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On-chip integrated laser-driven particle accelerator

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Science  03 Jan 2020:
Vol. 367, Issue 6473, pp. 79-83
DOI: 10.1126/science.aay5734

Miniaturizing particle accelerators

Particle accelerators are usually associated with large national facilities. Because photons are able to impart momentum to electrons, there are also efforts to develop laser-based particle accelerators. Sapra et al. developed an integrated particle accelerator using photonic inverse design methods to optimize the interaction between the light and the electrons. They show that an additional kick of around 0.9 kilo–electron volts (keV) can be given to a bunch of 80-keV electrons along just 30 micrometers of a specially designed channel. Such miniaturized dielectric laser accelerators could open up particle physics to a number of scientific disciplines.

Science, this issue p. 79

Abstract

Particle accelerators represent an indispensable tool in science and industry. However, the size and cost of conventional radio-frequency accelerators limit the utility and reach of this technology. Dielectric laser accelerators (DLAs) provide a compact and cost-effective solution to this problem by driving accelerator nanostructures with visible or near-infrared pulsed lasers, resulting in a 104 reduction of scale. Current implementations of DLAs rely on free-space lasers directly incident on the accelerating structures, limiting the scalability and integrability of this technology. We present an experimental demonstration of a waveguide-integrated DLA that was designed using a photonic inverse-design approach. By comparing the measured electron energy spectra with particle-tracking simulations, we infer a maximum energy gain of 0.915 kilo–electron volts over 30 micrometers, corresponding to an acceleration gradient of 30.5 mega–electron volts per meter. On-chip acceleration provides the possibility for a completely integrated mega–electron volt-scale DLA.

Dielectric laser accelerators (DLAs) have emerged as a promising alternative to conventional radio-frequency accelerators because of the large damage threshold of dielectric materials (1, 2); the commercial availability of powerful, near-infrared femtosecond pulsed lasers; and the low-cost, high-yield nanofabrication processes that produce them. Together, these advantages allow DLAs to make an impact in the development of applications requiring mega–electron volt energy beams of nanoampere currents, such as tabletop free-electron lasers, targeted cancer therapies, and compact imaging sources (37).

DLAs are designed by choosing an appropriate pitch and depth of a periodic structure such that the near fields are phase matched to electrons of a specific velocity (8, 9). These structures, together with focusing elements, integrated electron sources, and microbunching structures, form the building blocks to achieve mega–electron volt-scale energy gain through cascaded stages of acceleration (1013). Previous demonstrations of DLAs have relied on free-space lasers directly incident on the accelerating structure, often pillars or gratings made of fused silica or silicon (1420). However, free-space excitation requires bulky optics; therefore, integration with photonic circuits would enable increased scalability, robustness, and impact of this technology.

Integration with photonic waveguides represents a design challenge because of difficulties in accounting for scattering and reflections of the waveguide mode from subwavelength features. Although tuning the geometric parameters and location of a few etched holes in the waveguide is possible (21), this requires brute-force optimization of only a small subset of the design space. Instead, we used an inverse-design approach to develop a waveguide-integrated DLA on a 500-nm device layer silicon-on-insulator (SOI) platform, which allows for expansion of the design space (22). This on-chip accelerator is demonstrated by coupling light from a pulsed laser through a broadband grating coupler and exciting a waveguide mode that acts as the source for the accelerator (Fig. 1A).

Fig. 1 Inverse design of on-chip particle accelerator.

(A) Schematic (not to scale) depicting components of the on-chip accelerator. An inverse-designed grating couples light from a normally incident free-space beam into the fundamental mode of a slab waveguide (inset 1). The excited waveguide mode then acts as the excitation source for the accelerating structure. The accelerator structure, also created through inverse design, produces near fields that are phase matched to an input electron beam with initial energy of 83.4 keV. Inset 2 depicts the phase-matched fields and electron at half an optical cycle (τ/2) apart. (B) Geometry of the optimization problem. We designed on a 500-nm silicon (gray), 3-μm buried oxide layer (light-blue) SOI material stack. Periodic boundary conditions (green) are applied in the z-direction, with a period of Λ = 1 μm, and perfectly matched layers were used in the remaining directions (orange). We optimized the device over a 3-μm design region (yellow) with an input source of the fundamental TE0 mode. During the optimization, a 250-nm channel for the electron beam to travel in is maintained. (C) SEM image of the final accelerator design obtained from the inverse-design method. A frame from a time-domain simulation of the accelerating fields, Ez, is overlaid.

