Fibre amplifier
A fibre amplifier, an erbium-doped one (EDFA) to begin with: gain across its band, saturating on the light it amplifies, and amplified spontaneous emission out of both ends. The same part, as a semiconductor optical amplifier (SOA), gains both ways and less for one polarisation.
Ports
Ports in and out.
The model
Gain
The small-signal gain \(g_0\) (dB) is flat-topped across a band of width \(\Delta\lambda\) about the centre \(\lambda_c\):
\[G_0(\lambda) = 10^{\,g_0/\left(10\,(1 + u^6)\right)}, \qquad u = \frac{\lambda - \lambda_c}{\Delta\lambda/2}.\]Saturation
It saturates as a homogeneous amplifier does, on the total power \(P_\text{in}\) reaching its input. At the band centre,
\[G = \frac{G_0}{1 + G\,P_\text{in}/P_\text{sat}} \quad\Longrightarrow\quad G = \frac{-1 + \sqrt{1 + 4G_0 x}}{2x}, \qquad x = \frac{P_\text{in}}{P_\text{sat}},\]with \(P_\text{sat}\) its saturated output power. The ratio \(\ln G/\ln G_0\) then scales the gain, in the log, across the whole band. The network is solved, each amplifier’s gain set from what reached it, and solved again, until the gains settle (see Fibre optics: amplifiers).
Spontaneous emission
The amplifier sends out amplified spontaneous emission (ASE) from both ends, in each polarisation:
\[P_\text{ASE} = n_\text{sp}\,h\nu\,(G - 1)\,B, \qquad n_\text{sp} = \max\!\left(1, \tfrac{\mathrm{NF}}{2}\right),\]with NF the noise figure as a ratio. It is followed in 25 slices across 1.6 times the band, each its own broadband light, so a filter after it takes its share. It reaches photodiodes as broadband light and adds its beat noise to theirs (see Fibre photodetector: noise).
Forward and back
An EDFA has an isolator inside: light going back from out to in is cut by its isolation, \(10^{-X/20}\) in amplitude, and not amplified.
An SOA has no isolator. It gains both ways, and gains less for p than for s by its polarisation-dependent gain (PDG, dB):
\[\mathbf S_\text{in, out} = \mathbf S_\text{out, in} = \sqrt{G}\begin{pmatrix} 1 & 0 \\ 0 & 10^{-\mathrm{PDG}/20} \end{pmatrix}.\]An SOA starts with 25 dB of gain, a 10 dBm saturated output, an 8 dB noise figure and a 60 nm band.
Settings
| Field | Default | Meaning |
|---|---|---|
g0 | 20 | Small-signal gain (dB) |
psat | 17 | Saturated output (dBm) |
nf | 5 | Noise figure (dB) |
centre | 1545 | Band centre (nm) |
bw | 35 | Band width (nm) |
iso | 40 | Isolation backwards (dB) |
From the tool's own tables, file format version 1: the names are those in a .jekray file.
Also soa: true for a semiconductor amplifier, with pdg (dB, 0.5 to begin with) in place of the isolation.
Assumptions
- The gain is flat-topped and set, not worked out from the pump and the dopant’s cross-sections; the gain’s shape does not change as it saturates.
- Saturation is on the average power, with no gain dynamics: no transients, and no pattern effects in an SOA.
- An SOA’s gain adds no phase: no chirp or linewidth enhancement, and no four-wave mixing.
Related
- Fibre photodetector, for the noise ASE brings.
- Tunable filter, to cut the ASE outside the signal’s band.
- Gain medium, gain in free space.