Analytical Understanding of Multiple-Angle Incidence Resolution Spectrometry Based on a Classical Electromagnetic Theory

Infrared multiple-angle incidence resolution spectrometry (IR-MAIRS) is a unique spectroscopic technique to retrieve both surface-parallel (in-plane; IP) and -perpendicular (out-of-plane; OP) molecular vibration spectra simultaneously from an identical thin-film deposited on a high refractive index substrate, and the measurement theory was constructed by the use of a theoretical framework of regression equation. The core part of the MAIRS theory is found in the weighting factor matrix, R, used for a linear combination, which was constructed in an unusual manner. Because a regression equation does not strictly correlate the left- and right-hand sides of the equation, R matrix cannot directly be deduced from Maxwell’s equation. Although the conventional studies using IR-MAIRS gave excellent empirical results, a strict physical understanding of MAIRS is necessary; otherwise, we cannot rely on it at least quantitatively. In the present study, the MAIRS theory has first been analyzed by the use of Maxwell’s equations inductively. As a result, both MAIRS-IP and -OP spectra have readily been expressed as a linear combination of the Im(ε x ) and Im(−1/ε z ) functions that correspond to the conventional transmission and reflection−absorption spectra. Through the analysis of coefficients of the linear combination, MAIRS has proved to be reliably useful for analysis of thin film on a high refractive index substrate.