The Energy Cost of Optical Signalling
Landauer's
principle set the only fundamental price in computing: kT\ln 2 \approx
2.87\ \mathrm{zJ} per erased bit at room temperature — and communication,
which need erase nothing, has in principle no floor at all. Reality begs to differ: a
state-of-the-art optical link burns around a picojoule per bit, some
five to six orders of magnitude above Landauer. This lesson dissects that gap, item by
item, the same way the reversible-computing course dissected
the
cost of a CMOS switching event. The punchline is worth holding onto from the start:
every entry in the optical energy bill is engineering overhead — noise margins,
inefficient lasers, hungry electronics — and none of it is charged by fundamental physics. That is
precisely why the bill has fallen a thousandfold in three decades, and why this course keeps
treating "energy per bit" as a moving target rather than a law.
Item 1: the photon itself
Light is quantised, so the smallest possible optical signal is one photon. At the telecom
wavelength \lambda = 1550\ \mathrm{nm},
E_{\text{photon}} = \frac{hc}{\lambda}
\approx 1.28\times10^{-19}\ \mathrm{J} = 128\ \mathrm{zJ} \approx 0.8\ \mathrm{eV}.
Notice: a single photon already costs about 45\times kT\ln 2.
The quantum of light is a coarse-grained currency compared to the thermodynamic floor — a hint
that near-infrared photons are the wrong tool for approaching Landauer, and a big part of why
optical signalling budgets are quoted in attojoules and femtojoules, not zeptojoules.
- each 1550 nm photon carries hc/\lambda \approx 128\ \mathrm{zJ}
\;(0.8\ \mathrm{eV});
- for on–off keying with an ideal photon-counting detector, the only error is a "1" pulse
that happens to deliver zero photons; Poisson statistics give
\mathrm{BER} = \tfrac{1}{2}e^{-N_1}, so a
10^{-9} error rate needs N_1 \approx 20
photons per "1" — an average of ~10 photons per bit, the celebrated quantum limit;
- real room-temperature receivers are nowhere near it: thermal noise in the photodiode's
amplifier chain pushes the practical requirement to 10^3–10^4
photons per bit;
- every stage upstream divides by an efficiency: modulator loss, coupling loss, and a laser
that converts wall-plug power to light at only 10–30%.
Itemising a real link
Follow one bit backwards through a 100 Gb/s link, from detector to wall socket. Suppose the
receiver needs 1000 photons per bit — a decent room-temperature figure:
E_{\text{rx}} = 1000 \times 128\ \mathrm{zJ} = 0.128\ \mathrm{fJ}.
The path from laser to detector loses, say, 10 dB (coupling on and off chips, splitters,
propagation) — multiply by 10: 1.28\ \mathrm{fJ} must leave the laser.
The laser is 20% efficient wall-plug to light — multiply by 5:
6.4\ \mathrm{fJ} of electrical power per bit, for the light alone. Then
add the electronics: the modulator driver, the receiver amplifier, the serialisers and clocking —
in today's transceivers these dominate, bringing the total to roughly a picojoule per bit. Read
that bill again: the photons are the cheap part. The energy story of optical
interconnects is mostly a story about the electronic ends — a theme that returns with force in
Module 8's co-packaged
optics and in the honest accounting of
photonic
AI accelerators.
Run the whole budget yourself, and compare it to the two floors — the quantum limit and Landauer:
const h = 6.626e-34, c = 3.0e8;
const photonJ = (h * c) / 1550e-9; // energy of one 1550 nm photon
console.log("one photon: " + (photonJ * 1e21).toFixed(0) + " zJ");
const kTln2 = 1.380649e-23 * 300 * Math.log(2);
console.log("photon / Landauer bit: " + (photonJ / kTln2).toFixed(1) + "×");
// Link budget: photons/bit at Rx, link loss (dB), laser efficiency.
function wallPlugPerBit(photonsRx: number, lossDb: number, eff: number): number {
const rxEnergy = photonsRx * photonJ;
const txEnergy = rxEnergy * 10 ** (lossDb / 10); // undo the link loss
return txEnergy / eff; // wall-plug electricity for the light
}
const quantumLimit = wallPlugPerBit(10, 0, 1.0); // ideal: 10 photons, no loss
const realistic = wallPlugPerBit(1000, 10, 0.2);
console.log("quantum-limit light energy: " + (quantumLimit * 1e18).toFixed(2) + " aJ/bit");
console.log("realistic light energy: " + (realistic * 1e15).toFixed(1) + " fJ/bit");
console.log("gap to Landauer: " + (realistic / kTln2).toExponential(1) + "×");
It is tempting to file "~1 pJ/bit for an optical link" next to "kT\ln
2 per erased bit" as if both were constants of nature. They are not even the same
kind of number. Landauer's bound is charged by the second law, forever. The optical
budget is a stack of removable engineering taxes: the quantum limit assumes a particular format
(OOK), a particular detector (photon counting) and a particular target error rate — change any of
them, add coherent detection or error-correcting codes, and the photons-per-bit figure moves.
The thermal-noise tax vanishes with better (or colder) electronics; the laser tax shrinks with
efficiency; the loss tax with packaging. Even the energy that is delivered to the
detector is not thermodynamically owed: in principle received signal energy could be recycled
rather than dissipated. History agrees with the theory: links have gone from nanojoules to
picojoules per bit in thirty years, and sub-100 fJ/bit devices exist in the lab. When you meet an
energy-per-bit number in this course, always ask: which line items does it include, and which
are negotiable?
The quantum limit above says ~10 photons per bit — so surely one photon per bit is the dream
ceiling? Better than that: one photon can carry several bits. Deep-space laser
communication, where every photon arriving from a probe is precious, uses pulse-position
modulation: divide a time frame into, say, 64 slots and let a single photon's
arrival slot spell out \log_2 64 = 6 bits. NASA's lunar and
deep-space optical links have demonstrated multiple bits per received photon this way. The price
is exactly what Shannon would predict: enormous bandwidth and dead time per frame — you trade
photons for time slots. It is a beautiful illustration that "energy per bit" is a negotiable,
format-dependent quantity all the way down to the single-photon regime… and even that is not a
floor, since a photon's phase, polarisation and arrival time can be combined. The only
non-negotiable line in the whole ledger remains Landauer's: it is charged not for sending the
bit, but for forgetting it.
Where this goes next
The ledger is drawn: photons at 128 zJ a piece, receivers that demand thousands of them, lasers
that waste four watts in five, electronics that out-eat the optics — and a fundamental floor so
far below all of it that the engineering has decades of headroom. With the physics of light as
carrier now fully priced, the module turns from physics to history: the
next
lesson tells the story of the field that tried to compute with light once before —
and what its rise, collapse and resurrection teach about where these energy numbers actually
bite.