Stokes vector, modified

The coherency matrix and the Stokes vector are not the only representations of polarization and not always the most convenient ones. Two other frequently used representations are the real so-called modified Stokes column vector given by... 

This explains the usefulness of the modified Stokes representation of polarization given by Eq. (7.9) in situations involving linearly polarized light as follows. The modified Stokes vector has only one non-zero element and is equal to [/ 0 0 0] if = 7tl2 (the electric vector vibrates along the 0-axis, i.e., in the meridional plane) or [0/0 0] if = 0 (the electric vector vibrates along the (p -axis, i.e., in the plane perpendicular to the meridional plane), where T indicates the transpose of a matrix (see Fig. 8.1(c)). 

Most detectors of electromagnetic radiation, especially those in the visible and infrared spectral range, are insensitive to the polarization state of the beam impinging on the detector surface and can measure only the first Stokes parameter of the beam, viz., the intensity. Therefore, to measure the entire Stokes vector of the beam, one has to insert between the source of light and the detector one or several optical elements that modify the first Stokes parameter of the radiation reaching the detector in such a way that it contains information about the second, third, and fourth Stokes parameters of the original beam. This is usually done with so called polarizers and retarders. 

It then follows from the definition of the Stokes parameters that the Stokes vector of the wave modifies according to... 

The gauge transform Aq A + does not modify the value of the magnetic flux F calculated on the basis of Stokes theorem, as dehned above. However, this gauge transform does not allow us to cancel the external vector potential. This statement is in sharp contrast with, and even contradicts, what is usually claimed in the available literature. Indeed, Helmholtz decomposition of the vector potential A = + Ax shows that only the longitudinal component An is modified in this process ... 

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