Faraday rotator
A Faraday rotator turns linear polarisation by a set angle, the same way in the lab whichever way the light crosses it. Light that goes through and comes back is turned twice over, not undone: that is what makes isolators and Faraday mirrors work.
The model
A Faraday rotator is a thin plane across the beam, with a magnetic field along its normal. In the lab, it rotates the field by \(\beta\) about the direction of the magnetic field, whichever way the light travels. In the light’s own frame, that is a rotation of \(+\beta\) or \(-\beta\):
\[R(\pm\beta) = \begin{pmatrix} \cos\beta & \mp\sin\beta \\ \pm\sin\beta & \cos\beta \end{pmatrix},\]with the sign set by the direction of travel against the field, and by the parity of the ray’s p axis, which flips at each reflection (see Concepts: polarisation).
So light that crosses a 45° rotator, reflects from a mirror and crosses back comes back turned by 90°, not by 0° as it would through a waveplate. A reciprocal element can’t do that. The rotator is non-reciprocal, as it should be.
A rotation commutes with any other turn about the beam, so rolling a Faraday rotator about its normal changes nothing.
Settings
| Field | Default | Meaning |
|---|---|---|
length | 5 | mm aperture. |
rotation | 45 | degrees of rotation. |
From the tool's own tables, file format version 1: the names are those in a .jekray file.
Assumptions
- The rotation is the same at every wavelength. A real rotator’s Verdet constant changes with wavelength.
- The rotator is thin and lossless.
Related
- Isolator, a rotator between two polarisers.
- The fibre Faraday mirror, a 45° rotator and a mirror, which undoes a fibre’s birefringence on the way back.