Advanced Mueller Ellipsometry Instrumentation and Data Analysis

The main object of this chapter is to give an overview the possibilities offered by instruments capable of measuring full Mueller matrices in the field of optical characterization. We have chosen to call these instruments Mueller ellipsometers in order to highlight their close relation with instruments traditionally used in ellipsometry. We want to make clear to the reader the place that Mueller ellipsometry takes with respect to standard ellipsometry by showing the similarities but also the differences among these techniques, both in instrumentation and data treatment. To do so the chapter starts by a review of the optical formalisms used in standard and Mueller ellipsometry respectively. In order to highlight the particularities and the advantages brought by Mueller ellipsometry, a special section is devoted to the algebraic properties of Mueller matrices and to the description of different ways to decompose them. Matrix decompositions are used to unveil the basic polarimetric properties of a the sample when a precise model is not available. Then follows a description of the most common optical configurations used to build standard ellipsometers. Special attention is paid to show what can and what cannot be measured with them. On the basis of this knowledge it is shown the interest of measuring whole Mueller matrices, in particular for samples characterized by complex anisotropy and/or depolarization. Among the numerous optical assemblies able to measure full Mueller matrices, most of them are laboratory prototypes, and only very few have been industrialized so far. Because an extensive and comparative review of all the Mueller ellipsometric instruments developed to date is clearly out of the scope of this chapter, we limit our description to four Mueller ellipsometers, two imaging and two spectroscopic systems that have been developed by us in the past years. The technical description of the Mueller ellipsometers is accompanied by some examples of applications which, without being exhaustive, are representative of the type of analyses performed in ellipsometry, and also illustrate the advantages that can be brought by modern Mueller ellipsometers to optical metrology, materials science and biomedicine.