**1. Introduction**

The standard theoretical apparatus used for modeling the optical properties of multilayer systems is formulated in terms of linear optics, i.e., it is based on a linear relationship between the electric field strength and the polarization induced in the medium. Within this framework, commonly used calculation recipes, such as matrix formalism or the admittance approach, have been derived in relevant textbooks [1–4]. Practical applications for these approaches in optical coatings design, characterization, and reengineering tasks have formed the content of relevant monographs (see, for example, References [2–5]).

Nevertheless, in high-power laser systems, the electric field in the incident light beam may be strong enough to induce relevant nonlinear optical effects in the coating materials. In many cases, it is the third-order (cubic) optical nonlinearity that dominates the nonlinear response. The optical Kerr effect, as well as nonlinear two-photon absorption (TPA), are prominent examples of third-order processes [6].

In high-power laser applications, third-order nonlinearity may therefore have to be taken into account in order to correctly predict the optical properties of a coating [7]. Thus, Razskazovskaya et al. [8] demonstrated the effect of TPA on the reflectance of dielectric laser mirrors in a pre-damage regime. Similarly, the optical Kerr effect appeared to be responsible for an intensity-dependent shift of the rejection band edge in several Angstroms in edge filters [9]. As opposed to linear optics, the general effect is that coating reflectance (and transmittance) becomes intensity-dependent. As we have shown in a previous study, these effects can principally be incorporated into a manageable design algorithm [10] when describing each coating material by four (instead of two) optical constants, namely linear and

nonlinear refractive indexes as well as linear and nonlinear extinction or absorption coefficients. Concerning linear optical constants, an overwhelming number of studies exist that give an idea on the range of optical constants achievable for practically any relevant coating material depending on the deposition technique and parameters used. However, although there exist several manageable theoretical approaches for estimating nonlinear optical constants (see, for example, References [11–16]), reliable experimental data on the dispersion of nonlinear optical constants of thin-film materials are practically not available.

The motivation of this study was to contribute to an improvement of the data basis for nonlinear optical constants. We present results from the measurement of the two-photon absorption coefficient of TiO2 thin optical films at a wavelength of 800 nm and discuss the results with respect to the predictions of two different theoretical approaches.
