Partially polarized and unpolarized light

A quasimonochromatic wave, whose frequency spectrum is confined to a narrow bandwidth A/l (AA C A), can stiU be described by 

The average amplitudes of the electric field components in the x and y directions are the same, but the phase difference between them is completely random, i.e., A = A , cosS = sin 5 =0, and therefore the normalized Stokes vector is 

2 Linearly polarized light along a direction which makes the angle y/ with respect to the x axis 

When the light is linearly polarized along the x axis, = (1,1,0,0). When the light is linearly 

If there were only two parameters So and 5i, when 5i =0, there are three possibilities (1) unpolarized, (2) linearly polarized along the direction at 45°, and (3) circularly polarized. Therefore more parameters are needed to differentiate them. If there were only three parameters So, Si, and S3, when Si = 0 and S3 = 0, there are two possibilities (1) unpolarized and (2) linearly polarized along the direction at 45°. Therefore one more parameter is needed to differentiate them. The four parameters are necessary and also sufficient to describe the polarization of a light beam. The Stokes vectors of various polarizations are listed in Table 2.1. 

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