Attosecond Light Pulses

Flashes of Attoseconds

An attosecond is 10⁻¹⁸ of a second. There are as many attoseconds in one second as there have been seconds since the birth of the universe. Light travels only 0.3 nm in an attosecond. Electrons in atoms move on this scale: the atomic unit of time is about 24 as.

In 2001 two groups made and measured flashes this short for the first time: a train of pulses of 250 as each, and a single pulse of 650 as. The shortest single pulse published was 43 as in 2017, and 18 ± 2 as in 2026. The 2023 Nobel Prize in Physics went to Pierre Agostini, Ferenc Krausz and Anne L’Huillier “for experimental methods that generate attosecond pulses of light for the study of electron dynamics in matter”.

1 as = 10⁻¹⁸ s · 2001: 250 as (a train) and 650 as (single) · 2026: 18 ± 2 as

No Shorter Than a Cycle

However short a pulse of light is, it holds at least one oscillation. The infrared of a titanium–sapphire laser has a wavelength of 800 nm and a cycle of 2.67 fs; squeeze the pulse to a few cycles and it still lasts a few femtoseconds.

Shorter needs light of higher frequency: a 100 as pulse needs a wavelength below 30 nm, in the extreme ultraviolet (XUV). No tabletop laser gives that light directly, and it cannot cross even a millimetre of air. The way round is to let the infrared laser turn part of its own energy into XUV inside a gas, and only at a brief moment in each half cycle.

800 nm: one cycle 2.67 fs · a 100 as pulse needs a wavelength below 30 nm

Step One: Tunnel Out

Focus an infrared pulse of a few tens of femtoseconds into a small cell of argon or neon, and the intensity at the focus reaches 10¹⁴ W per square centimetre. At 2 × 10¹⁴ W/cm² the laser’s electric field is about 3.9 × 10¹⁰ V/m, about a thirteenth of the field on the electron in a hydrogen atom.

That is enough to bend the atom’s potential. Near each crest of the field, the barrier on one side is pushed down and thinned, and an outer electron gets through it: tunnel ionisation. Half a cycle later the field has turned round, and the next electrons leave from the other side.

Focus about 10¹⁴ W/cm² · field about 3.9 × 10¹⁰ V/m at 2 × 10¹⁴ W/cm²

Then Out and Back

The electron starts almost at rest; from then on only the laser’s field moves it, first away from the ion, then, once the field reverses, back again. An electron that leaves about 18° after a crest returns with the most kinetic energy, 3.17 Up. Up is the average energy a free electron has quivering in the light, proportional to the intensity times the wavelength squared: Up ≈ 9.33 × 10⁻¹⁴ × I × λ² eV (I in W/cm², λ in µm).

The returning electron recombines with its ion and gives off the ionisation energy and that kinetic energy as one photon, so the photons reach at most about Ip + 3.17 Up. In argon at 800 nm and 2 × 10¹⁴ W/cm² that is about 54 eV. The trajectories in the figure are the page’s, from this classical three-step model: for each return energy there is a “short” and a “long” path.

Cutoff Ip + 3.17 Up · Up ≈ 9.33 × 10⁻¹⁴ · I [W/cm²] · λ² [µm²] eV

Odd Orders Only

In 1987 Anne L’Huillier and colleagues sent 1064 nm infrared light into argon and saw a long row of high harmonics, at 3, 5, 7… times the laser’s frequency, nearly equally bright from the 5th to the 33rd, then gone. The flat stretch is the plateau; where it ends is the cutoff.

Only odd orders appear because the same thing happens every half cycle with the field reversed, so the light it gives off is reversed too. A signal that repeats every half cycle with its sign flipped contains only odd multiples of the laser’s frequency, neighbours two photons apart: 3.1 eV at 800 nm. The page’s spectrum comes from adding the three-step returns half cycle by half cycle with alternating sign, then taking the Fourier transform; the lines on the spectrometer’s phosphor screen are the same.

Odd harmonics · 3.1 eV apart (800 nm) · published 1988: up to the 33rd in argon

A Train of Flashes

If the harmonics are locked in phase, they add up to a flash every half cycle: one every 1.33 fs at 800 nm. Evenly spaced lines in frequency mean an evenly spaced train of pulses in time, the same relation as the frequency comb on the plate “The Optical Lattice Clock”, except that here the lines are two laser photons apart.

In 2001 Agostini and colleagues measured the train with harmonics 11 to 19 from argon: 250 as each. The method is called RABBITT. The XUV and a weak infrared beam ionise argon together, extra “sidebands” appear between neighbouring harmonics, and their strength rises and falls with the delay between the beams; the phase of that rise and fall gives the harmonics’ phases. With the same five harmonics, the page’s flashes are about 255 as each, close to the 250 as measured.

One every 1.33 fs (800 nm) · 2001: 250 as from harmonics 11 to 19

Just One

Each flash in a train is short, but to watch something that happens once it is best to have only one. The way is a driving pulse of only a few cycles: only the strongest half cycle in the middle sends electrons back with the most energy. Keep only the highest-energy light, and a single flash is left.

In 2001 Krausz and colleagues drove neon with a few-cycle 750 nm pulse, made XUV of about 90 eV, picked out the top of it with a multilayer mirror and a filter, and measured a single pulse of 650 ± 150 as. In the figure each half cycle’s cutoff is a bar: the page finds the strongest half cycle about 10 eV above its neighbours.

