Modulators
A laser produces the most boring signal imaginable: a constant. Perfectly steady light carries
exactly zero information
— no surprise, no bits. The modulator is the device that ruins the laser's calm on
purpose, imprinting a data stream onto the light at tens of gigabits per second. It is the
digital-to-optical converter of every fibre link on Earth: the transatlantic cables, the datacenter
east–west traffic, the optical I/O creeping toward the processor package — each begins with a
modulator flickering a steady beam into a torrent of symbols. This lesson assembles one from parts
you already own. Take a
fast phase
shifter, embed it in an
MZI
or a microring,
and the phase-to-power conversion you have already mastered becomes a bit-to-brightness converter.
What's genuinely new is the engineering scorecard — five numbers that decide whether a modulator is
a product or a paper.
Two architectures, one job
The Mach–Zehnder modulator (MZM) is the incumbent. Bias the interferometer at
quadrature — the half-power point, where the
\cos^2 transfer curve is steepest and most linear — and wiggle the arm
phase with a depletion or Pockels shifter: small voltage swings produce large, nearly linear power
swings. Because the MZI's response is set by geometry, not resonance, the MZM is
broadband and temperament-free: it works across tens of nanometres and shrugs off
temperature. The bill is size and drive — millimetres of phase-shifter length and, at speed, a
travelling-wave electrode engineered so the electrical drive surfs alongside the light it is
steering.
The ring modulator is the challenger. Park a laser just off a ring's resonance,
then use the embedded junction to yank the resonance a linewidth back and forth: the transmission at
the laser's wavelength slams between high and low. Riding a sharp resonance instead of a broad
interference fringe buys a spectacular discount — a ring modulator is ~10 µm across
(a thousandth of an MZM's footprint) and its junction capacitance is femtofarads, putting
its switching energy in single-digit femtojoules per bit. The bill is the ring's temperament from
last lesson: the resonance must be servo-locked against thermal drift, and the same high
Q that sharpens the resonance sets a photon-lifetime speed limit — light
stored for \tau cannot forget its state faster than
1/\tau, so extreme-Q rings make slow
modulators. Design is the art of choosing a Q just high enough.
The scorecard
Five numbers follow every modulator through its life:
| Metric | Meaning | Typical target |
|---|
| Bandwidth | how fast the output can follow the drive (3 dB electro-optic roll-off) | > 50 GHz for 100 Gb/s-class links |
| Extinction ratio (ER) | power ratio of a "1" to a "0", 10\log_{10}(P_1/P_0) dB | 3–6 dB suffices for links; more costs drive |
| Insertion loss (IL) | light lost just passing through, even on a "1" | a few dB — it comes straight off the link budget |
| Energy per bit | ≈ C V^2/4 for a charge-driven junction (OOK) | fJ/bit for rings; tens–hundreds of fJ for MZMs with drivers |
| Drive voltage | swing the driver IC must deliver (vs the shifter's Vπ) | ≈ 1 V to stay CMOS-friendly |
A worked energy number, because it anchors everything in Module 5: a ring modulator with junction
capacitance C = 10\ \mathrm{fF} driven at
V = 1\ \mathrm{V} spends about
E_{\text{bit}} \;\approx\; \tfrac{1}{4} C V^2 \;=\;
\tfrac{1}{4}\times 10\ \mathrm{fF} \times (1\ \mathrm{V})^2 \;=\; 2.5\ \mathrm{fJ/bit}
(the factor \tfrac14: on average half of random bits are transitions,
each costing \tfrac12 CV^2). Set that against the picojoules an
electrical trace burns moving a bit a few centimetres, and you see why optical I/O is eating the
datacenter from the outside in.
Putting bits on light: OOK and PAM4
The simplest code is on–off keying (OOK): full power is a 1, dark is a 0, one bit
per symbol slot. To send more without modulating faster, split the power axis finer:
PAM4 (four-level pulse-amplitude modulation) uses four evenly spaced power levels
— 00, 01, 10, 11 — carrying two bits per symbol, so a 50 Gbaud modulator
delivers 100 Gb/s. The standard 400G/800G datacenter links are exactly this: lanes of
50–100 Gbaud PAM4.
