Phase modulator
Writes a voltage-driven optical path across the whole beam without touching its polarization — invisible alone, and an amplitude modulator in one arm of an interferometer.
Open in the canvas →In the real world
A phase modulator is the simplest electro-optic device there is: a Pockels cell with the input polarisation aligned to one of the crystal's optical axes, so the polarisation state is untouched and the voltage moves only the phase[1]. Nothing about the beam changes that a detector can see. It is the component every other electro-optic modulator is built from, and on its own it is completely invisible.
What the crystal actually fixes is the optical path: the Pockels effect changes the refractive index in proportion to the applied field, so a given drive writes the same Δn·L at every wavelength. The phase that corresponds to therefore scales as 1/λ, which is why a modulator is specified together with a wavelength — a device that is half-wave at 532 nm is quarter-wave at 1064 nm[1][3].
Drive it sinusoidally and the output spectrum is no longer one frequency. A phase varying as β sin Ωt produces the carrier plus a pair of sidebands at every multiple of the drive frequency, with amplitudes given by Bessel functions[2]. Drive hard enough — a resonant modulator can reach large depth at modest voltage — and dozens of sidebands appear, which is how a modulator becomes a comb generator[1].
Those sidebands are what the device is usually bought for. Pound–Drever–Hall laser stabilisation writes them deliberately and asks how they come back from a cavity, deriving from that an error signal that says which way the laser has drifted[1]. It is worth being clear about what a phase modulator cannot do: it cannot produce a sustained frequency shift, because that would require a phase ramp increasing without bound[1]. An AOM shifts frequency; a phase modulator only wobbles it.
Making it visible
Since phase alone is undetectable, a phase modulator is put to work by letting it interfere with something. Place it in one arm of a Mach–Zehnder interferometer and the two arms recombine constructively or destructively according to the drive, so the phase becomes power at the output[1][2]. That is the Mach–Zehnder modulator, and its transfer function is the interferometer's own.
Almost all high-speed optical telecommunications runs on this arrangement, built as a waveguide interferometer on lithium niobate or silicon. On a chip the phase stability the layout demands is far easier to hold than on a bench, the electrodes sit micrometres apart so the drive voltage is low, and travelling-wave electrodes matched to the optical velocity push the bandwidth into the tens of gigahertz[1][2].
In OpticalSetup
The modulator writes one optical path across the whole beam — uniform, unlike the phase object, which varies its path across the aperture. It does not touch polarisation, intensity, or direction, so on its own it does nothing measurable at all: put a detector after it and the reading is exactly what it was.
The drive is set as the phase it writes at full deflection, in degrees at a design wavelength, which is how a device is chosen — half-wave, quarter-wave. That is converted to the fixed optical path the crystal really applies, so a modulator set to half a wave at 532 nm writes a quarter wave at 1064 nm, as a real one does. Hold it static, or drive it with a sine or square wave on the shared simulation clock.
In one arm of an interferometer it becomes the amplitude modulator above, following cos²(Δφ/2) exactly: half a wave takes the output from full to nothing, and the light that leaves one port arrives at the other, so the two always sum to the input.
That holds only where the tracer can reconstruct a coherent field, which means a CW laser in Beam with size mode with no bandwidth — the one source whose samples carry a recoverable phase. Drive the same interferometer with a pulsed or supercontinuum source, or with a CW laser in Simple line mode, and the two arms are added as intensities instead: both ports sit at half the light and the modulator changes nothing, whatever it is set to. The reading says so rather than leaving it to be inferred — it reports insufficient coherent overlap.
The interferometric behaviour above needs a sized monochromatic CW laser. That is not a property of this element but of what the tracer can reconstruct a phase through, and it applies to every interference effect in the app; it is repeated here because it decides whether this component appears to do anything at all.
Sidebands are not modelled, and could not usefully be: a 1 GHz drive at 532 nm puts them 9×10⁻⁴ nm from the carrier, and at 1 MHz it is 9×10⁻⁷ nm, against a spectrometer that resolves 0.1 nm. Everything the sidebands are used for — Pound–Drever–Hall locking, comb generation, anything reading the modulation in the spectrum rather than in time — is therefore out of reach. What is modelled is the phase itself, and what interference makes of it.
Nothing here is a voltage. The drive is set as a phase directly, so there is no half-wave voltage, no drive amplitude, no crystal and no material — which means the linearity of the Pockels effect is assumed rather than shown. The modulator is ideal: no insertion loss, no residual static birefringence, no thermal drift of the operating point, and a square drive that switches instantaneously with no driver bandwidth behind it. Resonant and travelling-wave designs, which is how real devices reach gigahertz, have no counterpart.
Related components
References
- “Electro-optic Modulators,” RP Photonics Encyclopedia (DOI 10.61835/7rv)
- Electro-optic modulator — Wikipedia
- T. A. Maldonado, “Electro-Optic Modulators,” ch. 13 in M. Bass (ed.), Handbook of Optics, Vol. 2, McGraw-Hill (1995)