Open Access
Add to BibSonomy
Abstract
Using an 800 nm, 45 fs pulse-front-tilted laser we demonstrate a record 315 keV energy gain in a dual grating dielectric laser accelerator (DLA) and average accelerating gradients of 560 MV/m over 0.5 mm. These results open a new regime in DLA characterized by significant evolution of the beam distribution in the longitudinal phase space, corresponding to > 1/4 of a synchrotron oscillation. By tilting the laser wavefront we control the resonant velocity of the DLA and observe a net energy gain, indicating that a tapered optical phase could be used to achieve very high energy gain.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Optical-scale dielectric structures powered by infrared lasers are rapidly being developed into novel low-cost electron accelerators. Driven by compact, high repetition-rate, short-pulse lasers these accelerators could find applications ranging from medical and industrial linacs, to x-ray light sources and particle colliders [1]. At the same time, DLAs intrinsically possess unique attractive features such as attosecond temporal bunch structure, ultrasmall transverse emittances and precise synchronization to external lasers [2].
DLA, in contrast to many other laser-driven acceleration schemes, is characterized by an accelerating gradient that is proportional to the applied electric field. This is accomplished by using a periodic dielectric structure to diffract an incident plane wave into evanescent fields which form a longitudinal accelerating mode [3–6]. The structure periodicity λg is selected to match the phase velocity of space harmonic n to the electron velocity v. For a laser incident perpendicular to the electron acceleration axis, the corresponding phase-matching condition is λg = βnλ, where λ is the laser wavelength in vacuum, β = v/c and c is the speed of light.
Efficient coupling to the accelerating mode is possible using a side-coupled laser geometry where the drive laser is polarized along the acceleration axis; but this implies that the laser group velocity is not co-aligned with the electron beam. Thus in all previous DLA experiments [7–12] the electrons slip out of the laser pulse envelope in approximately one laser pulse duration. And since the peak accelerating gradient is constrained by the material damage threshold, we favor ultrashort laser pulse durations which imply short interaction lengths. Several techniques have been proposed to extend the interaction, including the use of a tilted pulse front [3, 13], multi-stage guided wave coupling [14, 15], and powering the structure by a co-propagating laser [16].
In the present work we demonstrate electron acceleration using a DLA with an interaction length 50 times longer than the laser pulse duration by using a pulse-front tilted (PFT) illumination scheme. We note that concurrent with this work, the pulse front tilt technique has also been applied to accelerate lower energy (β ≈ 0.3) electrons over shorter distances [17]; however in both cases the increased interaction is significant because the resulting interaction length is not only long in terms of the number of optical periods, but also in terms of the longitudinal phase advance of the accelerating electrons. At the observed gradients, an interaction length of 0.5 mm corresponds to > 1 4 synchrotron oscillation in the accelerating wave potential, enabling for the first time the study/of longitudinal dynamics of relativistic electrons in a DLA.
Taking advantage of the PFT-enabled long interaction length, we show that tuning the resonant energy by tilting the laser wavefront yields a net energy gain for an initially unbunched beam.
2. Pulse front tilt DLA experimental setup
PFT works in a DLA by matching the laser envelope to the particle trajectories, so energy gain can occur along the entire length of the accelerator. With reference to Fig. 1, a coupling is introduced between z and t so that the laser peak intensity illuminating the vacuum channel (z axis) can be described as I(z, t) ∝ f (z/c − βgt) where f(t) represents the temporal profile of the un-tilted laser pulse and βg = cos θpft csc(θpft + θy) is the effective normalized group velocity. If βgc is matched to the electron velocity, the pulse envelope appears stationary in the electron beam frame. For speed-of-light electrons with normal incidence laser (θy = 0), the desired θpft = 45°.
Fig. 1 Schematic of DLA orientation illuminated by PFT laser, with field amplitude E 0 and central wave number k0, incident in the y-z plane at angle θy. The PFT angle θpft is group-velocity matched to an electron traveling in the z-direction.
