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LETTERdoi:10.1038/nature12664

Demonstration of electron acceleration in a

laser-driven dielectric microstructure

E. A. Peralta1, K. Soong1, R. J. England2, E. R. Colby2, Z. Wu2, B. Montazeri3, C. McGuinness1, J. McNeur4, K. J. Leedle3, D. Walz2,E. B. Sozer4, B. Cowan5, B. Schwartz5, G. Travish4 & R. L. Byer1

The enormous size and cost of current state-of-the-art acceleratorsbased on conventional radio-frequency technology has spawnedgreat interest in the development of new acceleration concepts thatare more compact and economical. Micro-fabricateddielectric laseraccelerators (DLAs) are an attractive approach, because suchdielec-tric microstructurescan supportaccelerating fields oneto twoordersof magnitude higher than can radio-frequency cavity-based accel-erators. DLAs use commercial lasers as a power source, which aresmaller and less expensive than the radio-frequency klystrons that

power todays accelerators. In addition, DLAs are fabricatedvia low-cost, lithographic techniques that can be used for mass production.However, despite several DLA structures being proposed recently14,no successful demonstration of acceleration in these structures has sofarbeenshown. Here we reporthigh-gradient (beyond 250MeV m21)acceleration of electrons in a DLA. Relativistic (60-MeV) electronsare energy-modulated over 5636 104 optical periods of a fusedsilica grating structure, powered by a 800-nm-wavelength mode-locked Ti:sapphire laser. The observedresults are in agreement withanalytical models and electrodynamic simulations. By comparison,conventional modern linear accelerators operate at gradients of 1030MeVm21, and the first linear radio-frequency cavity acceleratorwasten radio-frequency periods (one metre) long with a gradient ofapproximately1.6 MeV m21 (ref. 5).Our results setthe stagefor the

development of future multi-staged DLA devices composed of inte-grated on-chip systems. This would enable compact table-top accel-erators on the MeVGeV (106109 eV) scale for security scannersand medical therapy, university-scale X-ray light sources for bio-logical and materials research, and portable medical imaging devices,and would substantially reduce the size and cost of a future collideron the multi-TeV (1012 eV) scale.

In a dielectric laser accelerator, the large-amplitude fields respon-sible for the accelerating force are provided by a laser pulse. Of par-ticular interest are lasers that operate in the optical or near-infrared(NIR) portion of the electromagnetic spectrum to take advantage ofthe low loss and high damage threshold of dielectric materials at thesewavelengths. Direct acceleration of electrons using a NIR laser wasdemonstrated usinginversetransitionradiation6. Thatapproach, how-

ever, requires a materialboundaryin thepath of theelectronbeam andhas a limited interaction length. To achieve scalable acceleration, theelectric field must have a component parallel to the electron beamtrajectory, and a (speed-of-light) phase velocity that matches that ofthe (relativistic) particle beam.

Previous efforts to accelerate particleswith lasershave used a varietyof techniquesto phase-matchtheelectronbeamto a co-propagating laserfield. The inverse Cerenkov accelerator7,8 uses a gas to slow the phase

velocity of the laser light. The inverse free electron laser accelerator9,10

requires an undulatorat its resonance condition11 to give the electron asynchronous velocity component. However, using a gas cell leads todistortions of theelectron beam dueto multiple scattering, anduse of a

permanent magnet undulator limits the compactness of such a struc-ture and introduces deleterious synchrotron radiation effects.

An alternative way to satisfy the phase-velocity condition is by cre-ating tailored longitudinal modes in near-field structures. One suchapproach, the inverse SmithPurcell accelerator12, has been demon-strated using a metallic grating13, and more recently, in a dielectricgrating with a NIRlaser14. In configurations thatminimize thetransverseforces, these open structures do not support speed-of-light longitudinaleigenmodes and are therefore useful only at sub-relativistic particle

energies. Additionally, they produce an exponentially decaying accel-erating field pattern, which distorts the beam. To address these issues,designs using waveguides and photoniccrystals havebeen proposed13.These structures present challenging fabrication tolerances, and therequired modes are difficult to excite efficiently; as a result, no success-ful demonstrationhas been shown. To circumvent these challenges, weusea planar,phase-resetgrating accelerator structure4,whichpermitsarelatively simple fabrication process and excitation mechanism.

The DLA is fabricated out of fused silica15 and operates at the wave-length (l5 800 nm) of commercially available Ti:sapphire lasers. Thestructure consists of two opposing binary gratings of period lP, sepa-rated by a vacuum gap of height g, where the electron beam travelsperpendicular to the grating rulings. A scanning electron microscope(SEM) image of the structures longitudinal cross-section is shown in

Fig. 1a. To generate the required accelerating fields, a transverse mag-netic (TM) mode laser pulse is incident on the structure perpendicularto both theelectron beam direction of propagation andthe plane of thegratings. Thelaser pulse generates a series of grating diffraction modesinside the vacuum channel, and by matching the grating period to thelaser wavelength (lP5 l) we achieve phase synchronicity between thestrong first space harmonic and the particle beam16.

