Polarization coherence frustration

From the joint analysis of polarization and coherence properties of light, a remarkable concept referred to as polarization coherence frustration is introduced and analyzed. It is shown that two kinds of partially polarized and partially coherent light, with different levels of complexity, can be distinguished and that they mathematically correspond to different equivalence classes. On the one hand, light has polarization coherence properties that are not frustrated in a spatial domain D${\cal D}$ when there exists a configuration of local polarization devices at each location of the light field that allows the maximization of the modulus of the scalar degree of coherence between any couple of points in D${\cal D}$. Two conditions are shown to hold for light to be polarization coherence unfrustrated and their physical interpretations are analyzed. On the other hand, if one of these conditions is not verified, polarization coherence frustration occurs. These notions are discussed in analogy with well-known concepts of frustration and gauge transformations developed in statistical physics for spin glasses. Their relevance in the field of statistical optics is demonstrated through different theoretical results and examples.