly not for [itex]R_p[/itex]! I don't get it...One sees immediately that at high angles of incidence, the metal reflectivity is lowest, a fact resulting from eq. (2.2), but at the same time ...

Here's my work: image

The red graph is Rs and the blue graph is Rp.

So in my calculation [itex]R_s[/itex] has the dip and minimum in reflectivity, and not [itex]R_p[/itex]...

I'm kinda lost at this point. Who's wrong? Is there something wrong with my calculations? Am I colorblind? :p

I decided to look for another source, didn't find much but I did find a similar graph in my old optics textbook. They don't talk about s- and p-light though, but rather about TE and TM modes. It's been too long, but as far as I understand TE mode is where the electric field is perpendicular to the plane of incidence, so this should be the s-light?

When they show the graph of reflectivity versus angle of incidence (for a metal) they show that the TM mode has the dip whereas the TE mode does not. Basically, their TM mode graph corresponds to my [itex]R_s[/itex] graph (the red one with the dip) and their TE mode corresponds to my [itex]R_p[/itex] graph (the blue one).So, I am slightly more convinced that my calculations are correct and that it is indeed [itex]R_s[/itex] that has the dip in reflectivity, and not [itex]R_p[/itex] as the paper seems to state.I am now absolutely confused though, because as far as I understand the whole point of using IRAS on metals is that the reflectivity [itex]R_p[/itex] is lowest at high angle of incidence (which it is not if my calculations are correct) while the CHANGE in reflectivity (due toe absorption by the thin adsorbed material) is highest. If that isn't true then I don't know what to believe anymore...Any help on this matter?

Thanks![1] The paper might be hard to find, but:

F.M. Hoffmann. Infrared reflection-absorption spectroscopy of adsorbed molecules. Surface Science Reports, 3:107-192, 1983.