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Unformatted text preview: Lecture 18 Manipulation of polarization Jones and Mueller Matrices Both representations (Jones and Stokes) are vectors which can be transformed using Matrices Jones Stokes Jones Mueller Manipulation of polarized light Example: Example: Example: Example: 3 3. You have light which is polarized in 30 in respect to the horizontal direction. Describe the state of polarization of the light a # /4 retarder plate oriented along the 45 o (a) using Stokes vectors and Mueller matrices (b) Visualize the result on a Poincare sphere. 30 light 45 # /4plate fast axis For this example we need to transform Stokes vectors and Mller matrices 60 S 1 = S o cos 2 " ( ) cos 2 # ( ) S 2 = S o cos 2 " ( ) sin 2 # ( ) S 3 = S o sin 2 " ( ) Taking the denition We see that only S 1 and S 2 are changed by a coordinate transformation. A rotation by ! causes a rotation of the Poincare sphere by 2 " Rotation matrix: T = 1 cos2 " # sin2 " sin2 " cos2 " 1 $ % & & & ( ) ) ) Transformation of Stokes vectors In dealing with the element for which we do not nd a Mller Matrix in the proper coordinate system we have to deal with the following S out = T " 1 # M # T # S in We can look at this in the following way: S out = T " 1 # M # S ' in S out = T " 1 # S ' out But also as: S out = M ' " S in This we get for a our # /4 plate M ' = 1 " 1 1 1 # $ % % % & ( ( ( 1 1 1 " 1 1 " 1 # $ % % % & ( ( ( 1 1 " 1 1 # $ % % % & ( ( ( = 1 " 1 1 1 1 # $ % % % & ( ( ( Rotate 45 o Rotate 45 o Why 45 o ? Coordinate system in which the polarization is described Coordinate system in which the optical element is described Rotation by 45 o Using this we get S in = 1 1 2 3 2 " # $ $ $ % & S out = 1 " 1 1 1 # $ % % % & ( ( ( 1 1 2 3 2 # $ % % % & ( ( ( = 1 3 2 1/2 # $ % % % & ( ( ( In Out Light Polarization State A point P( S 1 ,S 2 ,S 3 ) on the Poincare sphere represents a light polarization state...
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This note was uploaded on 08/06/2008 for the course PHYS 352 taught by Professor Dierolf during the Fall '04 term at Lehigh University .
 Fall '04
 DIEROLF
 Light, Polarization

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