Normalized Stokes vectors

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., = , = < sin 5 > =0, and therefore the normalized Stokes vector is... 

Since the Maxwell equations involve the components of the Jones vector, it is normally easier to derive the Jones matrix, J, for complex, anisotropic media. Once J is obtained, it is generally convenient to transform it to the Mueller matrix representation for the purpose of analyzing the quantities measured in specific optical trains. This is because the components of the Stokes vector are observable, whereas the Jones vector components are not. Since it is the intensity of light that is normally required, only the first element of Sn,... 

Stokes vector, intensity of light linearly polarized at n degrees J = Bessel functions J = Jones matrix k = extinction coefficient m = dimensionality of z M = Mueller matrix, normalized Mueller-Jones matrix M vij = Mueller-Jones matrix n = refractive index Nq, N[, = complex refractive indices ... 

A few representatives sets of Stokes parameters, written as column vectors, are shown in Table 2.2 the irradiance / is normalized to unity. 

Barrett [50] has interestingly reviewed and compared the properties of the Abelian and non-Abelian Stokes theorems, a review and comparison that makes it clear that the Abelian and non-Abelian Stokes theorems must not be confused [83,95]. The Abelian, or original, Stokes theorem states that if A(x) is a vector field, S is an open, orientable surface, C is the closed curve bounding S, dl is a line element of C, n is the normal to S, and C is traversed in a right-handed (positive direction) relative to n, then the line integral of A is equal to the surface integral over 5 of V x A-n ... 

Physical interpretation of vorticity is facilitated by application of Stokes s theorem. This theorem states that for an area A with normal vector n enclosed by a curve or path P with contour element dr,... 

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