Infrared Attenuated Total Reflection Spectroscopy for a Layered Structure

For the analysis of a structural distribution in a range of thicknesses comparable with the wavelengths in the visible region of light, infrared attenuated total reflection (ATR) was derived on the basis of the wave vector and Poynting vector, paying attention to the phase of transmitted light. The absorption was ascribed to the energy flow into the rarer medium by the component of the Poynting vector in the <i>z</i> direction and further embodied for the layered structure. This derivation was validated based on three bands arising from the chelating group of ethyl acetoacetate (EAcAc) in a gel film of alumina with a geometric condition, in which a layer of amorphous alumina with known thickness was located between the gel film and the Ge prism.