Faraday mirror
A Faraday mirror is a 45° Faraday rotator in front of a mirror. Light comes back orthogonal to how it arrived, whatever the fibre did to its polarisation on the way. So a fibre Michelson made with two keeps full fringe contrast however its fibres are bent.
Ports
One port, in.
The model
The light is reflected back out of its port by
\[\mathbf S_{11} = r\begin{pmatrix} 0 & 1 \\ -1 & 0 \end{pmatrix} = r\,\mathbf J, \qquad r = 10^{-\ell/20}\sqrt R,\]with \(R\) its reflectance and \(\ell\) an extra loss (dB). \(\mathbf J\) turns any Jones vector into the one orthogonal to it.
Why the fibre does not matter
Light that goes through a length of fibre \(\mathbf M\) to the mirror comes back through its transpose, \(\mathbf M^{\mathsf T}\), since fibre birefringence is reciprocal. The round trip is
\[\mathbf M^{\mathsf T}\,\mathbf J\,\mathbf M = \det(\mathbf M)\;\mathbf J,\]for any 2 × 2 matrix \(\mathbf M\). For a lossless fibre \(\det\mathbf M\) is a phase. So what comes back is orthogonal to what went in, with only a common phase from the fibre, however the fibre is laid. Two arms of a Michelson both ending in Faraday mirrors return the same state, and interfere fully. That holds in JEKray for fibre set to as laid too.
Settings
| Field | Default | Meaning |
|---|---|---|
rmax | 99 | Reflectance (%) |
loss | 0 | Extra loss (dB) |
From the tool's own tables, file format version 1: the names are those in a .jekray file.
Assumptions
- The rotation is exactly 45° each way, at every wavelength.
- The mirror adds no delay of its own.
Related
- Fibre mirror, a plain mirror.
- Polarisation controller.
- Faraday rotator, in free space.