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HW8+Sol - Homework 8 with Solutions(1 Using Stokes Vectors...

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Homework 8 with Solutions (1) Using Stokes Vectors and Müller Matrices calculate the output polarization for an input polarzation of 45 o after the following for elements in series i. Polarizer at 60 0 ii. Polarizer at 45 o iii. λ / 2 plate oriented with slow axis at 0 o iv. λ / 4 plate oriented with slow axis at 45 o First the intuitive solution: First element: Changes polarization to 60 Second element: Changes polarization back to 45 Third element: Changes polarization to –45 Fourth element: does not do anything Input Polarization: 1 0 1 0 " # $ $ $ % & After first element: cos15 0 ( ) 2 1 " 0.5 3 2 0 # $ % % % & ( ( ( After second element cos15 0 ( ) 4 1 0 1 0 " # $ $ $ % & After third element cos15 0 ( ) 4 1 0 " 1 0 # $ % % % & ( ( (
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After fourth element cos15 0 ( ) 4 1 0 " 1 0 # $ % % % & ( ( (
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What kind of matrices to we need ? First element: 1 0 0 0 0 cos " 120 sin " 120 0 0 " sin " 120 cos " 120 0 0 0 0 1 # $ % % % & ( ( ( 1 2 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 1 # $ % % % & ( ( ( 1 0 0 0 0 cos " 120 " sin " 120 0 0 sin " 120 cos " 120 0 0 0 0 1 # $ % % % & ( ( ( = 1 2 1 " 0.5 3 2 0 " 0.5 0.25 " 3 4 0 3 2 " 3 4 0.75 0 0 0 0 0 # $ % % % % % 1 2 1 " 0.5 3 2 0 " 0.5 0.25 " 3 4 0 3 2 " 3 4 0.75 0 0 0 0 0 # $ % % % % % & ( ( ( ( ( 1 0 1 0 # $ % % % & ( ( ( = 0.933013 " 0.466506 0,808012 0 # $ % % % & ( ( ( = 0.933013 1 " 0.5 3 2 0 # $ % % % & ( ( ( Second element: Polarizer at 45: 1 2 1 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 " # $ $ $ % & 1 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 " # $ $ $ % & 0.933013 ( 0.466506 0.808012 0 " # $ $
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