The optical system used to create the PFT pulse for the present experiment is detailed in Ref. [18], and is based on similar techniques developed for single-cycle THz generation by optical rectification [19–21]. A 600 line/mm diffraction grating (see Fig. 2) introduces PFT which is tuned by imaging the grating onto the DLA with a variable magnification telescope. Since the DLA is very sensitive to the drive laser phase, the PFT optics must be engineered [22] to not only image the grating plane [23], but also to ensure a flat phase-front to minimize phase slippage of the electrons. The PFT angle and pulse duration are measured at the interaction x-z plane by cross-correlating the PFT laser with a non-tilted replica of the drive laser sent through a variable delay line (indicated in blue in Fig. 2) while adjusting the variable magnification telescope. To account for the 6.5 MeV electron energy (βg < 1), θpft = 45.3 ± 0.5° was used in this experiment.
Fig. 2 Schematic (not to scale) of experimental setup. A 6.5 MeV energy electron beam from the UCLA Pegasus gun-linac [24] is focused into the DLA by a solenoid (SOL). After PFT acceleration in the DLA, the electron beam is recollimated by a quadrupole doublet, deflected in y by a deflecting cavity (TCAV) and then in x by a dipole (Spectrometer), permitting the energy-time phase space of the beam to be imaged with an intensified camera (upper right inset).
Three DLA structures (Table 1) were used in the experiment. The structures were fabricated by etching rectangular grooves (height 700 nm, width 325 nm) into 500 µm thickness fused silica wafers [25]. A structure with smaller vacuum gap g results in a higher accelerating gradient G (for the same incident electric field E0), while shorter structures are less sensitive to dephasing.
Table 1. Geometries and results for structures A, B, and C.
The vertical angular aperture Δy′ = g/L of the vacuum channel is maximized for Structure A, but even in this case the focused electron beam (with root-mean-square (RMS) spot size and angular spread σy = 10 µm, ) overfills the aperture. Consequently, 2% of the particles are transmitted, and the rest strike the bulk wafer, scatter, and lose energy (median 290 keV, mean 400 keV). Some of the scattered particles are collected by the spectrometer and are visible in the top left of the spectra shown in Fig. 3.
Fig. 3 Measured phase space images (a, b) show that the DLA accelerates electrons in a temporal “slice” of the transmitted beam. The fraction of interacting electrons (referred to the transmitted beam charge, typically < 5 fC) is shown in (c) to track the measured laser pulse duration τ (in orange) as the laser compressor dispersion ϕ2 is adjusted.
3. Results
Among the transmitted electrons only a short temporal slice interacts with the PFT laser since the electron bunch duration (1 ps RMS) is significantly longer than the full width half-max (FWHM) laser pulse duration (τ = 45 fs).
To observe this effect, we recorded images of the time-dependent modulation of the beam energy by using a transverse deflecting cavity (“TCAV” in Fig. 2) to streak along y followed by a magnetic spectrometer to disperse the energy distribution along x. The resulting x-y transverse profile on the screen represents the beam longitudinal phase space, as shown in Fig. 3(a, b) where the DLA interaction appears as a temporal slice of accelerated electrons. The slice is correlated in time and energy due to time-of-flight difference during the 1.5 m drift from the DLA to the TCAV. Without PFT the images would show no such correlation, since the entire electron bunch would see the same acceleration.
We increase the fraction of electrons which interact with the laser (at the cost of laser intensity) by adjusting a grating compressor to add dispersion to the input laser pulse. In Fig. 3(c) we show that this fraction (measured with the TCAV off as the fraction of the total charge for which ) closely tracks the laser pulse duration (solid curve) measured via frequency-resolved optical gating; whereas without PFT, the pulse duration would be proportional to the interaction length. This effect illustrates the geometrical relationship between the tilted pulse and the electron beam and points towards a trade-off between the interaction length and the fraction accelerated. Note that Fig. 3 was obtained using structure ‘A’ (from Table 1), but similar results are obtained from structures ‘B’ and ‘C’.
