- #1

boxfullofvacuumtubes

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## Homework Statement

Suppose light is prepared in a coherent superposition of linear horizontal polarization and linear vertical polarization. What is the resulting polarization according to Jones calculus if it passes through:

- a linear polarizer at a 45-degree angle (0 degrees would be vertical)
- a linear polarizer at a -45-degree angle(0 degrees would be vertical)
- a quarter-wave plate with a fast axis oriented at a 45-degree angle(0 degrees would be vertical)

## Homework Equations

Jones calculus.

## The Attempt at a Solution

Superposition of LHP and LVP appears to be the same as 45-degree polarization (L+45):

$$\begin{pmatrix}1\\0\end{pmatrix} + \begin{pmatrix}0\\1\end{pmatrix} = \begin{pmatrix}1\\1\end{pmatrix}$$

If this light passes through a 45-degree polarizer, its polarization and intensity should remain unchanged:

$$\begin{pmatrix}0.5 & 0.5\\0.5 & 0.5\end{pmatrix} × \begin{pmatrix}1\\1\end{pmatrix} = \begin{pmatrix}1\\1\end{pmatrix}$$

None of this light can pass through a minus-45-degree polarizer because of its orthogonal polarization:

$$\begin{pmatrix}0.5 & -0.5\\-0.5 & 0.5\end{pmatrix} × \begin{pmatrix}1\\1\end{pmatrix} = \begin{pmatrix}0\\0\end{pmatrix}$$

A quarter-wave plate at 45 degrees turns the polarization to left circular and does not affect intensity:

$$\begin{pmatrix}1 & 0\\0 & -i\end{pmatrix} × \begin{pmatrix}1\\1\end{pmatrix} = \begin{pmatrix}1\\-i\end{pmatrix}$$

Did I make an error somewhere? Thanks for a sanity check!