A driver of only a few cycles · 2001: 650 ± 150 as at about 90 eV

Cut Open: A Line in Vacuum

XUV light does not get far in air, so from where it is made onwards the line is in vacuum: a string of stainless chambers joined by ConFlat flanges with copper gaskets, emptied by turbo pumps. The model is cut open along the beam, the near half removed.

After the laser’s output, a beam splitter makes two arms. One is focused into the gas cell in the generation chamber and makes the XUV; the other runs round the table through a delay stage, enters the vacuum through a window in the recombination chamber and joins the XUV. Both arms are the same length. Then come the toroidal mirror’s chamber, the interaction chamber under its upright electron time-of-flight tube, and last the XUV spectrometer.

A typical attosecond beamline (schematic) · parts to scale, distances shortened

The Driving Light

The driver is usually a titanium–sapphire chirped-pulse amplifier. One at Lund University gives pulses of 20 fs and up to 5 mJ at 800 nm, a thousand times a second. Five millijoules in 20 fs is a peak power of about 0.25 TW.

A single attosecond pulse also needs the pulse squeezed to a few cycles: sent through a hollow fibre filled with a noble gas, its spectrum broadens, and it can be compressed again; in 1997 that reached 4.5 fs with krypton. And the carrier–envelope phase, where the field’s crests sit under the envelope, has to be locked, or the strongest half cycle differs from shot to shot. A pair of 45° mirrors outside the output, a periscope, lifts the beam to the line’s height; the splitter sends a small part of the light to the probe arm, and the pump arm folds once behind the table so both arms are equal.

800 nm · 20 fs · 5 mJ · 1 kHz (Lund) · hollow-fibre compression to 4.5 fs (1997)

A Little Cell of Gas

In the generation chamber sits a gas cell a few millimetres long; the laser passes through small holes in its ends, and inside are a few tens of millibars of argon or neon. The ionised gas at the focus gives off a faint glow.

Conversion is weak: with an 800 nm driver, about 10⁻⁵ of the light comes out as XUV. The infrared left over is far brighter than the XUV and is stopped by an aluminium foil a fraction of a micrometre thick, which passes about 17 to 72 eV and blocks the infrared. Higher energies take zirconium, about 64 to 211 eV.

A cell of a few mm at tens of mbar · efficiency about 10⁻⁵ · aluminium passes about 17–72 eV

Mirrors at a Glance

XUV light is absorbed by almost everything. From X-ray optical constants, gold at 50 eV reflects only about 2% straight on, but about 83% at a grazing 5°. So the mirrors here are at grazing incidence: a gold toroidal mirror focuses the XUV onto the gas in the next chamber, and the line turns a little there, by twice the grazing angle.

In the recombination chamber is a mirror with a hole in the middle: the XUV goes through the hole, and the infrared probe, coming round from the table, hits the mirror around it and is reflected onto the same line.

Gold at 50 eV: about 2% straight on, about 83% at 5° grazing · a toroidal mirror focuses

An Attosecond Is 0.15 nm

A small difference between the arms is a large difference in time: light covers 0.3 nm in an attosecond. Each time the delay stage moves its roof mirror by 0.15 nm, the probe arrives an attosecond later, because the light goes there and back. A piezo drives the stage across a few femtoseconds of delay.

The whole line must hold steady to tens of attoseconds, which means the arms must not drift by more than a few nanometres: vibration of the table, moving air and changes of temperature all have to be held down. Published beamlines reach 13 to 50 as rms.

1 as ↔ 0.3 nm of path ↔ 0.15 nm of stage travel · stability 13–50 as rms

The Attosecond Streak Camera

How is a single attosecond pulse measured? Send it into a jet of gas together with the infrared. The XUV knocks electrons out, and each is pushed by the infrared’s field as it leaves: its final momentum loses the field’s vector potential at that instant, more or less depending on where in the infrared cycle it was born.

Change the delay between the beams and the electrons’ energy swings up and down with the infrared’s waveform, drawing a “streak”. The streak’s width and shape give the pulse’s length and chirp. Here the electrons rise from just above the gas nozzle into the upright time-of-flight tube to a microchannel plate at the top, and their flight times give their energies. The first measurement, in 2001, used electrons from krypton.

p = p₀ − eA(t) · the streak in the figure is computed by the page

Photoemission Takes Time

With this ruler one can ask what could not be asked before: how long does it take light to knock an electron out? In 2010, a single attosecond pulse of about 100 eV ionised neon, and electrons from the 2p orbital came out 21 ± 5 as later than those from 2s.

Twenty-one attoseconds is about 1/120 of a cycle of 750 nm light, too small to see on the streak in the figure. A measurement in 2017 found that another kind of ionisation, in which a second electron is excited at the same time, was mixed into that comparison; separated out, theory and experiment agreed. The applications the Nobel committee names are understanding and controlling how electrons behave in materials, for electronics, and identifying molecules in medical diagnostics.

Neon: 2p 21 ± 5 as after 2s (2010) · about 1/120 of a 750 nm cycle

Taken Apart

The chambers lift off one by one, the toroidal chamber’s lid comes away, and the time-of-flight tube rises highest; the laser, the optics on the table and the delay stage stay where they are.

Point at a part and it is lifted out on its own while the rest fade; at rest, every part is named.