The structure essentially acts as a longitudinally periodic phasemask, where each grating pillar imparts a p-phase shift on the electricfield, with respect to the adjacent vacuum space (Fig. 1b inset). As aresult, electrons launched at the correct optical phase (laser-electrontiming) remain phase-synchronous and experience net energy gain. Inourexperiment, the electron beam hasa duration of 429631 fs, muchlongerthan thelaser optical cycle (l/c5 2.6fs, where cis thevelocityof

light). Electrons therefore sample all phases of the laser field, causingthe laserelectron interaction to manifest as an energy modulation(broadening), with some electrons gaining energy from accelerationwhile some are decelerated.

Figure 1b depicts a diagram of the experiment performed at theNext Linear Collider Test Accelerator (NLCTA) facility at the SLACNational Accelerator Laboratory. The incident 60-MeV electron beamis focused by a permanent magnetic quadrupole triplet to a root meansquare(r.m.s.) spot sizeof 24mm3 8mm. Thesamplecontains multiple550-mm-long (,687 optical periods) DLA structures with a period of800 nm and apertures of both 500mm3 400nm and 500mm3 800nm. The 400-nm gap structure provides a higher acceleration gradient

1Department of Applied Physics, Stanford University, Stanford, California 94305, USA. 2SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, California 94025, USA. 3Department of

Electrical Engineering, Stanford University, Stanford, California 94305, USA. 4Department of Physics and Astronomy, University of California Los Angeles, Los Angeles, California 90024, USA. 5Tech-X

Corporation, 5621 Arapahoe Avenue, Boulder, Colorado 80303, USA.

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than an 800-nm gap structure but requires tighter tolerances on the

electron beam.The NIRpulses,1.2460.12 ps long,froma regenerativelyamplifiedTi:sapphire mode-locked laser are focused to an r.m.s. spot size of30mm3 300mm at the interaction point. We use a motorized four-axis stage forprecise alignmentof thestructure with theelectronbeam.Once aligned, the electron beam leaving the structure goes through apoint-to-point focusing spectrometer magnet, which disperses theoutgoing electron beam in energy onto a Kodak Lanex phosphorscreen that is imaged by an intensified CCD (charge-coupled device)camera. According to particle tracking simulations, 2.2% of the 60-MeV beam is transmitted through the vacuum channel of the 400-nmgap structure (see Methods). A segment of the spectrometer screenfocusing on this transmitted distribution is shown in Fig. 2a. Thehorizontal axis represents beam energy, and the entire image spans240 keV. The central pixel location of the 60-MeV beamis taken as thereference point, corresponding to zero energy deviation (DE).

The spectrometer image in Fig. 2a is a median filtered average of adozen shots. The least-squares fit to the distribution of electrons scat-tered by thefusedsilicasubstrate andthe grating teeth hasbeen removedfromthis image to emphasize thetransmitted distribution(seeMethods).A similarly averaged set of laser-on spectrometer images within 0.5 psof the optimal timing overlap for laser pulses with energy 93 mJ perpulse is shown in Fig. 2b.The white contour in both Fig. 2a and Fig. 2bdenotes the location where the spectral charge density is 4.5% of themaximum density (at the peak of the scattered distribution). In thepresence of a laser field, there exists a higher charge density on eitherside of the original peak at DE5 0. The white contour shows a sizablefraction of electrons with maximum energy that is ,60 keV higherthan in the laser-off case.

Thelaser-induced energy modulation is readily apparentin the energyspectra (Fig. 2c). Using the fits to these spectra, a maximum energyshiftof 53.1 keV iscalculatedfromthe abscissaof thehalf-width at half-maximum (HWHM) point in the high-energy tail. We use an analy-tical interaction model (see Methods and Extended Data Fig. 3) tocalculate an accelerating gradient from this measurement. Figure 2cshows the input electron beam distribution used in the model (bluecurve), which is a fit to the measured spectrumin the absence ofa laserfield (light blue crosses). The calculatedenergy modulation (red curve)agrees with our measurement (pink crosses), and gives a correspond-ing accelerating gradient of 151.2MeV m21 for this example. Particletracking simulations (black dots; seeMethods)at thisgradient level givean independent confirmation of the observed modulated spectrum.

