3. Data Analysis for Nanomaterials: Effective Medium Approximation, Its Limits and Implementations

We review here basic theoretical approaches to the optical response of nanostructured materials. We use the well established framework of Effective medium approximation (EMA) and discuss key issues of its use. The treatment of this extensive subject is adapted to the needs of ellipsometric/polarimetric measurements on nanostructured materials. In Sects. 3.1 and 3.2 we formulate the problems and establish notation. Then, we recall and discuss, in Sects. 3.3 and 3.4, several well-known formulae for the effective dielectric function. Sections 3.5 and 3.6 are devoted to a fairly detailed comparison of selected measured data with results of the EMA models. We also assess the uncertainties involved in the EMA approach by visualizing the differences between results of its different versions (Sect. 3.7) and by calculating the differences from exact solutions (Sect. 3.8). Finally, Sect. 3.9 is devoted to the discussion of possible resonant behaviour of EMA mixtures.