Sometimes you find the argument in literature that at high angle of incidence alpha (say, 80°) and p-polarized light an important factor for the comparable high signal in transflection measurements is the more than tenfold increased pathlength. This erroneous assumption obviously comes from the formula 2d/cos alpha, where d is the thickness of the layer. Can someone point me to the paper from which this mistake originates?
Dear Thomas,
Why don't you think this calculation is error? could you give some detailed description about the "erroneous"? thanks. Frankly, I believe this calculation is correct. :-)
Dear Pudung,
thank you for your answer/question!
Assume that your incidence medium is air or vacuum with an index of refraction n1=1 and the layer consists of some organic material (or an inorganic glass) with n2=1.5. The incidence angle alpha may be equal to 80°. According to Snell's law we find that the angle of refraction beta is about half that value (about 41°). Accordingly we also find that the pathlength is not increased by 2d/cos alpha (which would be about 11.5), but only by 2d/cos beta, i.e. a factor of only about 2.6...
Thomas,
to my understanding, the problem is rather thoroughly considered in:
Fourier transform infrared spectrometry / Peter R. Griffiths, James A. de Haseth. – 2nd ed., ISBN 978-0-471-19404-0
(Copyright 2007 by John Wiley & Sons, Inc. All rights reserved).
Specifically, cf.
Chapter 13.3. INFRARED REFLECTION–ABSORPTION SPECTROMETRY WITH METAL SUBSTRATES
13.3.1. Effect of Incidence Angle and Polarization
If the book is unattainable, I can send you a copy of the chapter privately.
Meanwhile, may be the authors reference list below (relevant to the topic) will be of some help
1. F. M. Hoffman, Surf. Sci. Rep. 3, 107 (1983).
2. W. G. Golden, Fourier transform infrared reflection–absorption spectroscopy, in Fourier Transform Infrared Spectroscopy: Applications to Chemical Systems, J. R. Ferraro and L. J. Basile, Eds., Academic Press, Orlando, FL, 1985, Vol. 4, p. 315.
3. M. Milosevic, Harrick Scientific Corporation, personal communication to P. R. Griffiths (2003).
4. M. Born and E.Wolf Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 6th ed., Cambridge University Press, Cambridge, 1998.
5. J. D. Jackson, Classical Electrodynamics, Wiley, New York, 1980.
6. R. P. Feynman, The Feynman Lectures in Physics, Addison-Wesley, New York, 1963, Vol. 2.
7. W. G. Golden, D. D. Saperstein, M. W. Severson, and J. Overend, J. Phys. Chem. 88, 574 (1984).
8. R. G. Greenler, J. Chem. Phys. 44, 310 (1966).
Finally, Thomas, I dare note that the equation 2d/cos alpha was suggested for IRRAS case. In particular, Peter R. Griffiths and James A. de Haseth recognize in their book the following:
"Because the beam is transmitted through the film and reflected from the substrate, the measurement of the spectra of relatively thick films on metal substrates is usually known as transflection spectrometry. The film thickness, d, of samples studied by transflection must be on the order of
one half-wavelength or more, so that the considerations that were discussed in Section 13.3 do not apply [which is why measurement of the spectra of very thin films (d 0:5l), the technique is known as transflection spectrometry]."
Good Luck!
Sorry, folks!
The "l" in the formulas above should read "lambda".
Erroneous copy/paste thing. I beg your pardon!
Alex
Dear Alexander,
many thanks for your answer and your kind offer, but I own a copy of the book. The problem I pointed out above is somehow symptomatic for this book (and for many others about infrared spectroscopy nowadays), were concepts from wave optics are often non tractably interwoven with concepts that are not compatible with Maxwell's equations like the quantity absorbance (which is not mentioned at all in ref. 4, the Born and Wolf, for good reasons). Anyway, I did not get how a thickness half of the wavelength should change the properties or be some kind of limit, except that the nature of the electric field standing wave effect changes somewhat somewhere in between (but there is no need to change the formalism to describe electromagnetic propagation or to use simplifying assumptions like the one above). If speaking of that, a quarter of a wavelength would be a more logical dividing line for the thickness of a layer for reasons that are explained in here: Article The electric field standing wave effect in infrared transfle...
P.S.: I would also strongly challenge what is mentioned in there about fringes and there occurrence or non-occurence due to metallic substrates... see also the article mentioned above.
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