Simplified formulas for non-normal reflection from monoclinic crystals

Based on Berreman's 4 × 4 matrix formalism [W. Berreman, J. Opt. Soc. Am. 62, 502 (1972)] we derive simplified expressions for the reflection formulas from the a–c crystal surface for non-normal incidence. The computational effort to apply the formulas was found to be only insignificantly higher than those for normal incidence, but considerably lower than for the general expressions. Consequently, the simplified formulas can be readily applied for dispersion analysis of spectra gained by spectroscopic ellipsometry or attenuated total reflection.