To determinethe maximum gradient at a given laser power level, we

measure theenergy modulation as the laser pulse is temporally scanned

across the electron beam, forming a cross-correlation signal. A sample

measurement at a laser pulse energy of 91.86

1.3m

J over a laser delayof 6 ps is shown Fig. 3a. The orange circles (laser-off data) show novariation correlated with laser delay, as expected, and have an r.m.s.deviation of 4.5 keV, which is taken as the noise floor level of the mea-surement. The blue circles (laser-on data) show the expected sech2 dis-tributionwith a full-width at half-maximum (FWHM)of 1.8960.09 ps,

Electronbeam

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Figure 1 | DLA structure and experimental set-up. a, Scanning electronmicroscope image of the longitudinal cross-section of a DLA structurefabricated as depicted in Extended Data Fig. 1a. Scale bar, 2 mm.b, Experimental set-up. Inset, a diagram of the DLA structure indicating the

field polarization direction and the effective periodic phase reset, depicted asalternating red (acceleration) and black (deceleration) arrows. A snapshot ofthe simulated fields in the structure shows the corresponding spatialmodulation in the vacuum channel. See text for details.

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Figure 2 | Demonstration of energy modulation. a, Image of thetransmittedelectron beam on the spectrometer screen, with the laser off. b, As abut whenthe laser field is present. c, Energy spectra from aand b showing energymodulation. A fit (blue curve) to the measured laser-off spectrum (light bluecrosses) is used as input for the simulations. The calculated energy modulation(red curve) and particle tracking simulations (black dots) agree with ourmeasuredspectrum(pink crosses).Images of the entire spectrometer screen are

shown in Extended Data Fig. 2.

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which is in agreement with the predicted value of 2.0060.13 ps (seeMethods). For each data set, the magnitude of the electronlaser inter-actionis determined by the amplitude of thesech2 fit, whichrepresentsthemaximum energy gain at an optimal temporal overlap. We use thisfigure to calculate the accelerating gradient. For the data set shown inFig. 3a, the observed maximum energy shift is 69.26 2.3 keV and theresulting gradient is 191.165.7MeVm21, which falls within theexpected range (see Supplementary Information).

The cross-correlation measurement was repeated at multiple pulseenergies up to 319mJ, the maximum pulse energy available. Figure 3bshows the acceleration gradient G as a function of peak incident fieldE0, along with analytical gradient calculations (see Methods) for thebest case (green line) and worst case (red line) structure fabrication.We findthat themeasuredgradient varies linearlywith incident electricfield as expected, and the measured values fall within the anticipatedrange. The highest gradient observed here is 309.8620.7MeV m21;this is twice the highest recorded values in radio-frequency (RF)-baseddemonstration cavities, and 610 times higher than typical operatinggradients in RF structures. The deviation of the high-energy datapoints in Fig. 3b below the predicted linear trend is probably due tostructural damage. Further optimizationof the fabricationand materialscan allow for operation at higher gradients below the laser damage

fluence level. Additionally, despite week-long exposure of the struc-ture, no electron-beam-induced charging or radiation damage wasobserved in the post-examination, demonstrating the robustness ofdielectric structures as accelerators17.

To further verify the linear dependence of the laserelectron inter-action on the electric field, the laser polarization and incidence angleswere varied at a fixed laser power level. As shown in Extended DataFig. 5, the measured gradientsshow good agreement with the expecteddependencies and confirm that an intensity-dependent ponderomo-tive force is not responsible for the observed laserelectron interaction.Additionally, the fit to the data reveals that the laserelectron inter-action occurs over N5 5636104 periods of the structure.

We have produced the first demonstration of scalable laser-drivenacceleration with gradientsexceeding250 MeVm21 in an ultra-compact

and inexpensive DLA. The results are in agreement with both the

analytical treatmentand particle tracking simulations. The pulse dura-tion of the electron beam used in this experiment is longer than theoptical cycle of the laser, which results in a modulation of the electronbeam in energy. An ideal DLA-matched electron source should notonly be sub-femtosecond in duration, but also have a nanometre-scalespot size, to efficiently utilize the maximum acceleration gradients inan optimized sub-wavelength aperture DLA accelerator. To createsuch a source, a method of bunching the electron beam at optical

frequencies has been previously demonstrated18 and needle cathodesare being developed to create high-brightness low-emittance laser-triggered electron beam sources19. By bunching the beam, the fractionof captured electrons can jump from a few tens of per cent in a 5%energy window to.80% with an energy spread of,1% (ref. 20).

Integrating these novel electron sources with DLA structures wouldallow phase-stable net acceleration of synchronous attosecond micro-bunches over manyacceleratingstages. Additionally, the relativelysmalloperating beam charge in these microstructures can be compensatedby the MHz repetition rate of current laser systems to achieve the beamluminosityrequired for high-energyphysics research21. Power efficiencyestimates for such DLA devices are comparable with conventional RFtechnology, assuming that similar power efficiency (near 100%) forguided wave systems can be achieved, 40% laser wall plug efficiencies

(feasiblewith solid statethulium fibrelaser systems)22 and 40% laser toelectron-beam coupling23. Continuously tunable radiation is a naturalby-product of accelerator technology, so this demonstration supportsthe viability of DLA for the development of compact sources of coher-ent, attosecond-scale X-ray pulses24 with applications in medical ther-apy, biological and materials research, and industrial processing.

