Photodetector
A free-space photodiode with a transimpedance amplifier. It takes in all of the light on its active area, and reads out the photocurrent, the output voltage, the beat notes in the light, the noise, and a demodulated signal such as a Pound–Drever–Hall error.
The model
The light it takes in
A photodiode takes in \(\lvert E\rvert^2\) over its active area, a disc of the diameter set. The Gaussian beams that reach it are rebuilt on its face as fields: each beam’s \(q\) in and out of the plane, where it lands, its tilt and its optical path. Beams of one launch add as fields, so a Michelson’s output diode sees its fringe, and a beam larger than the diode is clipped. A beam landing above or below the centre, sloped, or on a diode tipped out of the plane is rebuilt where and as it lands (see heights). Separate launches add as powers. Ray fans count ray by ray.
A diode can instead be read through its diffracted field, which is slower but right where rays are not: fringes, or a focus smaller than the diode’s edges.
Responsivity
The photocurrent is
\[I = \mathcal R(\lambda)\, P,\]with the responsivity \(\mathcal R\) (A/W) taken from a typical curve for the diode’s material, silicon, InGaAs or germanium, at the light’s wavelength, or set to a fixed value.
The amplifier
A transimpedance amplifier of gain \(G\) (V/A) turns the current into a voltage, \(V = G I\), up to its output limit, where it saturates and says so. Its bandwidth \(B\) is a single pole: a beat note at frequency \(f\) passes with the factor \(1/(1 + i f/B)\). Without the amplifier, a bare photodiode, the output is the current itself.
Beat notes
Light of one laser at two frequency offsets \(f_a\) and \(f_b\) (after an AOM, or an EOM’s sidebands) beats at \(f_b - f_a\):
\[P(t) = P_\text{DC} + \sum 2\operatorname{Re}\!\left(\mathbf E_a\cdot\mathbf E_b^*\, e^{i2\pi(f_b - f_a)t}\right),\]with \(\mathbf E\) the fields summed over the diode, and each pair of paths weighted by the laser’s coherence at their delay. Two different lasers beat at the difference of their frequencies, with a wandering phase and a line as wide as both of theirs. The diode’s Signal section shows the output on an oscilloscope and a spectrum analyser.
Noise
The noise is shot noise on the photocurrent and dark current, the gain resistor’s Johnson noise, and the amplifier’s input current noise, over the bandwidth:
\[\overline{i_n^2} = 2q\left(I + I_\text{dark}\right)B + \frac{4kTB}{G} + i_a^2 B, \qquad T = 295\ \text{K},\]and the signal-to-noise ratio is \(20\log_{10}(I / i_n)\).
Demodulation
Set a demodulation frequency \(f_d\), and the output is mixed down at it, with a phase \(\phi_d\). A tone of amplitude \(V\) and phase \(\phi\) at \(f_d\) gives the DC output
\[V_\text{mix} = \tfrac12 V \cos(\phi - \phi_d).\]With an EOM at the same frequency on the light going to a cavity, the reflected light gives a Pound–Drever–Hall error signal. Sweep the laser, or the cavity’s length, to trace it out.
Electrical output
The diode’s output is also an electrical port, which can be wired to the electronics: amplifiers, filters, lock-ins and instruments.
Settings
| Field | Default | Meaning |
|---|---|---|
length | 3.6 | mm: the active area’s diameter. |
material | "si" | one of the detector materials below. |
resp | 0.5 | A/W, used when material is "custom". |
gain | 10000 | V/A transimpedance. |
bandwidth | 1000000 | Hz. |
dark | 1 | nA dark current. |
ampNoise | 2 | pA/√Hz input noise. |
vmax | 10 | V output limit. |
demodF | 0 | MHz: mix the output down at this frequency (0: no mixer). With an EOM at fm, this gives a PDH error signal. |
demodPhase | 0 | degrees: the mixer’s phase. |
From the tool's own tables, file format version 1: the names are those in a .jekray file.
Assumptions
- The responsivity curves are typical ones for each material, not a particular part’s.
- The amplifier is linear up to its output limit, a single pole in frequency.
- The diode absorbs everything on its area; it does not reflect.
Related
- Electronics: where light meets the electronics.
- EOM, for Pound–Drever–Hall locking.
- Screen, for the profile of the light rather than its total power.
- Fibre photodetector, the fibre-coupled one, with balanced detection and noise from amplifier ASE.