To meet the phase-matching condition, the periodicity of the accelerating structure, Λ, is set by Λ = βλ, where β = v/c is the ratio of the velocities of the incident electrons to the speed of light and λ is the center wavelength of the pump laser (23). To match experimental parameters, we designed for a center pump wavelength of 2 μm and an input electron velocity of v = 0.5c, resulting in an accelerator period of Λ = 1 μm. Fig. 1B captures the geometry of the optimization problem. Using an in-house inverse-design software suite (2427), the design of the accelerator was optimized over a 3-μm region, ensuring the preservation of a 250-nm center channel for electron propagation. The accelerator was simulated with a fully-3D finite-difference frequency-domain (FDFD) solver meshed with a uniform grid spacing of 30 nm. Periodic boundary conditions were applied in the direction of electron propagation (z-axis) to enforce the accelerator period, and perfectly matched layers were used in the remaining axes (28). The structure was excited with the fundamental slab waveguide mode and the following 3D optimization problem was solved:maximizep,E1,E2,,Emi=1m|Gz(Ei)||Gy(Ei)|subject to×1μ0×Eiωi2ϵ(p)Ei=iωiJi,i=1,2,,m(1)We expressed the acceleration gradient, Gz(Ei), the integrated field that the electron experiences as it travels through one period of the accelerator, in the frequency domain (29). The second term, Gy(Ei), corresponds to the deflecting transverse gradients, which we penalized. The fields were subjected to Maxwell’s equations and the permittivity of the device, ε(p), was parameterized by a vector of design variables, p (30). This vector describes the permittivity of the device during the first, continuous stage of optimization and a level-set function that defines the boundaries of the device in the second, discrete stage of optimization. To have good spectral overlap with the broadband input pulsed laser spectrum, each objective function evaluation is the sum of m = 3 simulations, each with a different input source frequency, ωi. The three simulations uniformly sample a 30-nm total bandwidth around 2 μm. During the final optimization stage, an additional constraint was introduced to enforce a minimum fabricable feature size of 80 nm. Further details regarding the design of the accelerator and a time-lapse movie of the optimization can be found in the supplementary materials (31). A scanning electron microscope (SEM) image of a fabricated optimized accelerator is shown with a frame from simulated time-domain fields overlaid (Fig. 1C).

As the optimization was performed with periodic boundary conditions, the performance of a finite-length 30-period accelerator structure was verified in a 3D finite-difference time-domain (FDTD) simulation (32). The frequency response of the grating coupler and accelerator were computed and cascaded to determine the frequency-domain acceleration gradient (31). This complete acceleration gradient spectrum is shown in Fig. 2. The spectrum peaks at λ = 1.964 μm (Fig. 2A), indicating a shift from the design parameters caused by the finite length of the structure and numerical dispersion (33). With knowledge of the peak operating wavelength, the time-domain characteristics were modeled by propagating a 300-fs unchirped Gaussian pulse, centered at 1.964 μm, through the grating coupler, waveguide, and accelerator (31). The time-domain acceleration gradient (Gz) and deflecting gradients (Gy, Gx) are given by: Gk(t0)=1L0LEk(z,t0+z/βc0)dz(2)where t0 is the delay between the time of source injection and the electron entering the accelerator channel and L = 30 μm is the length of the accelerator. The accelerating and deflecting gradients down the center of the channel are evaluated at t0, which maximizes the acceleration gradient, Gz(t0) (Fig. 2B). As the time-domain gradients are normalized to the peak incident pulse amplitude, Fig. 2B also provides the simulated structure factors, the ratio of acceleration gradient to incident field. Although we obtained good suppression of the deflecting gradients, one can also operate at another time delay, t0′, such that the deflecting gradients, Gy(t0′) and Gx(t0′), are further minimized in the center of the channel.

Fig. 2 Simulated performance of optimized accelerators.

