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Exhaustive studies in the literature detail the Mueller matrices properties  through decomposition, optical entropy and depolarization formalism. It has been  applied for many years in rather different fields. In radar polarimetry,  mathematical basis of depolarizing systems, have been first developed. In the  visible range optics, standard diattenuation and retardance, decomposition is  currently used in turbid organic media. The optical entropy concept, developed  by S.R. Cloude, provides a very powerful analysis technique yielding important  surface parameters such as depolarization, correlation and roughness.  Complementary applications exist in scatterometry, for thin periodic grating  films. With high capability polarimeters, such as the next generation of angle  resolved polarimeters instruments, Polarimetry opens new fields of investigation  for nanotechnologies materials as well as for gratings and photonics structures  analysis: a program presently developed through a national consortium  ANR08-NANO-020-03. With this instrumentation progress, simulation remains a key  point to overpass as a challenge between future instruments. The theories for  surfaces spectral power density (PSD) and the random coupled wave approximation  (RCWA) in periodic structures are widely described in the literature. The  implementation of some of these codes is described here for surface analysis and  lithography scatterometry structures: grating overlay or double patterning

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Polarimetry of light scattered by surface roughness and textured films and periodic structures in nanotechnologies: a new challenge in instrumentation and modeling