Unpolarized light
[1] Conversely, the two constituent linearly polarized states of unpolarized light cannot form an interference pattern, even if rotated into alignment (Fresnel–Arago 3rd law).
Unpolarized light can be described as a mixture of two independent oppositely polarized streams, each with half the intensity.
However, in practice there are cases in which all of the light cannot be viewed in such a simple manner due to spatial inhomogeneities or the presence of mutually incoherent waves.
Mueller matrices are then used to describe the observed polarization effects of the scattering of waves from complex surfaces or ensembles of particles, as shall now be presented.
However any mixture of waves of different polarizations (or even of different frequencies) do not correspond to a Jones vector.
One such representation is the coherency matrix:[7]: 137–142 where angular brackets denote averaging over many wave cycles.
An alternative decomposition is into completely polarized (zero determinant) and unpolarized (scaled identity matrix) components.
Here Ip, 2ψ and 2χ are the spherical coordinates of the polarization state in the three-dimensional space of the last three Stokes parameters.
In quantum mechanics and computing, a related concept is the Bloch sphere.
) and the three significant Stokes parameters plotted in three dimensions will lie on the unity-radius Poincaré sphere for pure polarization states (where
Partially polarized states will lie inside the Poincaré sphere at a distance of
When the non-polarized component is not of interest, the Stokes vector can be further normalized to obtain When plotted, that point will lie on the surface of the unity-radius Poincaré sphere and indicate the state of polarization of the polarized component.
Any two antipodal points on the Poincaré sphere refer to orthogonal polarization states.
The overlap between any two polarization states is dependent solely on the distance between their locations along the sphere.
