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Effective absorption coefficient and effective thickness in attenuated total reflection spectroscopy

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Abstract

Since the introduction of attenuated total reflection (ATR) spectroscopy for the characterization of materials, attempts have been made to relate the measured reflectivity ($R$) to the absorption coefficient ($\alpha$) of the absorbing material of interest. The common approach is limited to the low absorption case under the assumption ${\rm{R}}\sim{\exp}(- \alpha {d_e})$, where ${d_e}$ is an effective thickness, which is evaluated for the lossless case. In this Letter, a more detailed derivation leads to $R = {\exp}(- \beta {d_p}/{{2}})$, enabling the definition of an ATR-effective absorption coefficient $\beta$ and the penetration depth ${d_p}$ of the electric field in the absorbing material. It is found that $\beta \sim4\pi {\varepsilon _2}/\lambda$, where ${\varepsilon _2}$ is the imaginary part of the complex dielectric function of the absorbing material, and $\lambda$ is the wavelength. An alternative formulation is $R = {\exp}(- \alpha {d_{\textit{ef}}})$, where ${d_{\textit{ef}}}$ is a generalized effective thickness for arbitrary strength of absorption which reduces to ${d_e}$ 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.

© 2021 Optical Society of America

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Supplementary Material (1)

NameDescription
Supplement 1       Experimental details, supplementary figures and equations

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Equations (13)

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