Fibre tip
A fibre tip joins free space to the fibre network. Light arriving on its face is taken in by its overlap with the fibre's mode. Light the network sends to it leaves into free space as a beam.
The model
The fibre’s mode
A single-mode fibre’s fundamental mode is close to a Gaussian. Its \(1/e^2\) radius comes from the core radius \(a\) and the numerical aperture by Marcuse’s fit:
\[w = a\left(0.65 + \frac{1.619}{V^{3/2}} + \frac{2.879}{V^6}\right), \qquad V = \frac{2\pi a\,\mathrm{NA}}{\lambda}.\]Light into the fibre
The field arriving on the face is rebuilt from the Gaussian beams that reach it: each beam’s \(q\) in the plane and out of it, where it lands, its tilt and its optical path. Beams of one launch add as fields first. The tip then takes in the overlap of that field with its mode, for each polarisation:
\[\eta = \frac{\left\lvert\int E\, M^*\, \mathrm dA\right\rvert^2}{\int \lvert E\rvert^2\, \mathrm dA \int \lvert M\rvert^2\, \mathrm dA}.\]So offset, tilt, a mismatched waist and a wrong focus all cost what they should, out of the plane as in it: a tip raised, tipped or rolled takes the beam where and as it lands (see heights). For two Gaussians of radii \(w_1\) and \(w_2\) meeting on axis at their waists, this is the familiar
\[\eta = \left(\frac{2 w_1 w_2}{w_1^2 + w_2^2}\right)^2.\]The light taken in enters the fibre network with its own delay: its optical path, plus the path before its source’s launch. Arrivals of one launch keep their own delays, so the network weighs them against each other by the laser’s coherence (see Fibre optics).
A tip needs a Gaussian source to couple from: a ray fan has no field to overlap.
Light out of the fibre
Light the network sends to the tip leaves into free space as the fibre’s mode, its waist on the face. It is a source split from the laser it came from, so it interferes with the rest of that laser’s light. There is one such source for each launch, or for a laser with a line of its own, one for each group of delays within a fiftieth of its coherence length, up to six. The beam is drawn as its outline or as its diffracted field, with a fan of up to 51 rays.
Multimode fibre
A multimode tip (cores of 50 or 62.5 µm, NA 0.22 or 0.275 are usual) takes in whatever lands on its core inside its acceptance cone. That is the share of each beam’s power on the core, times the share of its angular spectrum inside \(\pm\mathrm{NA}\) in each plane. It sends light out filling its core and NA, a beam of
\[M^2 = \frac{\pi a\,\mathrm{NA}}{\lambda},\]capped at 30. Its polarisation and phase are scrambled, and the speckle a real one makes is averaged out.
Settings
| Field | Default | Meaning |
|---|---|---|
length | 2.5 | mm: the ferrule face width. |
core | 4.4 | µm core diameter (mode field set from core and NA). |
na | 0.12 | numerical aperture. |
emitRays | 5 | rays in the fan it sends out, 0 to 51. |
mm | false | true for a multimode fibre (give it core 50 or 62.5 and na 0.22): it takes in what lands on its core inside its NA, and sends out a beam filling core and NA. |
From the tool's own tables, file format version 1: the names are those in a .jekray file.
Assumptions
- The single-mode mode is a Gaussian of Marcuse’s radius: close for a step-index fibre near its cut-off, rougher far from it.
- The face is flat and square to the fibre, with no reflection of its own: set an angled or flat end on the fibre itself.
- Light leaving a tip is not taken back into the fibres a second time: a loop of fibre, free space and fibre is followed one way round.
Related
- Fibre optics, for what happens in the network.
- Photodetector, which takes in all of the light on its area instead.