To better resolve the acceleration produced by each of the three structures we measure the electron beam energy spectrum with the TCAV turned off, as shown in Fig. 4. The most prominent feature is the main peak of non-interacting electrons followed by the small fraction of accelerated electrons reaching out to a cutoff energy of qΔEmax ≈ κE0Lint, where κ is a property of the DLA representing the ratio of peak gradient Gp to incident field (κ ≡ Gp/E0) and Lint is the interaction length. For comparison, the laser-on and laser-off spectra in Fig. 4 are normalized to have the same charge (3fC for ‘A’ and half that for ‘B’ and ‘C’) and a logarithmic scale is used to highlight laser-induced acceleration.
Fig. 4 Measured electron energy spectra with the laser off (black) and laser on (light blue) for the three different accelerators of Table 1. Particle tracking simulations are also shown (red dashed). Each spectrum is an average of 50 shots.
Simulated spectra (dashed curves in Fig. 4) are calculated by tracking particles (σr = 10 µm, σz = 250 µm) through the field of an initially Gaussian transverse laser distribution which has been propagated through the PFT optics and a nonlinear model of the DLA substrate [26] (wz = 0.65 mm, wx = 35 µm at the 1/e2 intensity). For the relativistic input energies used in this paper and the very low beam charge transmitted in the DLA channel, beam loading or collective effects are not expected to play any role in the dynamics. The structure factor κ for each gap was calculated using an electromagnetic solver [27].
Observed energy gains and gradients are summarized for the three structures in Table 1. The highest energy gain of 315 keV (Structure B) has the lowest average gradient since the interaction length is shortened from the full structure length L = 1 mm to Lint = 0.7 mm by a laser spot size wz = 0.65 mm (1/e2 in intensity) and a small misalignment in z of the laser axis relative to the center of the DLA. The Gaussian spatial distribution of laser intensity further lowers the average gradient due to dephasing from the nonlinear Kerr effect. The results of Table 1 are consistent with the expectation that average gradient is increased when L < wz and/or if a narrower gap g is used. Consequently, the highest gradient (G = 560 MeV/m) is observed in Structure C, which satisfies both conditions.
4. Discussion
The PFT scheme allows us to advance from accelerating a 1 ps electron bunch for ~ 20 µm, as in prior work [10, 26], to accelerating a 50 fs bunch for 0.5 mm. Hence, we greatly increase the interaction length while simultaneously utilizing the high gradients enabled by short laser pulse durations. The observed maximum energy gain is more than an order of magnitude greater than previous demonstrations using fs laser pulses without PFT [10, 26].
With an increased interaction length the electrons undergo dynamic evolution in the accelerating wave, which we demonstrate by tuning the resonant phase velocity in the structure. The phase of an electron in a Floquet harmonic of the DLA is Ψ = nkgz − ωt + ϕ(z), where kg = 2π/λg where ϕ(z) is the drive laser phase profile, which includes a linear phase shift (ω/c sin (θy) z controlled by the angle of incidence. Thus, the normalized phase velocity of the DLA is βres = ω/kresc, where kres = (ω/c) sin θy + kg (using n = 1 for the resonant harmonic).
Using Ψ, the electron energy gain can be heuristically approximated by
and further simplified by assuming a constant electron velocity such that t(z) = (z − z0)/βct is the arrival time of a particle at position z. Maximum energy gain is achieved when Ψ is constant, i.e. electron beam velocity β is matched to the structure phase velocity βres = ω/[kg + ω/c)θy]. Viewed in the frequency domain, a PFT thus allows the electron to interact with a broadband pulse (centered around ω0) by providing the angular dispersion θy(ω) = θ0 + tan(θpft)(ω0/ω) required to make all frequency components travel at the same velocity. We can then vary the offset θ0 by tilting the DLA structure to tune the phase velocity of the accelerating mode and control the dephasing length.The effect of dephasing on the measured maximum and minimum energy changes (ΔEmax, ΔEmin) was measured as a function of θy for the two g = 800 nm structures “A” and “B”, as shown in Fig. 5. The ideal tilt for our structure is offset from zero because the structure was designed for speed-of-light electrons (λg = λ = 800 nm, and βres = 1 at θy = 0). For the present experiment (λ = 803 nm, β = 0.9969), the optimal θy = 3.1 mrad. When varying θy around this value we observe that the particle-wave resonance is sharper in “B” (L = 1 mm) than in “A” (L = 0.5 mm) because in the longer channel the electrons have more periods over which to dephase. Quantitatively, the energy gain can be estimated by integrating Eq. (1) to obtain ΔE ∝ sinc(ω/cθ0L) but this only adequately describes the energy gain in the shorter L = 0.5 mm accelerator.