(A) Acceleration gradient spectrum for a finite-length accelerator composed of 30 periods, including frequency response of grating coupler. The gradient is normalized to the maximum frequency-domain amplitude of the incident Gaussian beam. Dashed line indicates optimal operation wavelength of the simulated structure, λ = 1.964 μm. (B) Time-domain accelerating gradients and transverse deflecting gradients as a function of input electron energy from simulated fields. Gradients were evaluated at time-delay, t0, which maximizes the acceleration gradient, Gz. Fields normalized to the peak electric field of the pulse incident on the grating coupler.

A 30-period accelerator, waveguides, and grating couplers were fabricated on a 500-nm-thick SOI wafer using electron beam lithography and reactive ion etching. The input grating coupler was separated by 50 μm of waveguide from the accelerator structure, and the output coupler was separated by 30 μm of waveguide from the accelerator. The entire structure had a width of 30 μm. To provide clearance for the electron beam, the area surrounding the accelerator was etched with an additional photolithography step to form a “mesa” (Fig. 3). Complete fabrication details can be found in the materials and methods section (31).

Fig. 3 Fabricated single-stage accelerator.

SEM image of a single-stage accelerator of 30 periods fabricated on a 500-nm SOI stack. The accelerator sits on a 25-μm-tall mesa structure to provide clearance for the input electron beam.

The experimental setup was adapted from previous direct-incidence pillar experiments to support normal incidence on a grating coupler (13, 18). Light, polarized in the direction of electron propagation (z), generated from a 300-fs FWHM pulse-length, 100-kHz repetition rate optical parametric amplifier was focused to a 40-μm, 1/e2-diameter spot. The beam is normally incident on the input grating coupler to excite the fundamental TE0 waveguide mode of the slab waveguide [for grating coupler design, see the materials and methods (31)]. A custom-built scanning transmission electron microscope was used as the source for the electron beam, which travels through the channel in the accelerator structure with an initial energy of 83.4 keV (v = 0.51c). Electrons that passed through the accelerator were separated by energy in a magnetic spectrometer before terminating at a microchannel plate detector to image the energy distribution [see the materials and methods section for additional details (31)].

The electron energy spectra (Fig. 4A) showed that electrons had been successfully accelerated by our structure. The blue curve depicts the energy spectrum of the electrons passing through the accelerator structure with the laser off, and the red curve shows the energy spectrum when the laser (3 mW average power, 335 MV/m peak field, at 1.94 μm) was incident on the grating coupler. Because the bunch length was larger than the optical cycle, we observed symmetric broadening of the energy spectrum, resulting in electrons being accelerated and decelerated. To characterize the broadening of the laser-on spectra, we introduced an energy spectrum width metric, ξ, which we define as the first trailing energy at which the difference between the laser-on spectra F(ε) and the laser-off spectra f(ε) was <0.01: F(ξ) – f(ξ) ≤ 0.01. For the spectra shown in Fig. 4A, centered at ε0 = 83.4 keV, this corresponds to a value of ξ = 84.31 keV. The dotted red curve depicts simulated performance of the accelerator based on a commercial particle-tracking code to propagate a distribution of particles consistent with experimental parameters through the 3D electromagnetic field map of Fig. 1C, providing agreement with the experimental spectrum (31). Because of the spread in energy and phase of the input electron spectrum, the maximal energy gain is a quantity not directly measurable from the laser-on spectrum. Instead, we could obtain this value from the particle-tracking simulations (31). From these simulations, we inferred a maximal energy gain of 0.915 keV over 30 μm, providing a gradient of 30.5 MeV/m and a structure factor (ratio of acceleration gradient to incident field) of 0.09.

Fig. 4 Experimental verification of accelerator.

(A) Electron energy spectrum (log-scale) without laser incident (blue curve) and with laser incident (3.0 mW, 335 MV/m peak field, at λ = 1.94 μm; red curve) on the grating coupler. Simulated spectrum is based on particle-tracking simulations shown in the dotted red curve. On the spectra, ε0 denotes the center energy of the distribution and ξ provides an energy spectral width metric that marks the energy at which the difference between the laser-on and laser-off spectra is below 0.01. (B) Energy spectral width broadening, Δξ = ξ – ε0, (blue, left axis), and peak depletion (green, right axis) for a fixed power at 2.75 mW, 321 MV/m peak field, as a function of varying the wavelength of the pump laser. (C) Measured energy spectral width, Δξ, at a fixed wavelength of 1.94 μm as a function of input power, with simulation from the tracking code superimposed as a dashed curve.

