polarization modes

The polarization modes, E and B have been devised in the study of polarization patterns of the cosmic microwave background (CMB), such as patterns over a patch of the sky or over the entire celestial sphere. (The modes are not a characteristic of polarization from a point, but a characteristic of the pattern of polarization across the sky, i.e., in one kind of CMB anisotropy.) The modes are oriented to the CMB's polarization states and don't capture every possible state of polarization. The names were chosen in analogy to electromagnetism with its somewhat similar-behaving electric and magnetic fields (E and B), but the modes aren't directly related to them. The E-mode is analogous to a curl-free component and the B-mode, to a divergence-free component. The analogy is not exact because the state of polarization is not a vector quantity: it has a magnitude, but its direction lacks any "arrow head" (i.e., a rotation of 180 degrees produces the identical polarization state but a 180-degree rotation of a vector would produce the negative of the vector).