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Gradient- and curl-type or E- and B-type polarizations have been routinelyanalyzed to study the physics contributing to the cosmic microwave backgroundpolarization and galactic foregrounds. They characterize the parity-even andparity-odd properties of the underlying physical mechanisms, for examplehydromagnetic turbulence in the case of dust polarization. Here we studyspectral correlation functions characterizing the parity-even and parity-oddparts of linear polarization for homogeneous and inhomogeneous turbulence toshow that only the inhomogeneous helical case can give rise to a parity-oddpolarization signal. We also study nonhelical turbulence and suggest that astrong nonvanishing (here negative) skewness of the E polarization isresponsible for an enhanced ratio of the EE to the BB (quadratic) correlationin both helical and nonhelical cases. This could explain the enhanced EE/BBratio observed recently for dust polarization. We close with a preliminaryassessment of using linear polarization of the Sun to characterize its helicalturbulence without being subjected to the pi ambiguity that magnetic inversiontechniques have to address.

E and B polarizations from inhomogeneous and solar surface turbulence