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Lecture18

# Lecture18 - Manipulation of polarized light Jones and...

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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:

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Example: 3 3. You have light which is polarized in 30 0 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 0 light 45 0 # /4-plate fast axis For this example we need to transform Stokes vectors and Müller matrices 60 0 S 1 = S o cos 2 " ( ) cos 2 # ( ) S 2 = S o cos 2 " ( ) sin 2 # ( ) S 3 = S o sin 2 " ( ) Taking the definition 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 0 0 0 0 cos2 " # sin2 " 0 0 sin2 " cos2 " 0 0 0 0 1 \$ % & & & ( ) ) ) Transformation of Stokes vectors In dealing with the element for which we do not find a Müller 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 0 0 0 0 0 " 1 0 0 1 0 0 0 0 0 1 # \$ % % % & ( ( ( 1 0 0 0 0 1 1 0 0 " 1 0 1 0 0 " 1 0 # \$ % % % & ( ( ( 1 0 0 0 0 0 1 0 0 " 1 0 0 0 0 0 1 # \$ % % % & ( ( ( = 1 0 0 0 0 0 0 " 1 0 0 1 0 0 1 0 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 0 " # \$ \$ \$ % & S out = 1 0 0 0 0 0 0 " 1 0 0 1 0 0 1 0 0 # \$ % % % & ( ( ( 1 1 2 3 2 0 # \$ % % % & ( ( ( = 1 0 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 Relation with Jones vector [ E X , E Y ] t Some specific points North pole : right circular polarization

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Lecture18 - Manipulation of polarized light Jones and...

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