Erbium (Er)

Silica optical fibre is at its most transparent at a wavelength of about 1550 nanometres. Below that, Rayleigh scattering rises; above it, the glass itself begins to absorb in the infrared. The minimum sits at roughly 0.2 decibels per kilometre, which means light at that wavelength can travel a hundred kilometres of fibre and still retain a usable fraction of its power.

Erbium ions in glass, dropping from their first excited state to their ground state, emit at almost exactly that wavelength.

Nothing connects those two facts. The transparency window is set by the vibrational and electronic properties of silicon dioxide; the emission wavelength is set by the spacing of energy levels in a 4f shell. They coincide, and that coincidence is arguably the single most economically consequential accident in the history of materials.

What the internet looked like without it

A long optical link loses signal, and before 1990 the only way to restore it was to convert back to electricity. An undersea repeater took the weak optical signal, turned it into an electrical one with a photodiode, amplified it, reshaped and retimed the pulses, and drove a laser to launch it onward. Every fifty to a hundred kilometres, on the seabed.

Those repeaters were expensive, they were the most failure-prone part of the system, and they were locked to one bit rate and one wavelength. Upgrading a cable's capacity meant recovering and replacing hardware sitting three kilometres underwater.

An amplifier with no electronics in it

The erbium-doped fibre amplifier removed all of that. Splice in a few metres of fibre whose core contains erbium, illuminate it with a pump laser at 980 or 1480 nanometres, and the erbium ions are lifted into an excited state. A signal photon arriving at 1550 nanometres stimulates them to drop, releasing photons identical to itself. The signal is amplified as light, directly, with no conversion at any point.

Two properties of the erbium transition make this work rather than merely happen. The excited state is metastable, lasting around ten milliseconds, so a modest pump keeps a large population of ions sitting ready. And in a glass host the transition is smeared across a band roughly 1530 to 1565 nanometres rather than being a single sharp line, because every ion sits in a slightly different local environment.

The second property is the one that changed the industry. A device that amplifies a whole band amplifies every channel in that band at once. That is what made wavelength-division multiplexing practical: instead of one signal per fibre, dozens and then hundreds of separate wavelengths could share the same strand and be boosted together by the same lump of erbium glass. The capacity of installed fibre grew by orders of magnitude without anyone laying new cable.

The amplifier was demonstrated at the University of Southampton by David Payne's group in 1987, with closely parallel work at Bell Laboratories. Transatlantic cables using optical amplifiers rather than electronic regenerators went into service in 1996. Because an erbium amplifier does not care what the light is encoding, those cables have been upgraded repeatedly since by changing only the equipment on shore.

Erbium remains the only practical option. It is also why the quantum communications community is so interested in erbium: of all the candidate ions for a quantum memory, erbium is the one that talks at telecom wavelength, and therefore the one that could connect quantum nodes over fibre that already exists.

Water's own wavelength

Erbium's other laser transition is at 2940 nanometres, and that number is chosen by water rather than by convenience. It sits on the strongest water absorption peak in the mid-infrared — roughly an order of magnitude more strongly absorbed than the 2.1 micrometre holmium line.

Light that strongly absorbed penetrates a few micrometres into tissue. An Er:YAG pulse vaporises a layer of cells and stops, depositing almost no heat in what lies beneath. That makes it the precision instrument of ablative medicine: skin resurfacing with far less thermal injury and faster healing than carbon dioxide lasers produce, and dental work in which decayed enamel and dentine are removed without a rotating bur, without vibration, and often without anaesthetic.

A third erbium laser, erbium in phosphate glass at about 1540 nanometres, is standard in military and surveying rangefinders — that wavelength is absorbed by the cornea before it can reach the retina, so a rangefinder built around it is eye-safe at power levels that a near-infrared laser could not use.

Why closed-cycle cryogenics reaches 4 kelvin

A regenerative cryocooler works by shuttling gas back and forth through a matrix that stores and returns heat each cycle. The matrix must have a large heat capacity at the temperature it is operating at, and below about 10 kelvin ordinary materials do not: lattice heat capacity falls off as the cube of temperature, and lead — the traditional choice — becomes useless.

Rare earth intermetallics get around this because they have a magnetic ordering transition down there, and a magnetic transition carries its own large heat capacity. Er₃Ni, an erbium nickel compound, has a peak in exactly the 4 to 10 kelvin range, and packing it into the second stage of a Gifford-McMahon cooler is what allows a closed-cycle machine to reach liquid helium temperature with no liquid helium in it.

The consequences are everywhere in modern laboratories and hospitals: cryopumps on semiconductor tools, precooling stages for dilution refrigerators in quantum computing, and MRI magnets designed to run for years without helium refills. A few hundred grams of an erbium compound is what makes each of them possible.

The oxide that turned out to be five elements

Erbium's name comes from the Swedish village of Ytterby, and it shares that origin with three other elements; the quarry and the naming are covered on the terbium page, along with the episode in the 1860s and 1870s in which the names erbium and terbium were exchanged with one another.

What is distinctively erbium's is what happened next. Carl Gustaf Mosander's erbia went on being subdivided for another forty years. It was eventually shown to contain five separate oxides: erbia itself, plus scandia, holmia, thulia and ytterbia. Four further elements came out of the bottle labelled erbium — a larger yield than any other rare earth fraction produced — which is why erbium's discovery date of 1843 refers to a substance quite unlike the element that now bears the name.

Erbium salts are pink, and erbium oxide is used as a colourant in glass and in synthetic gemstones for that reason. Among its six stable isotopes there is one artificial relative worth noting: erbium-169, a soft beta emitter with a nine-day half-life, is injected as a colloid into the small joints of the hand in radiosynovectomy, where its very short range confines the dose to the inflamed joint lining.