METHODS SUMMARY

The DLA structure was fabricated by bonding twofused-silica wafers, whichwereprocessed via standard optical lithography and reactive ion etching techniques15

(Extended Data Fig. 1). We used a conventional linear accelerator to generate arelativistic electron beam, with a 10 mm spot size. Owing to the dimensional mis-match between theelectronbeamand thesub-micrometreDLA aperture,manyofthe electrons experienced collisional straggling energy loss25 as they traversed thefused-silica substrate (rather than the vacuum aperture). This process generated

observable opticaltransition radiation (OTR) as a by-product,whichwassubsequently

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Figure 3 | Measurement of acceleration gradient in the 400-nm gap

structure. a, Maximum energy shift as a function of laser delay give a cross-correlation measurement of the laser-electron interaction. The orange filledcircles (laser-off data) show no variation with laser delay and have an r.m.sdeviation of 4.5 keV which is taken as the noise level (black dashed line). Theblue filled circles (laser-on data) show the expected sech2 distribution (bluecurve). b, Calculated acceleration gradient (blue filled circles), G, as a function

of peak incident longitudinal electric field, E0, showing expected linear

dependence (dashed blue line). Gradients in excess of 250 MeV m

21

areobserved within the simulated best-case (dashed green line) and worst-case(dashed red line) structure fabrication tolerance limits. Measurements on the800-nm gap structure are shown in Extended Data Fig. 4. Error bars in aandb, 68% confidence interval.

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used as a diagnostic to align thelaserpulse to theelectronbeam,both spatially andtemporally. The alignment of the electron beam to the aperture of the DLA struc-ture was optimized by maximizing the population of transmitted electrons, asindicated by the electron energy spectrum (Extended Data Fig. 2). Our under-standing of the observed spectrum was verified with G4Beamline26 simulations ofthe beam scattering and radiative losses. To quantify the maximum energy gain inour structure, we developed an analytical model (Extended Data Fig. 3) and per-formed particle tracking simulations, both of which agreed with our measure-ments. Damage threshold measurements27 of identical DLA structures yielded a

laser damage threshold of 0.856

0.14Jcm22

.

OnlineContentAny additionalMethods, ExtendedData display items and SourceData are available in the online version of the paper; references unique to thesesections appear only in the online paper.

Received 28 June; accepted 16 September 2013.

Published online 27 September 2013.

1. Lin, X.E. Photonic band gapfiber accelerator. Phys. Rev. Spec. Top.Accel. Beams 4,051301 (2001).

2. Mizrahi, A. & Schachter, L. Optical Bragg accelerators. Phys. Rev. E70, 016505(2004).

3. Cowan, B. M. Three-dimensional dielectric photonic crystal structures for laser-driven acceleration. Phys. Rev. Spec. Top. Accel. Beams 11, 011301 (2008).

4. Plettner, T.,Lu, P. P. & Byer, R. L. Proposed few-optical cycle laser-driven particleaccelerator structure. Phys. Rev. Spec. Top. Accel. Beams 9, 111301 (2006).

5. Ginzton,E. L.,Hansen, W.W. & Kennedy,W. R.A linearelectron accelerator. Rev.Sci.

Instrum. 19, 89108 (1948).6. Plettner, T. etal. Visible-laser acceleration of relativistic electrons in a semi-infinitevacuum. Phys. Rev. Lett. 95, 134801 (2005).

7. Shimoda, K. Proposalfor an electronaccelerator using an optical maser.Appl. Opt.1, 3335 (1962).

8. Piestrup, M. A., Rothbart, G. B., Fleming, R. N. & Pantell, R. H. Momentummodulation of a freeelectronbeam witha laser.J. Appl.Phys. 46, 132137 (1975).

9. Palmer, R. B. Interaction of relativisticparticles and free electromagneticwaves inthe presence of a static helical magnet. J. Appl. Phys. 43, 30143023 (1972).

10. vanSteenbergen, A.,Gallardo, J.,Sandweiss,J. & Fang, J.-M. Observation of energygain at the BNL inverse free-electron-laser accelerator. Phys. Rev. Lett. 77,26902693 (1996).

11. Marshall, T. C. Free-Electron Lasers 2426 (McMillan, 1985).12. Takeda,Y. & Matsui, I.Laser linac withgrating.Nucl.Instrum. Methods 62, 306310

(1968).13. Mizuno, K.,Pae,J., Nozokido,T. & Furuya, K. Experimental evidence of theinverse

Smith-Purcell effect. Nature 328, 4547 (1987).14. Breuer, J. & Hommelhoff, P. Laser-based acceleration of non-relativistic electrons

at a dielectric structure. Phys. Rev. Lett.. (in the press).

15. Peralta, E. A. et al. Design, fabrication, and testing of a fused-silica dual-gratingstructure for direct laser acceleration of electrons.AIP Conf. Proc. 1507, 169177(2012).

16. Plettner,T., Byer, R.L. & Montazeri, B.Electromagnetic forces inthe vacuumregionof laser-driven layered grating structures.J. Mod. Opt. 58, 15181528 (2011).