To determine the operating wavelength of our accelerator, the average power of the incident laser pulses on the grating coupler were fixed to be 2.75 mW (321 MV/m peak field) and the wavelength was swept (Fig. 4B). A peak was observed in the energy spectrum width, Δξ = ξ – ε0, at 1.94 μm. Moreover, the ratio of laser-on to laser-off counts at the center energy, referred to as “peak depletion,” was optimal at 1.94 μm, consistent with an increase in the number of modulated electrons at this wavelength. The greatest broadening of the energy spectra and dip in peak depletion suggested an operating wavelength of 1.94 μm. This wavelength was blue-shifted from the simulated operating value of 1.964 μm. Because of the cavity-like nature of this accelerator, we attribute this spectral shift and flattening of the gradient spectrum to fabrication imperfections. Additionally, as a consequence of the blue shift, the Λ = βλ design condition was no longer satisfied exactly and so some dephasing was to be expected, contributing to the diminished structure factor. Fixing the wavelength to 1.94 μm (Fig. 4C), we conducted a sweep of the input power from 0.5 to 5 mW (137 to 433 MV/m peak fields). As we increased the power, the measured values of the spectral width, Δξ, compared favorably with those obtained from the simulated particle-tracking spectra indicated by the dashed curve in Fig. 4C (31).

Although nonlinear dephasing has been observed in other DLA experiments (34, 35), the short waveguide distances (50 μm) in this experiment were much smaller than the hundreds of micrometers of propagation distance required to introduce nonlinear dephasing (36). Additionally, coupling into higher-order modes of the slab waveguide, specifically the TE2 waveguide mode, can result in dephasing. However, with 95% of the total power in the TE0 mode and only 3.8% of power expected to couple into TE2, this negative contribution would be minimal (31). Although not catastrophic to operation of the accelerator, postexperiment SEM imaging revealed laser-induced damage at the input grating coupler. Additional characterization identified this damage to occur after 3 to 4 mW of input power. System-level analysis of an SOI integrated accelerator such as the one presented here predicts acceleration gradients of 45.3 MeV/m (36). This suggests that work toward higher-efficiency grating couplers with greater resiliency to high-field hotspots provides an achievable path to this estimated value.

The fabricated devices accelerate electrons of an initial energy of 83.4 keV by an inferred maximum energy gain of 0.915 keV over 30 μm, demonstrating acceleration gradients of 30.5 MeV/m. In this integrated form, these devices, alongside focusing and bunching elements, can be cascaded to reach mega–electron volt-scale energies capitalizing on the inherent scalability of photonic circuits.

Supplementary Materials

science.sciencemag.org/content/367/6473/79/suppl/DC1

Materials and Methods

Supplementary Text

Figs. S1 to S4

References (3739)

Movies S1 and S2

References and Notes

  1. See the supplementary materials for additional information.
Acknowledgments: Funding: We thank all the members of the Accelerator on a Chip International Program for discussion and collaboration. This work was supported by the Gordon and Betty Moore Foundation (grant no. GBMF4744) and the U.S. Department of Energy, Office of Science (grant nos. DE-AC02-76SF00515 and DE-SC0009914). K.Y.Y. acknowledges funding from a Nano- and Quantum Science and Engineering Postdoctoral Fellowship. D.V. acknowledges funding from FWO and the European Union Horizon 2020 Research and Innovation Program (under Marie Sklodowska-Curie grant no. 665501). R.T. acknowledges a Kailath Graduate Fellowship. Part of this work was performed at the Stanford Nano Shared Facilities (SNSF)/Stanford Nanofabrication Facility (SNF), which is supported by the National Science Foundation under award no. ECCS-1542152. Author contributions: N.V.S. performed and led the design, simulation, and fabrication of the accelerator. K.Y.Y. and Y.M. assisted with fabrication. D.V. assisted with design. K.J.L. and D.S.B. conducted the electron acceleration experiment. R.J.E. performed the particle-tracking simulations. L.S. provided the grating coupler design code. R.T. assisted in simulation analysis. J.V., R.L.B., and O.S. organized the collaboration and supervised the experiments. All authors participated in the discussion and interpretation of the results. Competing interests: The authors declare no competing interests. Data and materials availability: All data needed to evaluate the conclusions in the paper are available in the main text or the supplementary materials.
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