Laser-Based Acceleration of Nonrelativistic Electrons at a Dielectric Structure

A proof-of-principle experiment demonstrating dielectric laser acceleration of nonrelativistic electrons in the vicinity of a fused-silica grating is reported. The grating structure is utilized to generate an electromagnetic surface wave that travels synchronously with and efficiently imparts momentum on 28 keV electrons. We observe a maximum acceleration gradient of $25\mathrm{MeV}/\mathrm{m}$. We investigate in detail the parameter dependencies and find excellent agreement with numerical simulations. With the availability of compact and efficient fiber laser technology, these findings may pave the way towards an all-optical compact particle accelerator. This work also represents the demonstration of the inverse Smith-Purcell effect in the optical regime.

Figure 1

(a)–(c) Three subsequent conceptual pictures of four charged particles (encircled numbers) passing the transparent grating (shaded structure, white: vacuum) that is illuminated by the laser from below. Time step between each picture: $1/4$ optical period. The laser is linearly polarized in the plane of projection and propagates upward. Snapshots of the electric field distribution of the first spatial harmonic ($n=1$) are shown above the grating. It falls off exponentially with increasing distance from the grating and copropagates synchronously with the charged particle along the grating surface. Depending on the position of the charged particle inside the field, the force acts accelerating (1), decelerating (2), or deflecting (3),(4) as indicated by the arrows and the color shading. Here, we take the design particles to be positrons. (d) Electric field distribution of the third spatial harmonic ($n=3$) as used in this work. (e) Simulated ratio between the acceleration gradient $G_{\mathrm{acc}}$ and the applied laser peak electric field $E_p$ for the first (upper curve) and third (lower curve) spatial harmonic for electrons passing a grating at a distance of 50 nm. Note that acceleration with the fundamental is more efficient because of diffraction effects. (f) Scanning electron microscope image of the fused silica grating. Details are given in the Supplemental Material [17].

Figure 2

Sketch of the experimental setup and detection scheme. Electrons emitted from a scanning electron microscope column (left) pass the transparent grating. Here they interact with the accelerating field excited by the laser pulses (propagating from bottom to top). A microscope objective is used to monitor the position of the laser focus. The electrons that can pass the spectrometer (center) are detected at the MCP. (The trajectories entering the spectrometer are drawn as slightly off-center, hence the deviation from the electron optical axis inside the spectrometer.) Details on the detection scheme are given in the Supplemental Material [17].

Figure 3

(a) Measurement of the accelerated fraction of electrons $I_{\mathrm{acc}}/I_{\mathrm{eff}}$ as a function of energy gain (bottom axis) and acceleration gradient (top axis), for two different laser peak electric fields [$E_p=2.85\mathrm{GV}/\mathrm{m}$ (circles), $E_p=2.36\mathrm{GV}/\mathrm{m}$ (squares)], with corresponding simulated curves. The only free parameters of the simulated curves are the distance $z_0$ of the electron beam center from the grating surface, implying $z_0=(120\pm 10)\mathrm{nm}$, and the overall amplitude. (b) Dependence of the accelerated fraction on the laser polarization angle $\varphi$. The data can be well fitted with the expected sinusoidal behavior (solid curve). 0° means that the laser polarization is parallel to the electrons’ momentum, 90° that it is perpendicular to it (see inset). (c) Measurement of the accelerated fraction versus the relative distance between the grating surface (shaded area) and the electron beam center. Note that due to the finite width of the electron beam some electrons are accelerated even when the beam center lies slightly inside the grating. Solid line: Gaussian fit. Note further that the accelerated fraction of electrons depends on the chosen energy threshold; hence, one may not expect to reach 50%. (d) Measurement (circles) and ab initio simulation (squares) of the maximum acceleration gradient as a function of the initial electron energy. In order to reduce the measuring time we define the maximum acceleration gradient in this measurement to lie at a larger accelerated fraction than in Fig. 3a ($4\times {10}^{-2}$ vs $5\times {10}^{-3}$), which explains why we measure a maximum gradient of $\sim 20\mathrm{MeV}/\mathrm{m}$ instead of $25\mathrm{MeV}/\mathrm{m}$. The slight deviation of the curves’ widths requires further investigations. This measurement confirms that efficient acceleration occurs only if the synchronicity condition is satisfied. The lines are guides to the eye. See the Supplemental Material [17] for details.

Figure 4

Sketch of an envisioned layout of an all-optical linear accelerator with electron gun (A), nonrelativistic (B), and relativistic sections (C), all driven by a common, for ease of operation fiber-based, laser source. The nonrelativistic section consists of grating structures with a tapered grating period to assure synchronicity with the accelerating electrons using the third (B1), second (B2), and first (B3) spatial harmonic. Inside the nonrelativistic section, the channel width can increase because of the increasing decay constant $\Gamma$ of the accelerating fields. Not to scale.