The 2023 Nobel Prize in Physics (Agostini, Krausz, L'Huillier) recognised attosecond light pulses, generated through the three-step model of high-harmonic generation:
- 1. Tunnel ionization — near a field peak, the laser bends the atom's binding potential enough for the electron to tunnel out with ≈zero velocity, at phase ωt₀.
- 2. Acceleration — the freed electron is driven by the oscillating field E(t) = E₀cos(ωt); its classical trajectory is
x(t) = (E0/ω²)[cos ωt − cos ωt0] + (E0/ω) sin(ωt0)·(t − t0)
v(t) = −(E0/ω)[sin ωt − sin ωt0]
- 3. Recombination — for birth phases 0° < ωt₀ < 90° the field reverses and drives the electron back through the parent ion. On recombination it emits a burst of XUV light with photon energy ℏω_XUV = Ip + KEreturn — an attosecond pulse, one per driving half-cycle.
The maximum return kinetic energy over all birth phases gives the famous cutoff law:
Up = E0² / (4ω²) (ponderomotive energy)
KEmax ≈ 3.17 · Up (at ωt0 ≈ 17°)
Cutoff photon energy = Ip + 3.17·Up
- E₀ / λ sliders — set the driving laser's peak field and wavelength (ω = 45.56/λ[nm] in atomic units); both set Up and the whole harmonic spectrum.
- Gas buttons — pick the target atom's ionization potential Ip, which shifts every emitted photon energy.
- Birth-phase slider — drag it to find the trajectory that returns with the most kinetic energy; "Snap to cutoff" jumps straight to the classic ωt₀ ≈ 17° maximum.
- Faint trajectories auto-spawn every half-cycle across the real ionization window (≈5°–80°); each recombination flash is colour-coded by its photon energy, and the top strip sketches the resulting attosecond pulse train.