Effects of multiple reflections on nonlinear absorption measurements

Accurate measurement of nonlinear absorption coefficients by transmission-based techniques, such as Z-scan and its modifications, remains challenging due to high measurement errors. In this Letter, we claim that one of the reasons for that could lie in ignoring multiple reflections of light in plane-parallel samples in the presence of multi-photon excitation. Closed-form formulations for transmittance and reflectance coefficients, considering both linear and multiphoton absorption, are obtained in the geometrical optics approximation. The contributions of multiple reflections to the total transmittance are calculated for several II-VI materials reported in the literature. The results show a nonlinear dependence on incident intensity, ranging from 15.7% down to 7.9% for CdS, from 10.3% down to 5.8% for CdSe, and from 18.1% down to 9.1% for ZnSe. The dependence of the contribution of multiple reflections on the sample thickness is shown to exhibit a near exponential decay.