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 expansioncoefficients 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 wavesandare used as anexpansion basis, the coefficients a, and az are:1AR = (A, - jA,), AL = (A, + jA,).(6.1-13)For example, a linearly polarized wave with a plane of polarization that makes an angle 0 withthe r axis (i.e., A, = cos e and A, = sin 6) is equivalent to a superposition of right andleft circularly polarized waves with coefficients e-" and e, respectively. A linearlypolarized 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 (6.1-9for light with Jones vector components Az and A, are given bySo = |A.? + |A,/?Si = |A_]? – |A,/²S2 = |A45|? – |A135|?S3 = |AR|? – |AL[²,(6.1-14a(6.1-14b(6.1-14с(6.1-14dwhere 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 righand left circularly polarized waves set forth in (6.1-13). Suggest a method of measuring the Stoke:parameters for light of arbitrary polarization.

Answered: Image /qna-images/answer/f3d28b2a-4f2e-45ba-a1f5-7cdc28a618e7.jpg

Measurement of the Stokes Parameters. Show that the Stokes parameters defined in (6.1-9 for light with Jones vector components A, and A, are given by So = |A,* + |A,/? Si = |A,P – |A,? S2 = |A4s/? – |A135/? S3 = |AR – |AL°, (6.1-14a (6.1-14b (6.1-14c (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.

Measurement of the Stokes Parameters. Show that the Stokes parameters defined in (6.1-9 for light with Jones vector components A, and A, are given by So = |A,* + |A,/? Si = |A,P – |A,? S2 = |A4s/? – |A135/? S3 = |AR – |AL°, (6.1-14a (6.1-14b (6.1-14c (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.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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