Fig. 5 Longitudinal dynamics in a DLA. Maximum energy gain and energy loss (at top and bottom of the plot respectively) are shown in (a) and their difference in (b) as a function of θy for structures A (purple) and B (blue). Dots are measurements and lines are simulation. Computed Hamiltonian dynamics are shown in (c) for structure B, corresponding to the three resonant energies marked by vertical lines in part (b). Each plot shows the potential energy (contours), the initial (black) and final (blue) beam distributions, individual trajectories (arrows), and histograms of the final distribution (top and right)
For the L = 1 mm accelerator there is an asymmetric energy gain/loss which can be interpreted by moving beyond the kinematic approximation to consider a one-dimensional normalized relativistic Hamiltonian expanded around the resonant energy :
where η ≡ (γ − γres)/γres and α ≡ eG/(kresmc2) is similar in magnitude to a radiofrequency (rf) proton linac [28] or small-signal free-electron laser [29]. This Hamiltonian is analogous to a pendulum and electrons near the fixed point (Ψ = η = 0) will perform simple harmonic motion with synchrotron wavenumber .Phase space trajectories are shown in Fig. 5(c) for three different resonant energies. The largest modulation is observed near a total energy γresmc2 = 6.5 MeV, but for other injection energies, the energy gain and loss are asymmetric due to the beam phase advance. In particular, when the beam is injected below the resonant velocity it gains energy, whereas when the beam is injected above the resonant velocity it loses energy. This is the origin of the asymmetry in the data that is seen by comparing the difference between the maximum energy gain and the maximum energy loss [Fig. 5(b)].
An estimate for the tilt angle yielding maximum net energy gain can be obtained by analyzing the evolution of a nearly-monochromatic unbunched beam in the Hamiltonian (Eq. 2). This system is analogous to a small signal free electron laser and the spectrum will be shifted up or down according to the small signal gain function , where [29]. Maximum energy gain occurs when , in our case where N = Lint/λg = 875. In terms of resonant energy mc2γres,m = mc2γres(1 + ηmax) = 7.3 MeV in excellent agreement with the data in Fig. 5(b). This approach neglects a small correction due to the Kerr-induced nonlinear phase modulation [26] which is included in the simulation lines shown in Fig. 5(a, b) and is responsible for the larger net energy gain than net energy loss. Larger net energy gains with smaller relative energy spreads could be obtained by tapering the phase velocity (either by chirping the periodic structure as in [17] or by modulating the laser phase) to create a moving bucket which adiabatically accelerates particles near the resonant phase to high energies.
5. Conclusion
In this letter we have presented the first demonstration of a DLA powered by a PFT laser pulse. Increasing the interaction length by an order of magnitude resulted in a record energy gain of 315 keV. The resonant velocity of the accelerating mode was tuned by tilting the laser illumination angle, resulting in spectra with net electron energy gain or loss.
Our results show the unique impact of the laser wavefront on longitudinal dynamics and suggest that a “soft tapering” of the interaction can be imposed by shaping the transverse phase profile of the laser in the PFT setup. For example, imaging a programmable liquid crystal phase mask onto the DLA would allow nearly arbitrary phase profiles to be applied, resulting in full control of beam dynamics in the DLA. Compared to physically varying the periodicity of the structure [17, 30, 31], such “soft-tapering” offers a tunable solution for future experiments.
