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Calculate Jones Vector of polarized light thorugh QWP

  1. Jun 7, 2013 #1
    1. The problem statement, all variables and given/known data

    Find the final polarization in terms of Jones vectors for vertical polarized, coherent light passing through a quarter waveplate rotated [itex]\theta = \pi/4[/itex]. The Jones matrix for the rotated waveplate is given as,

    [itex] J_Q = \frac{1}{\sqrt{2}} \cdot
    \left( \begin{array}{cc}
    1 + i\cos(2\theta) & i\sin(2\theta) \\
    i\sin(2\theta) & 1-i\cos(2\theta) \end{array} \right)

    [/itex]

    Which for the given angle results in:

    [itex]

    J_Q = \frac{1}{\sqrt{2}} \cdot
    \left( \begin{array}{cc}
    1 & i \\
    i & 1 \end{array} \right)
    [/itex]


    3. The attempt at a solution

    Now, this should be straight forward: [itex] J' = J_Q J_{VLP} [/itex]:

    [itex]

    J' = \frac{1}{\sqrt{2}} \cdot
    \left( \begin{array}{cc}
    1 & i \\
    i & 1 \end{array} \right) \cdot

    \left( \begin{array}{c}
    0 \\
    1 \end{array} \right)


    = \frac{1}{\sqrt{2}}\left( \begin{array}{c}
    i \\
    1 \end{array} \right)


    [/itex]

    The problem is that I am given the answer, which is not what i got, but rather:

    [itex]
    \frac{1}{\sqrt{2}}\left( \begin{array}{c}
    1 \\
    i \end{array} \right)
    [/itex]

    So I wonder: One of three possible outcomes: (1) since Jones vectors gived us the phase difference are these two vectors equivalent!?

    [itex]
    \left( \begin{array}{c}
    1 \\
    i \end{array} \right)

    \equiv

    \left( \begin{array}{c}
    i \\
    1 \end{array} \right)

    [/itex]
    .. overlooking the normalization constants.

    (2) I have calculated wrong: please help!
    (3) There is an error in the answer the problem.

    Thank you very much!!:)
     
  2. jcsd
  3. Jun 7, 2013 #2
    Perhaps your problem may come from some ambiguity as to what the plate was like before rotating. I get

    [itex]
    \frac{1}{\sqrt{2}}\left( \begin{array}{c}
    1 \\
    i \end{array} \right)
    [/itex]

    When I consider the fast axis of the quarter wave plate to be in the vertical direction before rotation.

    I get your answer when I consider the quarter wave plate before rotation to have the fast axis horizontal.

    And no, they do not represent the same polarization. They do not differ by a phase.
     
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