The paper asks whether structuring a solid target on the nanoscale can give in-situ, sub-femtosecond and nanometre-scale control over the relativistic electrons produced when an intense femtosecond laser hits it. In measurements with p-polarized 25 fs, 800 nm pulses at 3 × 10^18 W cm^-2 on arrays of silicon nanopillars (period 720 nm, height 700 nm), rear-side electrons above 100 keV formed a guided beam whose direction changed with the laser's angle of incidence (15°, 25°, 40°), with a 20–35° angular width versus about 60° from a flat target, about twice the rear flux, and a measured cutoff e

Plasma nanophotonics · Laser & Photonics Reviews 2025

A 25-femtosecond laser flash slams into a forest of silicon pillars, each thinner than a wavelength of light. In an instant they turn to plasma — and out of the back comes a beam of electrons with energies up to about 1.2 million electron-volts, the fastest moving at nearly the speed of light. Tilt the laser and the beam swings.

Drag the laser — or use the tilt slider.

Live illustration of the paper’s mechanism. Numbers marked measured or simulated come from the paper.

Measured beam 20–35° wide · up to 1.2 MeV

1 · The problem

Why aiming electrons is hard

Hit an ordinary flat solid with an intense laser and electrons spray out in broad cones, in directions fixed by how the surface was heated. Existing fixes — magnets, specially shaped targets — act after the electrons are born, and mostly just narrow the spray. Tricks that sculpt the light wave itself work in gases, but they need pulses shorter than 10 femtoseconds and are especially hard to use on solids, where the light cannot get inside.

To steer electrons while they are being born, you must shape fields on nanometre scales in less than a femtosecond. Scrub the ladder to feel how small that is.

Human hair · about 80 µm across

2 · The trick

A stadium wave of pillars

A tilted pulse does not hit every pillar at once. It reaches the lowest pillars first and sweeps upward, like a stadium wave running along the stands.

The pulse reaches the lower pillars first and sweeps upward. Which way will their combined wave go?

Pick a direction, then watch the ripples.

Timing across the comb sets the direction. Each pillar re-radiates when the pulse reaches it, so the ripples add up in the directions where every crest lines up. One such direction is simply straight on, along the laser.

But the pillars sit just under one wavelength apart (720 nm for 800 nm light). That creates one more direction, where each pillar’s ripple lines up exactly one full wave behind its neighbour — the same effect that splits white light into a rainbow on a CD. Antenna engineers use the same idea in phased arrays. The paper’s “grating rule” predicts this extra direction from the tilt and the spacing: sin θd = λ/d − sin θ.

3 · The mystery

The light that shouldn’t exist

Here is the catch. Within the first moments of the pulse the pillars are ionised into dense plasma — and dense plasma acts like a mirror for this light. So the “extra” diffracted beam cannot travel through the target. Yet in the paper’s experiments and simulations, the electrons leave exactly along its direction.

The resolution: the diffracted light lives in the vacuum gaps between the pillars . The simulations below show its field running along the gaps in the guiding direction — right where the electrons are pulled out of the pillar walls.

4 · The ride

Surf the gap light

In the gaps, the light does two jobs. One part of its field (pointing across the gap) tugs electrons out of the pillar wall with about 200 thousand electron-volts. Another part (pointing along the gap) forms a travelling landscape of hills and valleys that pushes them forward. Release an electron on the right slope and it surfs; on the wrong slope it is slowed or shoved back.

Watch the light pull electrons out by itself — then tap the pillar wall to release your own.

The lesson: land on the downhill side and keep pace with the moving hill, and you gain a lot of energy; land on the wrong side and you are slowed or lost. In the real target nobody has to aim — the pillar’s own field pulls electrons out at the right moment, and as the light’s phase runs along the pillar, more electrons join the same bunch in step. The paper calls this coherent bunching. Falling out of step, and collisions with background plasma, limit the gain.

5 · Your turn

Same rule, new situation

If the grating rule really sets the direction, you should be able to hit the same spot with different recipes: change the spacing of the pillars and the tilt.

Send the beam to 238° (the marker). Then find a second, different recipe.

6 · The evidence

What was measured

The team fired the laser at silicon nanopillar targets (pillars 700 nm tall, 720 nm apart, on quartz) at three tilts — 15°, 25° and 40° — and recorded electrons above 100 keV on imaging plates wrapped around the target. Each shot destroys its sample.

At 25°: rule 223.5°, experiment 213° (207–219°), simulation 216°

grating rule simulated measured

Flat target vs nanopillars

Measured: electrons above 100 keV. The pillar beam’s top energy is about three times the ~0.4 MeV that a simple estimate of the laser’s push (the ponderomotive energy) allows. At 25° the guided fraction varied from shot to shot (fabrication quality, alignment).

The raw data

A train of attosecond bunches

In the simulations the electrons leave not as a smooth stream but as bunches as short as ~500 attoseconds, a train from each pillar. Left: the tilted laser sweeping across the pillars. Right: what one pillar (outlined) experiences — the laser’s crests arriving, and the bunches it releases. The bunches repeat faster than the laser oscillates: every T·cos θ, where T = 2.66 fs is one laser cycle and θ is the tilt.

Drag the tilt and compare the two bars underneath: the steeper the tilt, the shorter the gap between bunches.

At 40° tilt: bunches every 2.04 fs · laser cycle 2.66 fs (77%)

7 · A twist

A little haze helps, then hurts

The rising edge of a real laser pulse puffs a thin haze of plasma off the pillar surfaces before the peak arrives. The paper simulated hazes of different thickness (the “scale length”). A little haze lets more electrons feel the gap light, so the beam gets brighter and tighter. More haze clogs the vacuum gaps and makes electrons collide and fall out of step — less energy, a wider beam.

8 · Why it matters

What this brings closer

Back to where we started: electrons steered while they are being born, by nothing more than a nanostructure and a tilt, at million-electron-volt energies. Earlier “dielectric laser accelerators” built from nanostructures use gentle light, below the damage threshold, and reach tens of keV over hundreds of micrometres. Here the light is relativistic, the structures are plasma, and the electrons reach MeV energies within a pillar layer less than a micrometre deep.

The authors see this as a route to in-situ control of high-energy particles — toward miniature laser-driven accelerators, attosecond electron pulses and bright extreme-ultraviolet light sources — and to steering other laser-driven beams, such as high harmonics and ions, in nanostructured plasmas.

Each shot ablates its sample, so every shot used a fresh target — 45–50 nanopillar targets in all.

Source & credits

Ankit Dulat, Sk Rakeeb, Sagar Dam, Amit D. Lad, Yash M. Ved, Sergey Kruk, G. Ravindra Kumar. “Coherent Control of Relativistic Electron Dynamics in Plasma Nanophotonics.” Laser & Photonics Reviews 2025, 19, 2401570. doi.org/10.1002/lpor.202401570 (publisher page). Open access under CC BY 4.0.

Data: Figshare, doi.org/10.6084/m9.figshare.26044792 (CC BY 4.0). The four imaging-plate scans shown are from this dataset, contrast-adjusted and resized.

Figures 1, 2, 3, 4 and 6 are reproduced from the paper (CC BY 4.0), cropped. The angle-vs-tilt, spacing and pre-plasma charts are redrawn from Figs. 3h, 5b and 6 with values read approximately from the figures.

All animations on this page — the tilt instrument, ripple tank, surfing game, bunch train and haze view — are illustrative or toy models written for this explainer. They are not the authors’ particle-in-cell simulations (EPOCH code); only numbers labelled measured or simulated come from the paper.

Type: Space Grotesk and IBM Plex Sans / Mono (SIL Open Font License).