Radio frequency particle accelerators are ubiquitous in ultrasmall and ultrafast science, but their size and cost have prompted exploration of compact and scalable alternatives such as the dielectric laser accelerator. We present the first demonstration, to the best of our knowledge, of high gradient laser acceleration and deflection of electrons with a silicon structure. Driven by a 5 nJ, 130 fs mode-locked Ti:sapphire laser at 907 nm wavelength, our devices achieve accelerating gradients in excess of and suboptical cycle streaking of 96.30 keV electrons. These results pave the way for high gradient silicon dielectric laser accelerators using commercial lasers and subfemtosecond electron beam experiments.
© 2015 Optical Society of America
Dielectric laser accelerators (DLAs) utilizing commercially available laser systems can support accelerating gradients one to two orders of magnitude higher than conventional radio frequency (RF) accelerators. They also have the capability to operate at the attosecond (as) timescale [1 –5]. Recently, relativistic accelerating gradients of up to were demonstrated using dual gratings , concurrently with subrelativistic accelerating gradients using single gratings [2,6,7]. These first demonstrations show the potential of DLAs to match or exceed state-of-the-art RF accelerators for a wide range of electron energies. Silicon is an attractive alternative to for bridging the accelerator gap between femtosecond photocathode electron sources and attosecond electron applications.
In this Letter, we present the first demonstration, to the best of our knowledge, of high gradient (more than ) acceleration and deflection of electrons with a silicon nanostructure. These results pave the way for attosecond electron beam experiments for ultrafast electron diffraction, time-resolved electron microscopy, and optical streak cameras [8,9]. Applications of relativistic DLA systems include compact radiation therapy devices, x-ray free electron lasers, and TeV energy physics facilities .
Silicon provides an excellent platform for future fully integrated accelerator-on-chip systems driven by ultrafast fiber lasers. Precision fiber v-grooves can be etched, low-loss and large-mode-area waveguides can be fabricated on it, and a variety of high-coupling-efficiency photonic structures can be fabricated for a fully monolithic accelerator system . At relativistic energies, similar laser field coupling efficiencies, , between high index of refraction contrast (e.g., Si/vacuum) and low index contrast structures (e.g., ) can be achieved. However, for subrelativistic applications, the high field coupling efficiencies of silicon structures enable comparable or higher acceleration gradients than with structures even though the laser damage threshold is much lower for silicon. The conductivity of silicon also prevents beam steering due to charge accumulation. structures require metal coatings or other anticharging treatment for sub- energies.
A variety of silicon accelerator structures have been proposed, including woodpile structures , photonic crystal slabs , and buried grating structures . For our first silicon accelerator demonstration with subrelativistic 96.3 keV electrons, we opted for the simpler reflection-configuration inverse Smith Purcell design. This configuration was first demonstrated with terahertz radiation and metallic gratings at keV/m accelerating gradients . Breuer and Hommelhoff used a inverse Smith Purcell grating in the transmission rather than the reflection configuration to achieve their accelerating gradient, and required a thin metal coating to prevent charging .
Our drive wavelength of 907 nm was a tradeoff between the thermal heating of silicon and the power output of our available Coherent MIRA 900 Ti:sapphire mode-locked laser. Silicon is an indirect bandgap semiconductor and is only transparent for wavelengths longer than 1.2 μm. However, the absorption length of silicon at 907 nm is 35 μm, so laser fields are minimally attenuated in 200 nm deep gratings . Bulk linear absorption limits our time-averaged laser intensity to or at 76 MHz repetition rate to prevent thermal damage. Ultrafast laser-induced breakdown in silicon occurs at approximately fluences in the near infrared . Silicon accelerators driven by Er:fiber or Tm:fiber lasers at 1.55 and 2 μm in wavelength, respectively, would be subject to two- and three-photon and free-carrier absorption, and could handle significantly higher average powers .
The accelerator devices are fabricated from 5 to 10 ohm-cm phosphorus-doped silicon. The grating patterns are written via electron beam lithography using a JEOL JBX-6300 and transferred to the wafer using reactive ion etching. The gratings are 15 μm long and have a period of 490 nm, which corresponds to the first spatial harmonic at an electron velocity and laser wavelength . The grating teeth are 210 nm wide and 200 nm deep, and the transverse magnetic (TM) mode reflectivity is measured to be . The gratings sit on a 3 μm high mesa for beam clearance.
We use finite difference time domain (FDTD) simulations to calculate the first harmonic TM mode of the grating. Figure 1(a) shows the accelerating electric field profile with the net force vectors for all optical phases superimposed. We show the dependence of the acceleration and deflection gradients on the optical phase in Fig. 1(b). The accelerating gradient and deflecting gradient are defined as the average accelerating and deflecting fields for an electron over one grating period:
The acceleration and deflection fields are out of phase, and both decay exponentially away from the grating surface with decay constant , for . The deflection gradient causes suboptical cycle streaking of the electrons, and the acceleration gradient causes longitudinal energy gain or loss. We measure both accelerating and deflecting forces of a single phase quadrant in our experiment.