17. Thompson, M. C. et al. Breakdown limits on gigavolt-per-meter electron-beam-driven wakefields in dielectric structures. Phys. Rev. Lett. 100, 214801 (2008).

18. Sears,C. M.S. etal. Production and characterizationof attosecond electron bunchtrains. Phys. Rev. Spec. Top. Accel. Beams 11, 061301 (2008).

19. Ganter, R. etal. Laser-photofield emissionfrom needlecathodes for low-emittanceelectron beams. Phys. Rev. Lett. 100, 064801 (2008).

20. Duris, J. P., Musumeci, P. & Li, R. K. Inverse free electron laser accelerator foradvanced light sources. Phys. Rev. Spec. Top. Accel. Beams 15, 061301 (2012).

21. Colby, E. R., England, R. J. & Noble, R. J. A laser-driven linear collider: sample

machine parameters and configuration. Proc. 24th Particle Accelerator Conf.C110328 262264 (2011).

22. Moulton,P. F. etal. Tm-dopedfiber lasers:fundamentalsand powerscaling. IEEEJ.Sel. Top. Quant. 15, 8592 (2009).

23. Siemman,R. Energy efficiency of laser driven, structure based accelerators. Phys.Rev. Spec. Top. Accel. Beams 7, 061303 (2004).

24. Plettner, T. & Byer,R. L. Microstructure-based laser-driven free-electronlaser. Nucl.Instrum. Methods A 593, 6366 (2008).

25. Warner, C. & Rohrlich, F. Energy loss and straggling of electrons. Phys. Rev. 93,406407 (1954).

26. Roberts, T. J. & Kaplan, D. M. G4beamline simulation program for matter-dominatedbeamlines. Proc. 22ndParticle Accelerator Conf.C070625 34683470(2007).

27. Soong, K.,Byer,R.L., Colby,E., England,R.J. & Peralta, E.A. Laserdamagethresholdmeasurements of optical materials for direct laser accelerators. AIP Conf. Proc.1507, 511515 (2012).

Supplementary Information is available in the online version of the paper.

Acknowledgements We thank R. Noble, J. Spencer, O. Solgaard and J. Harris fordiscussions,J. Nelson, D. McCormick and K. Jobefor technical assistance at SLAC, andM. Tang, M. Mansourpour, N. Latta, M. Stevens, J. Conway andU. Thumserfor technicalassistance at the StanfordNanofabricationFacility (SNF). This workwas supported bythe US DoE (grant no. DE-FG03-92ER40693) and DARPA (grant no. N66001-11-1-4199). Device fabrication took place at SNF, which is supported by the NSF undergrant ECS-9731293.

Author Contributions E.A.P., K.S., R.J.E., E.R.C. and R.L.B. designed the experiment.E.A.P.,K.S.,R.J.E.,E.R.C., Z.W. andB.M. built theexperiment,and withthe helpof C.McG.and J.McN., carried out the experiment. E.A.P. designed and fabricated the structure.E.A.P. and K.S. wrote the data analysis software and analysed the results, and E.B.S.contributedto thatsoftware.K.S. developed theanalyticalmodel. K.S., B.M., J.McN, B.C.and B.S. performed supporting simulations. G.T, J.McN, E.B.S. and K.J.L. providedfeedback to improve the experiment. K.S. and K.J.L. designed and constructed thevacuum damage threshold measurement set-up, and K.S. carried out suchmeasurements. D.W. performed hardware upgrades and installation. E.A.P. wrote themanuscript with contributions from K.S. and R.J.E. and revisions by all.

Author Information Reprints and permissions information is available at

www.nature.com/reprints. The authors declare no competing financial interests.Readersare welcome to commenton the online version of thepaper. Correspondenceand requests for materials should be addressed to R.L.B. (rlbyer@stanford.edu).

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METHODSGrating structure fabrication. Fabrication of the duallayer grating structures wascarried out at the Stanford Nanofabrication Facility (SNF). The gratings are pat-terned on fused silica wafers via optical lithography using an ASML PAS 5500i-line stepper and magnetically enhanced reactive ion etching on an AppliedMaterials P5000 etcher. This is shown schematically in steps 13 of ExtendedData Fig. 1a.

Four grating structures areincludedin every sampleto facilitate a switchduringthe experiment, two with a 400-nm gap, and two with an 800-nm gap. Once

patterned and etched, alignment channels of decreasing sizes (250 mm3 250mmR 80mm3 80mm R 80mm320mm) are cut into the wafers to facilitate thealignment of the electron beam with the structure. Two wafers are then bondeddirectly to each other via fusion bonding and diced into individual samples (steps45 of Extended Data Fig. 1a). The alignment tolerance of the bonding process is

,3mm so the grating-to-grating longitudinal alignment is not ensured. However,a perfectly aligned structure is not required to generate substantial accelerationgradients15. As a final step, a section of the sample is metal-coated to serve as areflector for the NIR laser,anda wedge iscutat 45u to be ableto image theinfraredlaser beam and optical transition radiation (OTR) simultaneously. These twofeatures, along with the alignment channels and the four grating structures, areshown in the schematic in Extended Data Fig. 1c.

