Optical isolators, however, are more typically built using an Faraday rotator, as shown in figure
2
Forward
polarizer
Faraday crystal
0°
polarizer
45°
45°
Pass
45°
Block
polarizer
90°
Faraday crystal
polarizer
Backward
Figure 2: a nice plot
The Jones vector for a Faraday (polarization) rotator is given by,
$J_F(\theta) = \begin{pmatrix} \cos^2 \theta & \sin \theta \cos \theta\\ \sin \theta \cos \theta & \sin^2 \theta \end{pmatrix}$
[2.1]
Derive the Jones matrix for the system above and show that it can indeed act as an optical
isolator. Determine whether it is possible to exchange the Faraday rotator with a quarter wave
plate to create an optical polarizer.