Why Compute with Light?

Here is the most expensive thing a modern computer does, and it is not arithmetic. In a state-of-the-art accelerator, a 32-bit floating-point multiply costs on the order of a picojoule; fetching the two operands from off-chip memory costs a hundred times more. The chip spends its power budget not on computing but on hauling bits down wires — and the wires are the one part of the system that stopped improving. When Dennard scaling ended around 2005, transistors kept shrinking but the energy to charge a millimetre of copper barely budged. Every generation since, a larger fraction of the power bill has gone to data movement, until today it dominates.

This is the door through which light walks in. The course overview promised a technology that is "a spectacular carrier and a stubborn switch"; this first module makes the carrier half of that sentence precise. Light — an electromagnetic wave obeying Maxwell's equations — brings three physical gifts that copper cannot match: a colossal carrier frequency, parallelism for free, and propagation that is very nearly lossless. This lesson takes the three gifts one at a time, with numbers, and ends with the crossover chart that explains where photonics is winning right now.

Gift 1: a 193-terahertz carrier

Any communication channel rides on a carrier, and you can only modulate a carrier at a rate that is a modest fraction of its own frequency. Telecom light at wavelength \lambda = 1550\ \mathrm{nm} oscillates at

\nu = \frac{c}{\lambda} = \frac{3.0\times 10^{8}\ \mathrm{m/s}} {1.55\times10^{-6}\ \mathrm{m}} \approx 1.93\times10^{14}\ \mathrm{Hz} = 193\ \mathrm{THz}.

One hundred and ninety-three trillion cycles per second. Modulating even a twentieth of a percent of that carrier is a 100 GHz signal — and the low-loss window of optical fibre (the "C-band" plus its neighbours) is 4–10 THz wide, thousands of times the entire usable radio spectrum. An electrical trace, by contrast, is in serious trouble long before 100 GHz: skin effect and dielectric loss make a printed-circuit trace at 28 Gb/s lose roughly a decibel per centimetre, which is why the fastest electrical links in a datacenter reach about a metre and then give up. The carrier frequency is not a detail; it is a five-orders-of-magnitude head start.

Gift 2: parallelism for free (WDM)

The second gift follows from a single word in Maxwell's equations: linear. In glass at ordinary powers, light waves superpose without interacting — two beams of different wavelengths occupy the same fibre and pass through one another as if the other did not exist. So you do not send one signal down a fibre: you send eighty, on eighty different wavelengths, and separate them at the far end with a filter. This is wavelength-division multiplexing (WDM), and there is no electrical analogue: two voltage signals on one wire simply add and are lost.

The arithmetic is cheerful. A standard C-band system carries 80 channels; at today's 400 Gb/s per channel that is

80 \times 400\ \mathrm{Gb/s} = 32\ \mathrm{Tb/s}

through a strand of glass thinner than a human hair. Later in the course the same trick becomes a computing resource: a photonic matrix engine can process one input vector per wavelength, simultaneously, in the same hardware — the subject of WDM parallelism in Module 5.

The laboratory records are absurd. By combining every trick in this module — dozens of wavelengths, two polarisations, high-order modulation formats, and fibres with multiple cores and spatial modes — research groups have pushed petabits per second through a single fibre: over 1015 bits every second, several times the average traffic of the entire public internet, in one strand. Nobody deploys that yet; the point is that the medium is not the bottleneck. The bottleneck — a theme this course returns to relentlessly — is the electronics and the energy at the two ends of the glass, where signals are generated, modulated and detected.

Gift 3: propagation that costs almost nothing

Modern optical fibre attenuates light by about 0.2\ \mathrm{dB/km} — half the power survives a 15 km journey, and 1% survives 100 km. Compare the copper world: an on-chip wire must be recharged through its own resistance and capacitance every millimetre (repeaters burn energy the whole way), and a high-speed board trace loses a dB per centimetre. The consequence for energy is the decisive chart of this lesson. An electrical link's energy per bit grows with distance — more capacitance to charge, more repeaters, more equalisation. An optical link pays a fixed entry fee — laser, modulator, photodetector — and then distance is very nearly free.

The crossover point is the whole industrial story of photonics in one number. With an optical entry fee of 2 pJ/bit and electrical wiring at 1 pJ/bit per centimetre, light wins beyond about 2 cm. Drive the entry fee down — better lasers, smaller modulators, co-packaging — and the crossover creeps inward: from between buildings (1980s), to between racks (2000s), to between boards (2010s), and now to between chips on a package. Every time the crossover moves a level down the packaging hierarchy, photonics eats another layer of copper. That march is the subject of Module 8; whether it can continue all the way into the chip is one of the open questions of the field.

Run the break-even calculation yourself, and the WDM capacity sum while you are at it:

// Energy per bit, in pJ, as a function of link length in cm. const elec = (cm: number): number => 0.3 + 1.0 * cm; // fixed I/O cost + wire cost per cm const opt = (cm: number): number => 2.0 + 0.002 * cm; // laser+modulator+receiver, distance ~free for (const cm of [0.5, 1, 2, 5, 20]) { console.log(cm + " cm electrical: " + elec(cm).toFixed(2) + " pJ/bit optical: " + opt(cm).toFixed(2) + " pJ/bit"); } // Break-even distance: 0.3 + 1.0 d = 2.0 + 0.002 d const breakEven = (2.0 - 0.3) / (1.0 - 0.002); console.log("break-even at " + breakEven.toFixed(2) + " cm"); // WDM aggregate capacity of one fibre. const channels = 80, gbpsPerChannel = 400; console.log("one fibre: " + (channels * gbpsPerChannel) / 1000 + " Tb/s");

The popular pitch for optical computing — "light is the fastest thing in the universe!" — is the one argument that is wrong. A signal on a copper wire is itself an electromagnetic wave, guided by the conductor but travelling in the dielectric around it at roughly 0.5c–0.7c. Light in glass travels at c/n \approx 0.67c — essentially the same speed. (In a silicon waveguide, with group index around 4, light actually propagates slower than a signal on a good transmission line.) Latency per metre is a wash. The genuine advantages are the three in this lesson — carrier bandwidth, wavelength parallelism, and low loss — plus their consequence, energy per bit that does not grow with distance. Whenever you see "computing at the speed of light" in a press release, read it as marketing; when you see "picojoules per bit per centimetre", someone is talking about the real contest.

Where this goes next

So light is a magnificent carrier: terahertz of bandwidth, channels that ignore each other, and distance nearly free. The obvious next question is how a beam of light physically holds bits — what, exactly, do you modulate? The next lesson inventories the degrees of freedom — amplitude, phase, polarisation, wavelength, spatial mode — and counts the bits each can carry. After that we confront the other half of the opening sentence: why this superb carrier makes such a poor switch.