Electron beam. Testing of the dielectric accelerator structures is conducted usingpre-accelerated electron bunches at the Next Linear Collider Test Accelerator(NLCTA)facility at SLACNational AcceleratorLaboratory. The electron bunches

are produced by an RF photoinjector and accelerated up to 60 MeV in a travellingwave RF cavity at a repetition rate of 10 Hz. Energy collimation is used to create astable monoenergetic slice of the electron bunch with a FWHM energy spread of24keV or0.04%, an r.m.s.lengthof 12969mm(0.436 0.03ps), andemittances of16mmmrad37 mmmrad inXand Y, respectively. Of the initial 5pC of charge,10% is transmitted through the energy collimators, giving an estimated charge of0.5 pC incident on the grating structure. Based on particle scattering simulations,2.2%of theseparticles are transmitted through the 400-nm gapstructures vacuumchannel. Consequently, the population of electrons that pass through the accel-erating channelof the400-nmgap devicecontains anestimated 11fC ofcharge perelectron bunch. A sample spectrometer image for the case of the electron beamtravelling entirelythrough vacuum (that is,in the absence of the structure)is shownin Extended Data Fig. 2a. The horizontal axis represents beam energy and theresolution limit of the spectrometer is 1.2 keV per image pixel so the entire imagespans 800 keV. The central pixel location of the narrow energy spread 60-MeVbeam is taken as thereference point,corresponding to zero energydeviation (DE).

Achieving electron transmission. Transmission of electrons through the sub-micrometre grating aperture is achieved with the help of alignment apertures ofdecreasing size that run parallel to the grating vacuum channels (see ExtendedData Fig. 1c). Once transmission on the large channel is observed, the structuresoptimal pitch and yaw are determined by maximizing the transmitted distribution.This is repeated for the smaller apertures until we see transmission through thegrating aperture. Once this is achieved, the laser beam incidence angle is adjustedto ensure perpendicularity.

Because the NLCTA beam is significantly larger than the structure aperture,only a small fraction of electrons travels through the vacuum channel when theDLAstructureis in place. ExtendedData Fig.2b shows the corresponding spectro-meter image for this case, containing two distinct distributions. The prominentbroad distribution, centred at DE52340 keV, represents the (majority) electronpopulation that travels primarily through the fused-silica substrate. The energy ofthese electrons is reduced due to collisional straggling loss in the material25. The

smaller, more compact distribution at DE5 0 keV corresponds to the populationof electrons that traverse the grating structure primarily through the vacuumchannel. Because the channel has a 1,280:1 aspect ratio (430nm tall, and 550 mmlong), these electrons are collimated with an acceptance angle of 0.04u. This dis-tribution therefore has a reduced vertical spread but retains its original energyspread. Henceforth, we refer to the higher-energy peak as the transmitted popu-lation and the lower-energy peak as the scattered population.

The formation of these two distributions is confirmed by simulations of thescattering and radiative losses of the electron beam as it traverses the gratingstructure. Extended Data Fig. 2c shows a projection of the spectrometer imageof Extended Data Fig. 2b onto the energy axis which gives the resulting electronenergy spectrum. Also shown is the calculated spectrum from particle scatteringsimulations, which has peak locations and relative amplitudes in agreement withthe observedexperimental data.Because the accelerating fields are strongestinsidethe vacuum channel, we focus on the transmitted distribution when studying theeffects of the laserelectron interaction. In our analysis, the resulting spectra are

fitted to a curve composed of two distributions (scattered and transmitted), using

the method of least-squares. A sample fit, shown (in orange) in Extended DataFig. 2c, matches the measured spectra closely.

Particle scatteringsimulations. Wemodelthe scatteringandradiativelosses oftheelectronbeam as it traverses thegratingstructure using theGeant4 codeG4Beamline26

to calculate the expectedelectronenergyspectrum. In thismodel, an electronbeamwith a transverse spot size of 24mm3 8mm and a transverse vertical emittance of3 mm mrad is sent through an approximate model of the grating structure with a400-nm gap. The model structure is made up of five layers. A central, 400-nm tall,

vacuum layer surroundedby two 660-nm-thick grating layers in the first 550mm of

the longitudinal dimension. Two 1.1-mm-long, 500-mm-thick layers of fused silicasurround the grating layers. Extended Data Fig. 2c shows the results of this simu-lation in agreement with the experimental data, giving the correct spectrum peakseparation of 340 keV and relative peak amplitude.

The simulations give a calculated percentage of 2.2% of the total number ofelectrons in the transmitted distribution. By comparison, simulations of the 800-nm gap structure yield 5.8% of the electrons in the transmitted distribution.

