Fibre EOM
A fibre-coupled lithium niobate modulator. As a phase modulator it puts sidebands either side of the carrier, at multiples of its drive; as a Mach–Zehnder it modulates the amplitude. With a fibre cavity and a demodulated photodetector it makes a Pound–Drever–Hall lock.
Ports
Ports in and out, and an electrical input, mod.
The model
Phase modulation
Driven at \(f_m\) with depth \(\beta\) (rad), the modulator multiplies the field by
\[e^{i\beta\sin 2\pi f_m t} = \sum_{n} J_n(\beta)\, e^{i 2\pi n f_m t},\]so each sideband \(n\) leaves with amplitude \(a\,J_n(\beta)\), shifted by \(n f_m\), with \(a = 10^{-\ell/20}\) for an insertion loss \(\ell\). The default depth, \(\beta = 1.08\), is where a Pound–Drever–Hall error signal is steepest. Pure phase modulation makes no beat on a photodiode by itself: the sidebands’ beats with the carrier cancel in pairs. Something that treats them differently, a cavity, a filter or a dispersive fibre, turns it into amplitude modulation.
Amplitude modulation
A Mach–Zehnder of two arms driven in opposition, at bias \(\phi_0\):
\[E_\text{out} = a\,E_\text{in}\cos\!\left(\frac{\phi_0}{2} + \frac{\beta}{2}\sin 2\pi f_m t\right),\]so the sidebands have amplitude
\[c_n = a\,J_n\!\left(\tfrac{\beta}{2}\right)\cos\tfrac{\phi_0}{2} \quad (n \text{ even}), \qquad c_n = i\,a\,J_n\!\left(\tfrac{\beta}{2}\right)\sin\tfrac{\phi_0}{2} \quad (n \text{ odd}).\]At 0° it transmits fully; at 90° it is at quadrature, where the power follows the drive most linearly.
The sidebands are the same going backwards through it.
A drive
Wired to the electronics, the mod input is a slow drive \(v\) on top of the RF. In phase mode it adds a phase \(\pi v/V_\pi\); in amplitude mode it adds to the bias, \(V_\pi\) moving it 180°. \(V_\pi\) is 5 V to begin with.
Settings
| Field | Default | Meaning |
|---|---|---|
fm | 1000 | Drive (MHz) |
beta | 1.08 | Depth β (rad) |
bias | 90 | Bias (°, amplitude mode) |
loss | 3 | Insertion loss (dB) |
From the tool's own tables, file format version 1: the names are those in a .jekray file.
Also emode: phase or amplitude.
Assumptions
- The modulation is pure: no residual amplitude modulation from the phase modulator, no chirp from the amplitude modulator.
- Its response is flat to any drive frequency, and the same both ways and for both polarisations.
Related
- EOM, the free-space modulator.
- Fibre photodetector, for demodulation.
- Fibre AOM.