Several groups around the world are working to develop and demonstrate concepts needed to make a fully integrated working accelerator based on the DLA approach. For example, various schemes are being explored to simultaneously focus and bunch a beam inside the accelerator [6, 16, 32]; fiber coupling designs are being studied to robustly deliver power to a DLA chip and distribute it between multiple acceleration stages [14, 15]; and improvements in source brightness resulting from the adoption of tip-based electron emitters [33] and the use of round-to-flat beam transformations [34] can increase the bunch charge. Increasing the charge up to the beam loading limit would increase efficiency to a few percent for single-bunch operation or tens of percents for multi-bunch operation [35]. Recent progress on these fronts sets the stage for chip-based MeV-scale acceleration modules that could be used as ultra-compact pulsed radiation sources in medicine, industry, or microscopy. These and other potential applications are being evaluated to capitalize on the unique features of DLA that distinguish it from other accelerators, such as chip-scale fabrication, modest drive laser requirements, high repetition rates, and production of sub-femtosecond particle bunches.
Funding
Gordon and Betty Moore Foundation (GBMF4744); National Science Foundation (NSF) (PHY-1734215, PHY-1535711); U.S. Department of Energy (DE-AC02-76SF00515, DE-SC0009914).
References
1. R. J. England, R. J. Noble, K. Bane, D. H. Dowell, C.-K. Ng, J. E. Spencer, S. Tantawi, Z. Wu, R. L. Byer, E. Peralta, K. Soong, C.-M. Chang, B. Montazeri, S. J. Wolf, B. Cowan, J. Dawson, W. Gai, P. Hommelhoff, Y.-C. Huang, C. Jing, C. McGuinness, R. B. Palmer, B. Naranjo, J. Rosenzweig, G. Travish, A. Mizrahi, L. Schachter, C. Sears, G. R. Werner, and R. B. Yoder, “Dielectric laser accelerators,” Rev. Mod. Phys. 86, 1337–1389 (2014). [CrossRef]
2. K. P. Wootton, R. J. England, S. Tantawi, R. W. Aßmann, I. Hartl, F. X. Kärtner, W. Kuropka, F. Mayet, A. Ruehl, L. Rivkin, P. Hommelhoff, J. Illmer, A. Li, J. McNeur, A. Mittelbach, N. Schönenberger, A. Tafel, R. Ischebeck, Y.-J. Lee, M. Qi, D. S. Black, R. L. Byer, H. Deng, S. Fan, J. S. Harris, T. Hughes, N. Sapra, O. Solgaard, J. Vučković, B. M. Cowan, O. Boine-Frankenheim, T. Egenolf, U. Niedermayer, and P. Musumeci, “Towards a fully integrated accelerator on a chip: Dielectric laser acceleration (DLA) from the source to relativistic electrons,” in Proceedings of the 8th International Particle Accelerator Conference, (JACoW, Geneva, Switzerland, 2017), pp. 2520–2525.
3. T. Plettner, P. P. Lu, and R. L. Byer, “Proposed few-optical cycle laser-driven particle accelerator structure,” Phys. Rev. ST Accel. Beams 9, 111301 (2006). [CrossRef]
4. T. Plettner, R. L. Byer, and B. Montazeri, “Electromagnetic forces in the vacuum region of laser-driven layered grating structures,” J. Mod. Opt. 58, 1518–1528 (2011). [CrossRef]
5. A. Szczepkowicz, “Guided-mode resonance, resonant grating thickness, and finite-size effects in dielectric laser acceleration structures,” Appl. Opt. 55, 2634–2638 (2016). [CrossRef] [PubMed]
