Extracted text: EXAMPLE 6.1-1. Expansions in Linearly Polarized and Circularly Polarized Bases. Using the a and y linearly polarized vectors [6) and [9) as an expansion basis, the expansion coefficients for a Jones vector of components A, and A, with |A, + |A,° = 1 are, by definition, a = A, and az = Ay. The same polarization state may be expanded in other bases. - In a basis of linearly polarized vectors at angles 45° and 135°, i.e., J1 = *G, the expansion coefficients a, and az are: * G) and Ja = A, + A,), As = (A, – A.). (6.1-12) • Similarly, if the right and left circularly polarized waves and are used as an expansion basis, the coefficients a, and az are: 1 AR = (A, - jA,), AL = (A, + jA,). (6.1-13) For example, a linearly polarized wave with a plane of polarization that makes an angle 0 with the r axis (i.e., A, = cos e and A, = sin 6) is equivalent to a superposition of right and left circularly polarized waves with coefficients e-" and e, respectively. A linearly polarized wave therefore equals a weighted sum of right and left circularly polarized waves. Measurement of the Stokes Parameters. Show that the Stokes parameters defined in (6.1-9 for light with Jones vector components Az and A, are given by So = |A.? + |A,/? Si = |A_]? – |A,/² S2 = |A45|? – |A135|? S3 = |AR|? – |AL[², (6.1-14a (6.1-14b (6.1-14с (6.1-14d where A45, and A135 are the coefficients of expansion in a basis of linearly polarized vectors at angle: 45° and 135° as in (6.1-12), and AR and AL are the coefficients of expansion in a basis of the righ and left circularly polarized waves set forth in (6.1-13). Suggest a method of measuring the Stoke: parameters for light of arbitrary polarization.