Nothing is free: PAM4's three "eye openings" each get roughly a third of the amplitude range OOK
gives its one, so each is ~9.5 dB more vulnerable to noise, and the four levels must land
accurately — which is awkward on a \cos^2 transfer curve. Real PAM4
transmitters pre-distort their drive levels to undo the curve's compression, and the receiver's
noise budget, not the modulator's speed, usually decides whether PAM4 flies. Run the trade:
// Bit rate and energy for a modulated link
function bitRate(baudGBd: number, levels: number): number {
return baudGBd * Math.log2(levels); // Gb/s = Gbaud × bits/symbol
}
console.log("50 GBd OOK : " + bitRate(50, 2) + " Gb/s");
console.log("50 GBd PAM4: " + bitRate(50, 4) + " Gb/s");
console.log("100 GBd PAM4: " + bitRate(100, 4) + " Gb/s per lane, 8 lanes -> " +
8 * bitRate(100, 4) + " Gb/s");
// Energy per bit: ring vs MZM (driver included, rough numbers)
function ringEnergy(C_fF: number, V: number): number {
return (C_fF * V * V) / 4; // fJ/bit
}
console.log("ring, 10 fF at 1 V : " + ringEnergy(10, 1).toFixed(1) + " fJ/bit");
console.log("ring, 20 fF at 1.5 V : " + ringEnergy(20, 1.5).toFixed(1) + " fJ/bit");
console.log("MZM + driver (typ) : ~100-500 fJ/bit");
// PAM4's price: each eye gets 1/3 of the swing -> SNR penalty
console.log("PAM4 eye penalty: " + (20 * Math.log10(3)).toFixed(1) + " dB");
You can — it is called direct modulation, and cheap short-reach transceivers do it:
wiggle the laser's drive current and the output power follows. The trouble is that a semiconductor
laser is not a light bulb but a dynamical system. Photons and carriers inside the cavity chase each
other (we will meet the rate equations in the
lasers
lesson), so a current step launches relaxation oscillations — ringing at a few
gigahertz that caps clean modulation speed. Worse, changing the carrier density changes the gain
medium's refractive index, so amplitude modulation drags frequency modulation
("chirp") along with it: each pulse is smeared across wavelengths, and fibre dispersion then smears
it across time, garbling long links. External modulation — laser runs steady, a separate
Mach–Zehnder or ring does the flickering — decouples the light source from the data entirely, which
is why every serious link beyond a few kilometres, and every wavelength-fussy WDM system, pays for
the extra component. The laser is the engine; the modulator is the gearbox.
Both are quoted in decibels, both describe "how much light", and conflating them is a classic
link-budget blunder. Insertion loss compares the modulator's "1" against
no modulator at all: it is light gone forever, subtracted straight off the link budget for
every symbol. Extinction ratio compares the "1" against the "0"
(10\log_{10}(P_1/P_0)): it measures how distinguishable the
symbols are, and a finite ER hurts twice — the residual light in the "0" both wastes transmit power
and drags the decision levels together at the receiver. A device can have superb ER and terrible IL
(a long, lossy MZM driven hard) or the reverse (a weakly driven ring: barely any loss, barely any
contrast). And the two trade: on an MZI, pushing the "0" deeper into the null costs more
drive swing; on a ring, deeper extinction means operating nearer critical coupling, where the "1"
state's own loss grows. A datasheet quoting one number without the other — or an "ER" measured at a
drive swing the CMOS driver will never deliver — is telling you half a story.
Where this goes next
Bits now ride the light. But a photodiode at the far end sees only photons per second — someone must
turn the optical torrent back into electrons, decide 1-or-0 in the teeth of noise, and do it for
milliwatts. That is the receiver's
job, next. Further along, this lesson's scorecard — energy per bit, insertion loss,
drive voltage — becomes the vocabulary in which
co-packaged
optics and photonic accelerators are judged: in photonics, the modulator's electronics,
not the light, is usually where the energy goes.