In this chapter we introduce the Stokes parameters and the Stokes vector representation of a polarized beam. This representation is particularly important to us because it can be easily measured and is the most common way to represent a beam's propagation along a complex path such as we encounter in remote sensing. The Stokes representation is also important because it allows us to represent both fully and partially polarized beams. Our discussion in Chapter 3 presented ways to describe a beam in which all of the EM energy was polarized. For an unpolarized or randomly polarized beam, no preferred orientation or rotational behavior is associated with the electrical field. Most EM radiation is partially polarized and can be thought of as being composed of both an unpolarized component and a polarized component.
4.1 The Stokes Parameters
Recall from Eq. (3.27) that for a fully polarized beam, we can express the polarization ellipse as Îµ 2 x (t) Îµ 2 0x +Îµ 2 y (t) Îµ 2 0y â2Îµ x (t)Îµ y (t) Îµ 0x Îµ 0y cosÏ=sin 2 Ï. Stokes (1852) showed, with some algebraic manipulation including taking the time averages, that this leads to an expression of the form (Îµ 2 0x +Îµ 2 0y ) 2 =(Îµ 2 0x âÎµ 2 0y ) 2 +(2Îµ 0x Îµ 0y cosÏ) 2 +(2Îµ 0x Îµ 0y sinÏ) 2 .
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