Figure 2 shows the experimental setup. A scanning electron microscope (SEM) based on a Kimball Physics EGH-8103 100 keV thermal cathode provides a continuous electron beam for the experiment. The electron beam full angle is 2.2 mrad, and the focal waist radius is 50–100 nm. The nominal electron beam current is 150 pA. An imaging magnetic prism spectrometer  mounted on an X–Y stage and a CMOS direct detector (Thorlabs DCC1545M with cover glass removed) are used to analyze the electron energy. A knife covers the lowest 30 pixels of the camera and blocks sample-scattered electrons from being detected. The spectrometer entrance has a 1 mm diameter entrance aperture that is used to spatially filter the direction laser deflected electrons from the main beam to further reduce background noise from scattered electrons. Electrons must experience a minimum deflection gradient to enter the spectrometer and a minimum accelerating gradient to be detected by the CMOS camera. This window corresponds to less than 600 as per 3 femtosecond optical cycle in our experiment. The electron beam angle is determined with a transfer matrix model of the spectrometer and the electron energy by direct comparison against increased cathode potential with no structure present . The spectrometer energy and angular resolutions are approximately and at 96.30 keV, respectively. Measuring both acceleration and deflection simultaneously produces a 100:1 signal-to-noise ratio.
The Ti:sapphire laser is focused on the grating using an aspheric lens to a beam waist radius of as measured by the knife edge. The laser is aligned to the electron beam using the aspheric lens as a microscope objective and an uncoated pellicle beam splitter to create a basic microscope with the sample backreflected image. Typical laser characteristics for the experiment are , 400 mW average power, repetition rate, and FWHM pulse length, corresponding to a peak fluence of and a peak incident electric field of .
We accumulate electron spectra for 200 s for each measurement to increase the signal-to-noise ratio. The typical accelerated electron count rate for the experiment is , which is in the expected range given the effective electron current , the expected detection quantum efficiency of the CMOS camera, and the optical phase window for deflection and acceleration. Space-charge and wakefield effects are expected to be negligible due the low beam current at electrons per laser pulse.
For the results shown in Fig. 3, the knife edge blocks electrons that gain less than 245 eV, and the spectrometer entrance aperture blocks electrons less than 2.4 mrad off axis from the electron beam center. We model the accelerated and deflected electron charge density as a 1D Gaussian electron beam centered 150 nm above the grating with a beam waist radius of 65 nm that interacts with the exponentially decaying grating fields. This produces a ‘donut’ charge density profile in acceleration and deflection phase space with a peak density ring corresponding to the deflection and acceleration experienced at the electron beam center. The model’s predicted charge density distribution agrees well with the experimental data as shown in Fig. 3(a).
We integrate over our observed acceleration and deflection phase space to determine the accelerated electron fraction as a function of energy gain. The model accelerated fraction predictions are compared to the experimental accelerated fraction in Fig. 3(b) and show good agreement. We infer from our simulations that electrons can approach the grating surface within 10 nm. We observe a maximum energy gain of before our accelerated fraction drops to the background scattered electron noise level. A maximum beam angle of 7.5 mrad from the beam axis is observed. Using our model and the starting divergence of the beam, we estimate that the peak deflection observed was , for a transverse energy gain of .
Following , the characteristic laser–electron interaction distance is
The observed acceleration and deflection gradients vary linearly with the incident laser field as shown in Fig. 4. This confirms the acceleration field ratio of and deflection field ratio of , in agreement with FDTD simulations. This is comparable to the acceleration field ratio demonstrated with relativistic dual gratings . FDTD simulations indicate that acceleration field ratios of 0.20 can be achieved at from a silicon reflection grating as opposed to 0.04 for a comparable grating, requiring less fluence for a given gradient at 96.30 keV .
Figure 5(a) shows a fit to the acceleration and beam deflection data for the incident laser polarization angle and confirms the expected trend.
The accelerating gradient drops off asymmetrically away from the nominal 907 nm drive wavelength, as shown in Fig. 5(b). Accelerated electrons gain momentum from the laser interaction, and they phase match better with drive wavelengths that are slightly too short. The deflection gradient does not affect the phase matching as much and is nearly symmetric about 907 nm. Particle tracking simulations by numerically integrating the Lorentz force over the full grating FDTD fields agree with the experimental data with no fitting parameters. The experimental energy gains have been normalized for an equivalent incident electric field. In future devices, the grating period can be chirped to keep the accelerating field in phase with the electrons as they gain energy.
Symmetrically illuminated double grating and photonic crystal structures would enable control of the deflection gradients [3,5,11,12,19]. Beam deflection and position control are critical for cascaded structures with longer interaction lengths or for beam steering or undulator applications. Future experiments with femtosecond photocathode electron sources would allow full characterization of the attosecond electron bunches .
In summary, we have demonstrated, to the best of our knowledge, the first silicon-based laser accelerator and deflection structure, with accelerating gradients of more than with subrelativistic electrons. We have also measured the deflection characteristics of DLA structures for the first time, to the best of our knowledge. The dielectric, electrical, and mechanical properties of silicon, combined with its superb micro-fabrication capabilities, make silicon DLAs well suited to acceleration of electrons for attosecond applications. Single-stage DLAs could be used for optical streaking, compression, or chopping of electron beams at attosecond timescales for ultrafast electron diffraction experiments and time-resolved electron microscopy. Cascaded, chirped DLA structures for compact, high-brightness x-ray FELs, radiation therapy devices, and high-energy physics could make these technologies accessible at dramatically lower cost and size scales than with RF technology.
Air Force Office of Scientific Research (AFOSR) (FA9550-14-1-0190); Defense Advanced Research Projects Agency (DARPA) (N66001-11-1-4419); U.S. Department of Energy (DOE) (DE-SC0010511).
We thank J. Perales, M. Hennessy, K. Urbanek, E. Wei, and A. Ceballos for technical assistance, and P. Hommelhoff, J. Breuer, R. J. England, O. Solgaard, C. M. Chang, M. Morf, B. Lantz, and D. Waltz for helpful discussions. Devices were fabricated in the Stanford Nanofabrication Facility and Stanford Nano Center.
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