The Effective Thickness in Internal Reflection Spectroscopy

Abstract

In internal reflection spectroscopy the intensity loss per reflection can be described conveniently in terms of a parameter de, the effective thickness of the absorbing sample. There is a temptation to seek correlation between this parameter and the extra path length L that arises when the Goos-Hanchen shift is included in the rat picture for total internal reflection (Fig. 1). This shift occurs because, under conditions of total internal reflection, the effective reflecting plane does not coincide with the physical interface. As a result the specularly reflected ray is displaced parallel to itself by the distance D and there is a corresponding shift L = D/cos θ along the interface. Hirschfeld has compared the functional forms for de and L, as given in the literature, and has observed that the two quantities agree only at the critical angle. In this note we examine the power flows associated with both the Goos-Hanchen shift and the power dissipated in the absorbing sample. This approach allows us to determine the ratio de/L without having to carry out an explicit calculation for the separate quantities, and provides a physical basis for understanding why this ratio differs from unity at all angles but the critical.