6. U. Niedermayer, T. Egenolf, and O. Boine-Frankenheim, “Beam dynamics analysis of dielectric laser acceleration using a fast 6D tracking scheme,” Phys. Rev. Accel. Beams 20, 111302 (2017). [CrossRef]
7. E. A. Peralta, K. Soong, R. J. England, E. R. Colby, Z. Wu, B. Montazeri, C. McGuinness, J. McNeur, K. J. Leedle, D. Walz, E. B. Sozer, B. Cowan, B. Schwartz, G. Travish, and R. L. Byer, “Demonstration of electron acceleration in a laser-driven dielectric microstructure,” Nature 503, 91–94 (2013). [CrossRef] [PubMed]
8. J. Breuer and P. Hommelhoff, “Laser-based acceleration of nonrelativistic electrons at a dielectric structure,” Phys. Rev. Lett. 111, 134803 (2013). [CrossRef] [PubMed]
9. K. J. Leedle, A. Ceballos, H. Deng, O. Solgaard, R. F. Pease, R. L. Byer, and J. S. Harris, “Dielectric laser acceleration of sub-100 keV electrons with silicon dual-pillar grating structures,” Opt. Lett. 40, 4344–4347 (2015). [CrossRef] [PubMed]
10. K. P. Wootton, Z. Wu, B. M. Cowan, A. Hanuka, I. V. Makasyuk, E. A. Peralta, K. Soong, R. L. Byer, and R. J. England, “Demonstration of acceleration of relativistic electrons at a dielectric microstructure using femtosecond laser pulses,” Opt. Lett. 41, 2696–2699 (2016). [CrossRef] [PubMed]
11. M. Kozák, M. Förster, J. McNeur, N. Schönenberger, K. Leedle, H. Deng, J. S. Harris, R. L. Byer, and P. Hommelhoff, “Dielectric laser acceleration of sub-relativistic electrons by few-cycle laser pulses,” Nucl. Instrum. Methods Phys. Res., Sect. A 865, 84–86 (2017). [CrossRef]
12. M. Kozák, P. Beck, H. Deng, J. McNeur, N. Schönenberger, C. Gaida, F. Stutzki, M. Gebhardt, J. Limpert, A. Ruehl, I. Hartl, O. Solgaard, J. S. Harris, R. L. Byer, and P. Hommelhoff, “Acceleration of sub-relativistic electrons with an evanescent optical wave at a planar interface,” Opt. Express 25, 19195–19204 (2017). [CrossRef] [PubMed]
13. Y. Wei, M. Dehler, E. Ferrari, N. Hiller, R. Ischebeck, J. Smith, C. Welsch, and G. Xia, “Dual-grating dielectric accelerators driven by a pulse-front-tilted laser,” in Proceedings of the 8th International Particle Accelerator Conference, (JACOW, Geneva, Switzerland, 2017), pp. 3299–3301.
14. T. W. Hughes, S. Tan, Z. Zhao, N. V. Sapra, K. J. Leedle, H. Deng, Y. Miao, D. S. Black, O. Solgaard, J. S. Harris, J. Vuckovic, R. L. Byer, F. Shanghui, R. J. England, Y. J. Lee, and M. Qi, “On-chip laser-power delivery system for dielectric laser accelerators,” Phys. Rev. Appl. 9, 054017 (2018). [CrossRef]
15. K. Koyama, S. Otsuki, M. Uesaka, M. Yoshida, and A. Aimidula, “Parameter study of a laser-driven dielectric accelerator for radiobiology research,” J. Phys. B: At. Mol. Opt. Phys. 47, 234005 (2014). [CrossRef]
16. B. Naranjo, A. Valloni, S. Putterman, and J. B. Rosenzweig, “Stable charged-particle acceleration and focusing in a laser accelerator using spatial harmonics,” Phys. Rev. Lett. 109, 164803 (2012). [CrossRef] [PubMed]
17. M. Kozák, J. McNeur, N. Schönenberger, J. Illmer, A. Li, A. Tafel, P. Yousefi, T. Eckstein, and P. Hommelhoff, “Ultrafast scanning electron microscope applied for studying the interaction between free electrons and optical near-fields of periodic nanostructures,” arXiv:1805.07402 [physics] (2018). ArXiv: 1805.07402.
