Wiki / Modulators / Electro-optic modulator (EOM)

Electro-optic modulator (EOM)

Applies voltage-controlled polarization retardance — either a fixed waveplate-like shift, or a square-wave switch between two retardance states at a set frequency; an analyzer converts either into intensity modulation.

Open in the canvas →

A live trace, not a picture of one — but this preview is not interactive. Open it in the canvas to move things, change parameters, and save or export your own version.

In the real world

An electro-optic modulator controls light with a voltage. Almost all of them work through the Pockels effect: in a crystal without inversion symmetry, an applied electric field changes the refractive index in proportion to the field strength^[1]^[3]. Put a few hundred volts across a centimetre of lithium niobate and the optical path through it changes by a fraction of a wavelength — with no moving part, and in nanoseconds.

The quantity that describes a device is the voltage needed to shift the phase by π, the half-wave voltage. For a bulk Pockels cell it is hundreds or thousands of volts, which is why these devices come with high-voltage drivers; a waveguide modulator, where the electrodes sit micrometres apart rather than millimetres, needs far less and switches far faster^[1]^[2].

\Delta n \propto E \qquad\Longrightarrow\qquad \Delta\varphi = \pi\,\frac{V}{V_\pi}

The Pockels effect is linear in the applied field, so the phase shift is linear in the voltage. Vπ, the half-wave voltage, is the whole specification in one number.

What makes the family confusing is that one physical device — a crystal with electrodes on it — becomes three quite different instruments depending on how the light is sent through it and what is placed after it.

Phase modulator

The simplest arrangement, and the one everything else is built from: the input polarisation is aligned to one of the crystal's optical axes, so the polarisation state is untouched and only the phase moves^[1]. Drive it sinusoidally and the output is not one frequency but a comb — the carrier plus sidebands at every multiple of the drive frequency, with amplitudes given by Bessel functions^[2].

e^{i\beta\sin\Omega t} = \sum_{n=-\infty}^{\infty} J_n(\beta)\, e^{in\Omega t}

The Jacobi–Anger expansion: phase modulation of depth β puts sidebands at ω ± nΩ with amplitude Jₙ(β). Drive hard enough and dozens of them appear, which is how a modulator becomes a comb generator.

Those sidebands are the point of the device in laser stabilisation: the Pound–Drever–Hall technique locks a laser to a cavity by asking how the sidebands it wrote come back^[1]. Worth noting what a phase modulator is not good for: it cannot produce a sustained frequency shift, since that would need a phase ramp increasing without limit^[1]. An AOM does that instead.

Polarisation modulator

Orient the crystal so the two polarisation axes see different index changes, and the cell becomes a voltage-controlled waveplate^[1]^[2]. Linear light entering at 45° to the axes leaves elliptical in general; at exactly a half wave of relative retardance it leaves linear again, rotated by 90°. Drive it randomly and it is a polarisation scrambler.

Amplitude modulator

Two routes, and they belong to different worlds. Put a polariser after a polarisation modulator and the polarisation swing becomes an intensity swing — the classic bulk arrangement, and the basis of Q-switches, cavity dumpers and pulse pickers^[1]. Or put a phase modulator in one arm of a Mach–Zehnder interferometer, so the two arms interfere constructively or destructively according to the drive^[1]^[2]. The interferometric route is what integrated optics uses, because on a chip the phase stability that arrangement demands is far easier to hold than on a bench — and it is the workhorse of optical telecommunications.

Beyond the Pockels effect

Kerr cells use the quadratic electro-optic effect and are uncommon^[1]. Electro-absorption modulators change absorption rather than index, through the Franz–Keldysh effect or the quantum-confined Stark effect in a semiconductor, and so are not electro-optic in the same sense at all^[1]^[2]. Plasmonic modulators, exploiting surface plasmon polaritons at metal surfaces, are extremely fast at low energy^[1].

Materials matter, and the trade-offs are specific: KD*P gives excellent optical quality and high extinction over large apertures, which makes it the standard for Q-switches, but it is hygroscopic and rings piezoelectrically, limiting the repetition rate. BBO handles high average power and switches faster. Lithium niobate dominates waveguide devices for its large electro-optic coefficients^[1]. Devices intended for stability often use two matched cells in an athermal pairing that cancels the temperature drift of the relative phase, or four crystals to cancel walk-off as well^[1].

In OpticalSetup

This element is the polarisation modulator of the three: a Pockels cell used as a voltage-controlled waveplate. It applies a retardance between the two axes of a crystal whose orientation you set, either as a fixed value or switching between two states as a square wave on the shared simulation clock.

The default switching mode flips between orthogonal linear polarisations, which is the half-wave switch a Pockels cell is usually bought for and needs no crystal-axis reasoning at all. Put a polariser or a polarising beamsplitter after it and that becomes real intensity modulation — the bulk amplitude modulator above, built the way it is built on a bench. With a pulsed source, individual pulses are routed by whichever state they meet, so a photodetector on a screen shows the modulated train and the element works as a pulse picker.

Simplified vs. reality

This element is the polarisation modulator alone. The phase modulator is a separate component — see Phase modulator — and the amplitude modulator is built rather than provided: a polariser after this one, which works with any source, or a phase modulator in one arm of an interferometer, which needs a sized monochromatic CW laser for the arms to interfere at all.

Nothing here is a voltage. Retardance is set in degrees directly, so there is no half-wave voltage, no drive amplitude, and no relation between the two — which also means the linearity of the Pockels effect, the whole basis of the device, is assumed rather than shown. The crystal is ideal and achromatic: a retardance set here applies equally at 405 nm and 1550 nm, where a real cell is calibrated for one wavelength and scales roughly as 1/λ. No material is chosen, so none of the material trade-offs appear.

Switching is instantaneous and perfectly square. Rise time, driver bandwidth, piezoelectric ringing, thermal drift of the operating point, and the residual static birefringence a real cell has at zero volts are all absent, as is any insertion loss. Resonant and travelling-wave designs, which is how real devices reach gigahertz, have no counterpart.