Energy modulation simulations. The fields in the structure vacuum channel arecalculated using the finite-element frequency-domain code HFSS and importedinto a MATLAB-based code that computes the resulting relativistic Lorentz forceon a test particle as it traverses the structure. In our simulations, we approximatetheNLCTAelectronbeamusing2,500testparticles, whose positionand momentummatch those of the experiment. Owing to the long computation time required toperform such particle tracking simulations, we elect to model and scale a 100-period structure rather than model the entire 650-period structure. Based onconvergence tests, we find that this approach produces accurate results, which is

expected from the linearity of the acceleration effect, at a fraction of the computa-tion cost. The final energy distribution of the 2,500-particle ensemble is thencalculated from the results of each individual particle trace.

Analyticaltreatment of energy modulation. The interaction between a NIR laserpulse and a picosecond-scale electron bunch in a grating accelerator structure canbe described analytically by partitioning the long electron bunch into a series ofshort finite slices of length t, as shown in Extended Data Fig. 3a, where each slicesatisfies the relation t=l/c. In the presence of the sinusoidally varying electricfields of the structure, each slice of the electron bunch will experience a net energyshiftwitha negligible effecton theenergyprofile. Forexample,a sliceof anelectronbunch with an asymmetric energy profile typical of the NLCTA will experience anet energy gain of 50 keV if injected at the optimal phase in a millimetre-longstructurecapable of 50MeV m21 gradients (see green slice in ExtendedData Fig. 3b).The net effect of the structure is calculated by superimposing the effect for eachindividual slice. For a long pulse, we find that the predicted effect on the electronenergy spectrum is a transition from a single peaked distribution to a doublepeaked profile of lower amplitude, as shown in Extended Data Fig. 3c.

Energy spectrum fits. The projectedenergy spectra are fitted to curves containingthe two distinct,scatteredand transmitted, electron distributions. Several differentprofiles including asymmetric Gaussian, Lorenztian, sech2 and Landau distribu-tions, along with combinations of these were initially employed. These were com-paredagainstthe measuredsingle-peak data (thatis, electron beam incidenton thefused-silica sample but away from the grating vacuum channel) to determine aprofile that minimized the x2 value of the fits. The scattered distribution wasultimately fitted to a half Lorenztian on its low-energy side, and a half sech2 onits high-energy side. The transmitted distribution was fitted to a double-peak

version of the scattered distribution, with the separation of the two peaks as a freeparameter and mirrored about its centre. The sum of the two distributions fit theobserved spectra very well, as indicated in Extended Data Fig. 2c.

On the basis of comparisons with the particle scattering simulations and theanalyticaltreatment, we findthat a partially-straggledpopulationexists, composed

of electrons which are scattered (partially) by the grating teeth. This is accuratelyaccounted for by the low-energy side Lorentzian function used to fit the transmit-teddistribution. To isolate thefullytransmittedelectrons (asshownin Fig. 2c), wesubtract both the straggled distribution and the partially straggled distribution.Thedifference between theabscissaof theHWHMpointin thehigh-energy tail fora laser-on spectrum and a laser-off spectrum gives a measurement of the laser-induced maximum energy shift.

Spatial overlap. We usea miniaturealuminium pelliclemirror anda longworkingdistance Cassegrain telescope to image the back of the grating sample with aresolution limit of 8mm per image pixel. To perform the spatial alignment, wesimultaneously determine the location of the OTR origin on the sample and thelaser beam scattering offthe fabricated 45u wedge shown in ExtendedData Fig. 1c.The laser beam is then steered until the observed scattering lines up with the OTRlocation to within,10mm.

Temporal overlap. A fast photodiode (25-GHz bandwidth) is used to detect theOTR signal the electron beam generates at an aluminium pellicle located down-

streamof thesample. ThetransmittedNIR pulseis also measured simultaneously,

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onthe same detectorand oscilloscope. Weobservethe measuredarrivaltime ofthetwo signals and adjust a four-pass optical delay line to achieve sub-nanosecondoverlap. A motorized delay line provides gross overlap to within the 50-ps reso-lution limit of the oscilloscope, and a voice coil actuated retroreflector is scannedduring the experiment to achieve picosecond-scale timing.Cross-correlation measurement. A typical cross-correlation signal in our experi-mentconsistof 300independentelectronlaser interaction events measuredat 150unique temporal overlap positions. The resulting cross-correlation signal follows ahyperbolic secant squared (sech2) pattern as expected based on the laser pulse

profile indicated by autocorrelation measurements.Typical cross-correlation measurements co-propagate two signals through aninteracting medium, while varying the temporal overlap. In this case, the cross-correlation signal is solelydependent on the temporal dimension. However, in ourcross-correlation measurement,we use two signals incident at perpendicular angles,and as a result, the cross-correlation signal is a function of both the temporal andspatial dimensions of our electron bunch and our laser beam. The expected out-comeof thisinteraction can by calculatedby simulating the perpendicular crossingof an electron bunch with a laser beam, with the temporal and spatial dimensionssetto matchthe experimental values. From this calculation, wepredict a FWHM of2.006 0.13ps for the sech2 fit to the cross-correlation signal. This is in strongagreement with our experimental findings, where a cross-correlation FWHMequal to 1.896 0.09 ps was observed.Damage threshold measurement. Damage threshold measurements of DLAstructures from the same wafer as the one used in the acceleration experimentwereperformedusing an experimental set-up similarto the onedescribed in ref.27.