18. D. Cesar, J. Maxson, P. Musumeci, X. Shen, R. J. England, and K. P. Wootton, “Optical design for increased interaction length in a high gradient dielectric laser accelerator,” Nucl. Instrum. Methods Phys. Res., Sect. A 201812 (2018). [CrossRef]
19. J. Hebling, K.-L. Yeh, M. C. Hoffmann, B. Bartal, and K. A. Nelson, “Generation of high-power terahertz pulses by tilted-pulse-front excitation and their application possibilities,” J. Opt. Soc. Am. B 25, B6–B19 (2008). [CrossRef]
20. Z. Bor and B. Rácz, “Group velocity dispersion in prisms and its application to pulse compression and travelling-wave excitation,” Opt. Commun. 54, 165–170 (1985). [CrossRef]
21. J. Hebling, “Derivation of the pulse front tilt caused by angular dispersion,” Opt Quant Electron 28, 1759–1763 (1996). [CrossRef]
22. A. G. Kostenbauder, “Ray-pulse matrices: a rational treatment for dispersive optical systems,” IEEE J. Quantum Electron. 26, 1148–1157 (1990). [CrossRef]
23. D. Kreier and P. Baum, “Avoiding temporal distortions in tilted pulses,” Opt. Lett., OL 37, 2373–2375 (2012). [CrossRef]
24. D. Alesini, A. Battisti, M. Ferrario, L. Foggetta, V. Lollo, L. Ficcadenti, V. Pettinacci, S. Custodio, E. Pirez, P. Musumeci, and L. Palumbo, “New technology based on clamping for high gradient radio frequency photogun,” Phys. Rev. ST Accel. Beams 18, 092001 (2015). [CrossRef]
25. E. A. Peralta, E. Colby, R. J. England, C. McGuinness, B. Montazeri, K. Soong, Z. Wu, and R. L. Byer, “Design, fabrication, and testing of a fused-silica dual-layer grating structure for direct laser acceleration of electrons,” AIP Conf. Proc. 1507, 169–177 (2012).
26. D. Cesar, S. Custodio, J. Maxson, P. Musumeci, X. Shen, E. Threlkeld, R. J. England, A. Hanuka, I. V. Makasyuk, E. A. Peralta, K. P. Wootton, and Z. Wu, “Nonlinear response in high-field dielectric laser accelerators,” arXiv:1707.02364 [physics] (2017). ArXiv: 1707.02364.
27. Lumerical Inc.
28. T. P. Wangler, “Standard Linac Structures,” in RF Linear Accelerators, (Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, Germany, 2008), pp. 83–134, 2nd ed. [CrossRef]
29. S. Y. Lee, Accelerator Physics (World Scientific Publishing Company, Singapore, 2011), 3rd ed. [CrossRef]
30. F. Lemery, K. Floettmann, P. Piot, F. X. Kärtner, and R. Aßmann, “Synchronous acceleration with tapered dielectric-lined waveguides,” Phys. Rev. Accel. Beams 21, 051302 (2018). [CrossRef]
31. A. Hanuka and L. Schächter, “Trapping of sub-relativistic particles in laser driven accelerators,” Phys. Plasmas 24, 123116 (2017). [CrossRef]
32. J. McNeur, M. Kozak, N. Schonenberger, K. J. Leedle, H. Deng, A. Ceballos, H. Hoogland, A. Ruehl, I. Hartl, R. Holzwarth, O. Solgaard, J. S. Harris, R. L. Byer, and P. Hommelhoff,“Elements of a dielectric laser accelerator,” Optica 5687 (2018). [CrossRef]
33. J. McNeur, M. Kozak, D. Ehberger, N. Schönenberge, A. Tafel, A. Li, and Peter Hommelhoff, “A miniaturized electron source based on dielectric laser accelerator operation at higher spatial harmonics and a nanotip photoemitter,” J. Phys. B: At. Mol. Opt. Phys. 49, 034006 (2016). [CrossRef]
34. A. Ody, P. Musumeci, J. Maxson, D. Cesar, R. J. England, and K. P. Wootton, “Flat electron beam sources for DLA accelerators,” Nucl. Instruments Methods Phys. Res. Sect. A: Accel. Spectrometers, Detect. Assoc. Equip. 86575 (2016).
35. Y. C. N. Na, R. H. Siemann, and R. L. Byer, “Energy efficiency of an intracavity coupled, laser-driven linear accelerator pumped by an external laser,” Phys. Rev. ST Accel. Beams 8, 031301 (2005). [CrossRef]
