Abstract
Particle accelerators are essential tools in a variety of areas of industry, science and medicine1,2,3,4. Typically, the footprint of these machines starts at a few square metres for medical applications and reaches the size of large research centres. Acceleration of electrons with the help of laser light inside of a photonic nanostructure represents a microscopic alternative with potentially orders-of-magnitude decrease in cost and size5,6,7,8,9,10,11,12,13,14,15,16. Despite large efforts in research on dielectric laser acceleration17,18, including complex electron phase space control with optical forces19,20,21, noteworthy energy gains have not been shown so far. Here we demonstrate a scalable nanophotonic electron accelerator that coherently combines particle acceleration and transverse beam confinement, and accelerates and guides electrons over a considerable distance of 500 μm in a just 225-nm-wide channel. We observe a maximum coherent energy gain of 12.3 keV, equalling a substantial 43% energy increase of the initial 28.4 keV to 40.7 keV. We expect this work to lead directly to the advent of nanophotonic accelerators offering high acceleration gradients up to the GeV m−1 range utilizing high-damage-threshold dielectric materials22 at minimal size requirements14. These on-chip particle accelerators will enable transformative applications in medicine, industry, materials research and science14,23,24.
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Data availability
Source data for Fig. 2 are provided at https://doi.org/10.5281/zenodo.8220588 (ref. 50).
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Acknowledgements
We acknowledge discussions with the members of the Accelerator on a Chip International Program (ACHIP). We thank the Max Planck Institute for the Science of Light clean-room facility staff, in particular O. Lohse and F. Gannott, for continued assistance, C. McGray from Modern Microsystems Inc. for advising on fabrication methods, and Y. Tsur and N. Lindlein for discussions on the zoom lens design. We acknowledge funding by the Gordon and Betty Moore Foundation (GBMF4744 and GBMF11473), ERC Grants NearFieldAtto (616823) and AccelOnChip (884217) and BMBF projects 05K19WEB and 05K19RDE.
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S.K. and L.B. measured and analysed the data. R.S. designed the structures and performed simulations. J.L. fabricated the structures. T.C., S.K., L.B. and R.S. built the set-up. S.K. and R.S. designed and built the pulse-front-tilt set-up. T.C., R.S. and P.H. wrote the paper. P.H. supervised the experiment.
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Extended data figures and tables
Extended Data Fig. 1 Schematics of the experimental setup.
Ultraviolet (UV) laser pulses of 257 nm wavelength (blue) and infrared (IR) laser pulses of 1.93 μm wavelength (red) are generated in an optical parametric amplifier (OPA) and fourth harmonic generation setup (two BBO crystals). The UV pulses are focused onto the SEM cathode tip to generate electron pulses that are injected into the nanophotonic structure. The IR pulses are diffracted at a grating and imaged with a cylindrical zoom lens system to generate a pulse front tilt of α = 71° at the structure. The pulse-front-tilted beam is focused in x-direction onto the structure with a cylindrical aspheric lens of 20 mm focal length. The time delay between IR pulses and electron pulses is adjusted with a motorized delay stage. A home-built magnetic spectrometer is used to measure the electron energy. The energy spectrum is recorded by imaging the micro-channel plate (MCP) detector screen with a camera.
Extended Data Fig. 2 Particle trajectories depicting energy gain vs. longitudinal dimension.
The design curve (see text) is shown in grey, whereas the black curve is the particle trajectory that best matches the energy gain design curve using a least-squares fit. The colour scale indicates the energy gain from 0 (blue) up to 12.8 keV (red), as does the vertical position (left axis). The green curve shows the number of particles that follow the design curve with up to +/−1 keV deviation (the only curve in this graph referring to the right axis). Importantly, a whole number of trajectories around the main black trajectory follow closely the design curve. These trajectories reflect the particles in the coherently accelerated bucket. Below the design curve, another band of trajectories appears to follow the average gradient – these are electrons that fell off synchronicity and were captured by the next “bucket”, however, these also suffer from strong deflection forces which eventually result in loss of most of these particles to the physical boundaries of the channel. The rest of the trajectories (mostly blue) represent electrons that quickly fell out of synchronicity and oscillate in energy. The action of the 25 APF phase jumps representing 13 APF periods is reflected in the saw tooth-like pattern. While there are sections in which the coherently accelerated particles are decelerated, they are accelerated for the most part and obviously undergo net acceleration (energy gain). The blue vertical lines in the top panel show the distance between individual pillars along the structure: the phase jumps of each APF period stand out: 120° jumps are the shorter outstanding lines, while the 240° jumps are the longer ones. Likewise, the tapering of the structure period needed to maintain synchronicity with the accelerated particles is evident from the structure input (z = 0) to the output (z = 500 μm) by the overall increase of the period length, i.e., the noticeable positive overall slope. See also Video 2.
Extended Data Fig. 3 Trajectories (transversal vs. longitudinal dimension).
30,000 electrons are uniformly distributed in time over a full laser cycle (6.45 fs) and around x = 0 with a full width of 20 nm. They are injected into the simulation prior to the structure, and at z = 0 immediately start to undergo transverse deflection due to the optical forces, along with acceleration. Only those electrons that are injected at the correct time are captured and accelerated, which, in this representation, can only be seen by the changing colour: As before, the colour indicates the instantaneous energy of the particle at a specific position (dark blue: 0 energy gain, red: 12.8 keV energy gain). These captured electrons perform oscillations transversely in accordance with the APF phase jumps, along with complementary longitudinal oscillations (see Extended Data Fig. 2). The electrons which are not captured oscillate as well, although out of phase, and most eventually crash into the physical boundaries of the structure and are lost (at x = +/−112 nm). Similar to Extended Data Fig. 2, here we mark the particle that best matches the design (black); like before, the top panel again depicts the tapering and the APF phase jumps along the structure. See also Video 1.
Extended Data Fig. 4 SEM view of the part of the structure from top.
We show a top view of the first 50 μm of the accelerator structure. Two short 120° APF jumps and a long 240° jump are clearly visible. The macrocells are slightly coloured matching the colour code of Fig. 1.
Extended Data Fig. 5 Zoomed-out SEM view of several accelerator channels sitting on mesas.
Tilted view showing an overview of mesas with accelerator structures on a chip. On each chip there are multiple structures of the same design in case one or more structures are damaged.
Extended Data Fig. 6 Alternating phase focusing effect on uncaptured electrons.
Electron spectra around the zero-loss peak for various structure lengths both with (red) and without (grey) laser illumination. Units on the horizontal axis are keV. The extra current visible for shorter structures with laser illumination is a consequence of alternating phase focusing. The effect is less pronounced for the 400 μm structure and completely vanishes for the 500 μm structure (see text for details).
Supplementary information
Supplementary Video 1
Transverse positions of the electrons versus the z axis of the accelerator. The change in colour describes the change of the energy of accelerated electrons from the injection energy (28.4 keV, blue) towards full energy gain (over 40 keV, red). The captured electrons also show a ‘breathing’ motion, focusing and defocusing, as expected from the APF theory.
Supplementary Video 2
The energy gain of the captured electrons versus the z axis in a comoving frame around the best-matching electron (black disk). After roughly 100 µm of propagation, a bounding ellipse in this energy–position space can be fitted (not shown), oscillating and breathing in a complementary fashion to the behaviour in the transverse picture.
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Chlouba, T., Shiloh, R., Kraus, S. et al. Coherent nanophotonic electron accelerator. Nature 622, 476–480 (2023). https://doi.org/10.1038/s41586-023-06602-7
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DOI: https://doi.org/10.1038/s41586-023-06602-7
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