Fibre photodetector
A fibre-coupled photodetector: a photodiode with an amplifier, reading the power that arrives, its beat notes and its noise. It also comes as a balanced photodetector, two diodes with the second's current taken from the first's, and as a bare photodiode with no amplifier.
Ports
One optical port, in, and an electrical output, out. A balanced detector has two optical inputs, in + and in −.
The model
The light it reads
The detector reads the power arriving, the paths of one laser added as fields and weighted by its coherence, and different lasers as powers (see Fibre optics: solving the network). Its photocurrent is
\[I = \mathcal R\,P,\]with the responsivity \(\mathcal R\) (A/W) from a typical curve for its material (silicon, InGaAs or germanium) at the wavelength of the strongest light reaching it, or set to a fixed value.
The amplifier
A transimpedance amplifier of gain \(G\) (V/A) and bandwidth \(B\) turns the current into a voltage, \(V = G I\), up to its output limit. A beat note at frequency \(f\) passes through a single-pole response:
\[H(f) = \frac{1}{\sqrt{1 + (f/B)^2}}, \qquad \arg H = -\arctan(f/B).\]A bare photodiode has no amplifier: its output is the photocurrent itself, in amps, for a transimpedance amplifier or a scope in the electronics.
Beat notes
Light of one laser at two frequency offsets, from an AOM or an EOM, beats at their difference; two different lasers beat at the difference of their frequencies, with no fixed phase (see Electronics: photodiodes).
Noise
The noise current, in the detector’s bandwidth \(B\), is the sum of
\[\overline{i_n^2} = 2q\left(I + I_\text{dark}\right)B + \frac{4kTB}{G} + i_a^2 B + \sigma^2_{s\text{-}\mathrm{ASE}} + \sigma^2_{\mathrm{ASE}\text{-}\mathrm{ASE}},\]shot noise on all the light and the dark current, the gain resistor’s Johnson noise at 295 K, and the amplifier’s input current noise \(i_a\) (pA/√Hz). A bare photodiode has only the shot noise. Where broadband light arrives (an amplifier’s ASE, an LED, a source set incoherent), it beats with the signal and with itself:
\[\sigma^2_{s\text{-}\mathrm{ASE}} = 2\mathcal R^2 P_s\,S(\lambda_s)\,B, \qquad \sigma^2_{\mathrm{ASE}\text{-}\mathrm{ASE}} = \mathcal R^2 B \sum_j \frac{P_j^2}{B_j},\]with \(P_s\) the signal’s power, \(S(\lambda_s)\) the broadband light’s power per hertz at the signal’s wavelength, and \(P_j\) the power in each slice of it, \(B_j\) wide in frequency. The panel gives the noise in volts (or amps, for a bare photodiode), which part of it is largest, and the electrical signal-to-noise ratio of the DC signal.
Balanced detection
A balanced detector’s current is the difference of its two diodes’, \(I = \mathcal R\,(P_+ - P_-)\). What is the same on both, such as an amplifier’s ASE beating with itself, cancels to the common-mode rejection: the beat noise is multiplied by \(10^{-\mathrm{CMRR}/10}\). What differs, such as the interference between a coupler’s two outputs, which is opposite in them, doubles. Shot noise from both diodes adds.
Demodulation
Set a demodulation frequency \(f_d\) and phase \(\phi_d\), and the output is mixed down: the detector reports
\[V_\text{mix} = \sum_{f = f_d} \tfrac12 V_f \cos(\phi_f - \phi_d)\]over the beat notes at \(f_d\). With an EOM on the light going to a fibre cavity, this is a Pound–Drever–Hall error signal (see Photodetector: demodulation).
Settings
| Field | Default | Meaning |
|---|---|---|
resp | 1 | Responsivity (A/W) |
gain | 10000 | Gain (V/A) |
vmax | 10 | Output limit (V) |
bandwidth | 1000000000 | Bandwidth (Hz) |
dark | 1 | Dark (nA) |
ampNoise | 2 | Noise (pA/√Hz) |
demodF | 0 | Demod. at (MHz) |
demodPhase | 0 | Demod. phase (°) |
From the tool's own tables, file format version 1: the names are those in a .jekray file.
Also material: si, ingaas, ge, or custom for the fixed responsivity above; balanced, with cmrr (dB, 30 to begin with); and diode, for a bare photodiode.
Readouts
The optical power, the photocurrent, the output (held at its limit, and flagged, when it would go past it), the broadband light reaching it, the noise and signal-to-noise ratio, the beat notes and the mixer’s output. Its Signal views show the output on an oscilloscope and a spectrum analyser.
Assumptions
- The responsivity curves are typical ones for each material, not a particular part’s, read at one wavelength: the strongest light’s.
- The amplifier is a single pole and linear up to its output limit. Its readout stops at the limit, but the signal the electronics take is not clipped there.
- Noise from two broadband sources reaching one detector is taken as uncorrelated.
Related
- Photodetector, the free-space one, which shares this model.
- Electronics, for what its output drives.
- Fibre amplifier, whose ASE sets the beat noise.