Effective absorption coefficient and effective thickness in attenuated total reflection spectroscopy

Since the introduction of attenuated total reflection (ATR) spectroscopy for the characterization of materials, attempts have been made to relate the measured reflectivity ( ) to the absorption coefficient ( ) of the absorbing material of interest. The common approach is limited to the low absorption case under the assumption ∼ (- ), where is an effective thickness, which is evaluated for the lossless case. In this Letter, a more detailed derivation leads to = (- /2), enabling the definition of an ATR-effective absorption coefficient and the penetration depth of the electric field in the absorbing material. It is found that ∼4 / , where is the imaginary part of the complex dielectric function of the absorbing material, and is the wavelength. An alternative formulation is = (- ), where is a generalized effective thickness for arbitrary strength of absorption which reduces to in the low absorption limit. The experimental data for water, the biopolymer chitosan, and soda-lime glass prove the reliability of the ATR-effective absorption coefficient in the infrared range.