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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![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe116b05f-4c27-45b1-8d08-00941e4ec3cb%2Ff3d28b2a-4f2e-45ba-a1f5-7cdc28a618e7%2Fa8qfwk_processed.png&w=3840&q=75)
Transcribed Image 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.
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