Calculate Jones Vector of polarized light thorugh QWP

[mhsd91]

Homework Statement

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

$J_Q = \frac{1}{\sqrt{2}} \cdot <br /> \left( \begin{array}{cc}<br /> 1 + i\cos(2\theta) & i\sin(2\theta) \\<br /> i\sin(2\theta) & 1-i\cos(2\theta) \end{array} \right)<br />$

Which for the given angle results in:

$<br /> J_Q = \frac{1}{\sqrt{2}} \cdot <br /> \left( \begin{array}{cc}<br /> 1 & i \\<br /> i & 1 \end{array} \right)$

The Attempt at a Solution

Now, this should be straight forward: $J' = J_Q J_{VLP}$:

$<br /> J' = \frac{1}{\sqrt{2}} \cdot <br /> \left( \begin{array}{cc}<br /> 1 & i \\<br /> i & 1 \end{array} \right) \cdot<br /> <br /> \left( \begin{array}{c}<br /> 0 \\<br /> 1 \end{array} \right)<br /> <br /> <br /> = \frac{1}{\sqrt{2}}\left( \begin{array}{c}<br /> i \\<br /> 1 \end{array} \right)<br /> <br />$

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

$\frac{1}{\sqrt{2}}\left( \begin{array}{c}<br /> 1 \\<br /> i \end{array} \right)$

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

$\left( \begin{array}{c}<br /> 1 \\<br /> i \end{array} \right)<br /> <br /> \equiv<br /> <br /> \left( \begin{array}{c}<br /> i \\<br /> 1 \end{array} \right)<br />$
.. 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!:)

 

[MisterX]

Perhaps your problem may come from some ambiguity as to what the plate was like before rotating. I get

$\frac{1}{\sqrt{2}}\left( \begin{array}{c}<br /> 1 \\<br /> i \end{array} \right)$

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.