Anarrayof accelerator structures wasplaced in a vacuumchamberat a pressureof

1025 torr. The NIRpulses from ourTi:sapphire laser systemwas then focused to a

r.m.s. spot size of 27 mm3 53mm and incident on the structure, in the same

manner as in the acceleration experiment. The laser fluence was then gradually

increased from an initial value of 2.00 mJ in increments of 1.85 mJ, while the illu-

minated site was monitored with a camera. At each energy level, approximately

5,000 laser pulses were applied to the structure. Damage was determined to occur

when a visiblechange inthe strengthand consistencyof thescattedinfraredlightat

the illumination site was observed. A total of 24 independent damage threshold

measurements were taken, andeach damagesite wasafterwards inspectedunder ahigh powered optical microscope to verify the occurrence of laser damage.

The results of these measurements indicate a laser damage threshold of

0.856 0.14Jcm22 for our grating accelerator structures. From post-examination

of thestructureit is clear that this damagethreshold valuewas exceeded during the

course of the experiment. However, we continued to see acceleration up to the

maximum available pulse energy. On the basis of post-analysis of a laser damage

site, we deduced that our laser r.m.s. spot size during the experiment was actually

76mm3 294mm, yielding a maximum fluence of 0.85 J cm22 on the gratings.

Error analysis. The corresponding error bar for each data point represents a 68%confidence interval for the plotted fit parameter, as calculated by the Jacobian ofthe weighted nonlinear least-squares regression. The noise floor in the plots isdefined by the laser-off data for each set of measurements. Specifically, we definethe gradient of the laser-off data as zero gradient, and used the positive tail of the68% confidence interval as the noise floor.

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Extended Data Figure 1 | DLA sample preparation. a, Diagram of thestructure fabrication process. In side view, the electron beam traverses thestructure from left to right. In front view, the beam goes into the page. Laser isincident from above. See Methods for details. b, Picture of a completed waferwith hundreds of DLA structures. c, Diagram of a finished sample ready for

beam tests including four DLA structures, alignment channels, a wedge forspatial alignment of the laser to the electron beam, and a metal coating forperpendicular alignment of the laser. d, Picture of a single DLA structure on afingertip.

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Extended Data Figure 2 | Reference spectrometer screen images andspectrum. a, Spectrometer screen image showing the 60-MeV beam with noDLA structure in place. b, Spectrometer screen image of the beam aftertraversingthe grating structure. c, Projection ofb onto theenergy axis yields theenergy spectrum (black crosses) in agreement with particle scatteringsimulations (blue dots). The corresponding least squares spectrum fit (orangecurve) is also shown.

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Extended Data Figure 3 | Analytical treatment of laser-driven electronenergy modulation. a, Picosecond-scale electron beam partitioned into aseriesof finiteslices over oneopticalcycle of thelaser(that is,the greenslice isat

optimal phase for acceleration). b, Each slice samples a different phase of thelaser pulse and therefore experiences a corresponding net energy shift with anegligible effect on the energy profile (that is, the green slice experiences netenergy gain). c, When all contributions are superimposed, the initial singledistribution (dashed blue line) becomes a double-peaked profile (red line), inagreement with particle tracking simulations (black crosses).

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Extended Data Figure 4 | Gradient measurement on 800-nm gapstructure. Calculated gradient (blue filled circles) G as a function oflongitudinal electric field E0 showing expected linear dependence (dashed blueline) and reduced strength when compared to the 400-nm gap structure, asexpected for a larger gap. The dashed black line is the measurement noise level.

Error bars, 68% confidence interval.

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Extended Data Figure 5 | Experimental verification of direct laser

acceleration. a, Gradient in the800-nm gapstructure foran input pulse energyof 105.26 3.6mJ. As thelaser polarization is rotated away fromthe direction ofelectron propagation by an angle w, the acceleration gradient varies asG / cosw. Data for w, 0 were taken last, and beam quality had degraded.b, Gradient in the 400-nm gap structure at an input pulse energy of29.36 0.4mJ, averaging the observed modulation over many shots taken at anoptimal timing overlap. As the laser incidence angle deviates fromperpendicular by an angle h, the observed gradient decreases according to theexpected relationship, equation (2) in Supplementary Information. Data areshown as blue filled circles with the corresponding least squares fit shown asgreen lines. The dashed black line is the measurement noise level. Error bars,68% confidence interval.

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