Fibre laser
A laser coupled straight into fibre, the start of most fibre networks. It launches its light into the fibre on its one port. The same part, as a fibre-coupled LED, launches broadband, incoherent light instead.
Ports
One port, out. Light arriving back at it is absorbed: the laser has no cavity of its own for it to disturb. Put an isolator after it to model one that would.
The model
The field it launches
The laser launches a Jones vector \(\mathbf E = (E_s, E_p)\) of power \(P\) into its fibre. In fibre, s and p are labels for two orthogonal axes. They become out of the bench plane and in it where a fibre tip meets free space. The polarisation is one of
| Polarisation | \(\mathbf E / \sqrt P\) |
|---|---|
| s | \((1, 0)\) |
| p | \((0, 1)\) |
| linear at \(\theta\) from s | \((\cos\theta, \sin\theta)\) |
| circular, right-handed | \(\tfrac{1}{\sqrt2}(1, -i)\) |
| circular, left-handed | \(\tfrac{1}{\sqrt2}(1, i)\) |
| unpolarised | s and p halves of \(P/2\), which never interfere |
Right- and left-handed are as the screens’ Stokes \(S_3\) counts them.
Its spectrum
A laser is one of three kinds of source.
- Single frequency. Every path of its light interferes with every other in full, however long the difference.
- A line, with a coherence length \(L_c\): a linewidth \(\Delta\nu = c/L_c\), or \(\Delta\lambda = \lambda^2/L_c\), Lorentzian (a laser’s own line) or Gaussian (Doppler, many modes).
- Incoherent, broadband. A Gaussian spectrum of a set width. It is followed through the network in slices (see Fibre optics: broadband light), so filters, WDMs and Bragg gratings shape it.
Two paths of a line’s light a distance \(\Delta L\) apart interfere with a fringe contrast
\[\gamma(\Delta L) = e^{-\pi\lvert\Delta L\rvert/L_c} \;\;\text{(Lorentzian)}, \qquad \gamma(\Delta L) = \exp\!\left(-\frac{(\pi\,\Delta L/L_c)^2}{4\ln 2}\right) \;\;\text{(Gaussian)}.\]The network weighs every pair of paths by \(\gamma\) at their delay (see Fibre optics: solving the network). Separate lasers never interfere, though they beat on a photodiode.
Pulses
Give the laser a pulse duration \(\tau\) (FWHM, fs) and it is mode-locked. Its pulses are sech² or Gaussian, at a repetition rate \(f_\text{rep}\), with an average power \(P\) and a chirp (GDD) at the laser. Its spectrum is then the pulse’s, and its coherence length follows from it. Each fibre’s dispersion chirps the pulse on its way, and a pulse strong enough undergoes self-phase modulation (see Fibre optics: dispersion and self-phase modulation).
A fibre-coupled LED
The LED is the same part as broadband light: spontaneous emission, unpolarised to start with (it can be set otherwise), never pulsed. Its band is a width in nm, 40 nm to begin with. Its power is the power into the fibre.
External control
Tick External control and the laser gets two electrical inputs:
- mod, which sets its power: \(P = P_0\,(1 + m v)\), never below zero, with \(m\) in % per volt;
- fm, which tunes its frequency: \(\Delta\nu = k v\), with \(k\) in GHz per volt. Its wavelength shortens as the frequency rises.
So a vapour cell’s line, a cavity or a filter turns the frequency drive into a change in power (see Electronics: drives).
Settings
| Field | Default | Meaning |
|---|---|---|
wavelength | 1550 | Wavelength (nm) |
power | 1 | Power (mW) |
coh | 0 | Coherence length (mm) |
polAngle | 0 | Polarisation angle from s (°), for pol "linear" |
tau | 0 | Pulse duration (fs; 0: continuous) |
rep | 80 | Repetition rate (MHz) |
gdd0 | 0 | Chirp at the laser (fs²) |
From the tool's own tables, file format version 1: the names are those in a .jekray file.
Also: the polarisation, pol (above); the spectrum, cmode: single, line or broad; the line shape, lorentz or gauss; the band, bw (nm), for broadband light; the pulse shape, pshape: sech2 or gauss; and led, which makes it a fibre-coupled LED.
Readouts
The panel gives its linewidth or band, its coherence length, and for a pulse its bandwidth, energy and peak power at the transform limit, and, with a chirp, how long it leaves. Its port row gives the power it sends out and any that comes back.
Assumptions
- Light coming back into the laser does not disturb it: no feedback, no injection locking. Use an isolator to make that explicit.
- Its power and wavelength are what are set: there is no threshold, no relaxation oscillation and no intensity noise of its own.
- A pulse’s spectrum is a smooth sech² or Gaussian, without the structure of a real mode-locked spectrum.
Related
- Fibre photodetector and optical spectrum analyser, to see what it sends.
- Source, the free-space laser, which shares its coherence and pulse models.
- Isolator.