Thick samples, nonlinear absorption

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)... 

Figures 12a and b compare in effect the spectral dependence of the normalized photocurrent of an undoped a-Si H film illuminated from the front and through the Coming 7059 substrate (back-lit). The absorption coefficient a instead of the photon energy hv is used as the abscissa in order to facilitate comparison with the theory of Schetzina (1979) on surface recombination. The sample was d=il fim thick hence for a > 5 X 1(P cm all incident photons are absorbed, after reflection losses are accounted for, and contribute to the photocurrent. A fraction f of the available photons are absorbed in the absorption depth a. The photocurrent is normalized by the incident photon flux, and this flux F was adjusted such that oF was constant to provide a nearly constant generation rate in the absorption depth. Since the photocurrent 7p was nearly proportional to the photon flux in this sample, actually 7p we believe that this small nonlinearity is not...

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) ... 

---