EOM
An electro-optic modulator writes a modulation onto the light: phase modulation, which puts sidebands either side of the carrier, or amplitude modulation, through a biased Mach–Zehnder. With a cavity and a demodulated photodiode it makes a Pound–Drever–Hall lock.
The model
Phase modulation
A phase modulator driven at \(\Omega = 2\pi f_m\) with depth \(\beta\) (radians) multiplies the field by
\[e^{i\beta\sin\Omega t} = \sum_{n=-\infty}^{\infty} J_n(\beta)\, e^{i n\Omega t},\]the Jacobi–Anger expansion. Each sideband \(n\) leaves as a branch of its own, \(n f_m\) from the light that came in, with field amplitude \(J_n(\beta)\), a Bessel function. At \(\beta = 1.434\) the carrier and each first sideband carry equal power; at \(\beta = 2.405\) the carrier is gone.
Amplitude modulation
An amplitude modulator is a Mach–Zehnder of two such arms driven in opposition, biased at \(\phi_0\):
\[E_\text{out} = E_\text{in}\,\cos\!\left(\frac{\phi_0}{2} + \frac{\beta}{2}\sin\Omega t\right),\]which expands the same way into sidebands of amplitude \(J_n(\beta/2)\). At a bias of 90° it is at quadrature, where the power follows the drive most linearly.
At an angle
Light crossing the modulator at an angle \(\theta\), turned in the bench plane or tipped out of it, is modulated over a path \(1/\cos\theta\) longer, so its modulation depth is \(\beta/\cos\theta\).
Beat notes and locking
Sidebands at different offsets make no steady fringes with each other, but they beat on a photodiode at multiples of \(f_m\). Put a cavity after the EOM and a photodiode on the reflected light, demodulated at \(f_m\) (see Photodetector: demodulation). Each sideband meets the cavity at its own detuning, and the demodulated signal is the Pound–Drever–Hall error signal.
A drive
The EOM’s modulation is also an electrical input. Wired to the electronics, its drive sets the modulation through time.
Settings
| Field | Default | Meaning |
|---|---|---|
length | 4 | mm aperture. |
fm | 20 | MHz drive. |
beta | 1.08 | modulation depth in radians. |
emode | "phase" | "phase" (sidebands) or "amplitude". |
bias | 90 | degrees, for "amplitude". |
loss | 0 | dB insertion loss. |
From the tool's own tables, file format version 1: the names are those in a .jekray file.
Assumptions
- The modulation is pure: no residual amplitude modulation from a phase modulator, and no chirp from an amplitude modulator.
- The modulator is thin and does not deflect the light. Its loss is the insertion loss set.
Related
- AOM, a frequency shifter.
- Photodetector.
- Fibre EOM, the fibre-coupled one.