Thick samples, nonlinear absorption measurements

Figure 3.15. Nonlinear absorption measurement of a thick sample. (Adapted from Ref. [53].)...

The final point concerns the units in which a DR spectrum of adsorbed species should be represented for quantitative analysis. The application of DRIFTS for quantitative measurements is restricted not only by the variation in band intensities caused by irreproducible sample preparation but also by the nonlinear behavior of the reflectance due to scattering effects [168]. To increase the linear range, some authors [168-170] use KM units [Eq. (1.133)], while others [171-174] prefer absorbance, -logRoo (or l/Roo), where Roo is the reflectance spectrum of an inflnitely thick sample relative to that of a nonadsorbing reference. For small values of K/S (where K and S are the KM absorption and scattering coefficients, respectively), such as is the case for DRIFTS of ultrathin films. Burger et al. [175] have shown that absorbance is proportional to the square root of KM units ... 

If the primary aim is to characterize the nonlinear absorption, several direct techniques are more easily implemented or interpreted. Conceptually, the simplest technique is to measure the transmitted intensity as a fimction of the incident intensity on the sample. Separating the linear and nonlinear contributions depends upon the spatial and temporal characteristics of the laser, however, as well as the thickness L and reflectivity R of the sample surfaces. For example, if the laser provides a CW beam of uniform spatial intensity, normally incident on a sample, the transmission T may be expressed as a product T = TlTVi, of the linear transmission Tl = (1-R ) and a nonlinear factor = l/d + f)... 

TPA cross-section (ajPA) values were determined from experimentally measured two-photon absorption coefficient, p, which is obtained by measuring the nonlinear transmissivity (Ti) of chromophores in solution for a given input intensity, / , and a given thickness of a sample solution, lo, from the following relationships (23,24) ... 

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