Roll the slab waveguide of the last two lessons into a cylinder — a doped-silica core about 9 µm across inside a 125 µm silica cladding, sheathed in plastic — and you have the optical fibre: the waveguide idea's greatest triumph, and the physical layer of essentially everything. When this page loaded, its bits crossed at least one strand of glass; a transoceanic message crosses thousands of kilometres of it without once becoming electrical. Whether any of that works comes down to a single figure of merit this lesson is about: loss. Guide light through a material and some of the power flowing down the guide is scattered or absorbed per metre. How much survives 10,000 km? The answer in 1965 was "none — not one photon in a googol"; the answer today is "plenty". The story of that reversal is one of the great engineering rescues of the twentieth century, and it begins with learning to count in decibels.

Counting loss in decibels

Attenuation is exponential: each kilometre multiplies the surviving power by the same fraction. Multiplying fractions across mixed components is miserable arithmetic, so engineers take logarithms once and add forever after.

Work one example end to end. Modern fibre achieves \alpha = 0.2 dB/km at its best wavelength. Over a 100 km span the total loss is 0.2 \times 100 = 20 dB — a factor of 100, so a 1 mW (0 dBm) launch arrives as 10 µW (−20 dBm): easily detected. Now feel what the numbers meant in 1965, when good optical glass lost about 1000 dB/km. That is 1 dB per metre: half your light gone every 3 m, one photon in 10^{100} surviving the first kilometre. Nobody plans a phone network around that. The code below is the whole calculus of link budgets in ten lines:

The last line is sobering: even miracle glass loses 1600 dB over an ocean, which is why long-haul systems re-boost the light every ~80 km (originally by converting to electronics and back; since the 1990s with in-fibre erbium amplifiers that never leave the optical domain). Loss engineering did not eliminate amplification — it stretched the hops from 3 metres to 80 kilometres.

Kao's wager, and the anatomy of loss

In 1966 Charles Kao and George Hockham, at Standard Telecommunication Laboratories in Essex, published a claim most colleagues found somewhere between bold and absurd: the 1000 dB/km of contemporary glass was not the glass's fault. Measure after measure, they traced the loss to impurities — above all iron and other transition-metal ions, at parts-per-million levels — rather than to silica itself. Purify the glass, they argued, and loss below 20 dB/km (1% surviving a kilometre — enough for repeatered links) was achievable. Kao then spent years criss-crossing the world's glasshouses persuading somebody to try. Corning got there in 1970 with 17 dB/km; within a decade fibre was in the ground, and today's best fibre sits near 0.14 dB/km — within about a factor of two of the fundamental floor for silica. What remains when the impurities are gone? Three intrinsic terms, each with its own signature:

• Rayleigh scattering — frozen-in density fluctuations of the glass, far smaller than a wavelength, scatter light with the same fierce \lambda^{-4} law that blues the sky. Halve the wavelength, sixteen times the scattering: this walls off the visible and pushes fibre into the infrared;
• infrared absorption — beyond ~1.7 µm, photons start exciting vibrations of the Si–O lattice itself, and absorption climbs steeply. Rayleigh falling and IR rising pincer out a minimum near λ = 1.55 µm: the third telecom window, home of nearly all long-haul traffic (with an older window at 1.31 µm where dispersion vanishes, and 0.85 µm for short links);
• the water peak — residual OH⁻ ions vibrate resonantly near 1.38 µm, historically spiking the loss between the 1.31 and 1.55 µm windows. Modern "dry" fibre all but removes it.

Slide the water peak down to see a modern low-water-peak fibre: the barrier between the 1.31 and 1.55 µm windows melts away, opening one continuous band some 50 THz wide. That bandwidth — tens of terahertz through a strand thinner than a hair — is the resource photonic systems spend for the rest of this course.

Dispersion: the other enemy

Loss shrinks a pulse's height; dispersion smears its width. A data pulse is not one wavelength but a band of wavelengths superposed, and in glass each component travels at a slightly different group velocity, so the components drift apart in transit. Fibre engineers quote the drift as a dispersion parameter D in ps/(nm·km) — picoseconds of spreading per nanometre of spectral width per kilometre travelled:

Standard fibre at 1.55 µm has D \approx 17 ps/(nm·km). Take a laser with \Delta\lambda = 0.1 nm across a 50 km span: \Delta t = 17 \times 50 \times 0.1 = 85 ps. At 10 Gbit/s the bit slot is 100 ps — the pulse has smeared across its neighbours' slots, and the eye at the receiver is closing. The fixes (narrower lasers, operating at the 1.31 µm zero-dispersion wavelength, dispersion-compensating fibre, and ultimately digital equalisation in coherent receivers) each bought another order of magnitude of capacity. The deeper lesson for a computing course: in optics the channel does not merely weaken a signal, it reshapes it — a linear, predictable, wavelength-by-wavelength transformation. Keep that thought; later modules compute with exactly such transformations on purpose.

Where this goes next

Fibre solves the between-machines problem so thoroughly that the interesting frontier moves inside the machine. Can the same guided-light physics be printed onto a chip, in a material a semiconductor fab already knows how to handle, with waveguides packed micrometres apart rather than strung across oceans? The next lesson answers with the platform that carries essentially all of this course: silicon photonics on silicon-on-insulator — including the awkward things silicon refuses to do.