Resonant phase matching by oblique illumination of a dielectric laser accelerator

In dielectric laser-driven accelerators (DLA), careful tuning of drive-laser wavelength and structure periodicity is typically required in order to hit the resonant condition and match the phase velocity of the accelerating wave to the electron beam velocity. By aggressively detuning (up to 30 mrad) the angle of incidence of the drive laser on a double grating DLA structure, we show that it is possible to recover resonant phase matching and maximize the energy modulation of an externally injected 6 MeV beam in an 800 nm period structure driven using a 780 nm laser. These results show that it is possible to power DLA structures away from their design working point, and excite accelerating fields in the gap with phase profiles that change by a relatively large amount period-to-period. This flexibility is a key feature of DLAs and a critical element in the realization of phase modulation–based ponderomotive focusing to demonstrate MeV energy gain and large capture in a single DLA stage.

Figure 1

Schematic of the Pegasus beamline for DLA acceleration. A 1–2 pC beam generated by a modified SLAC/UCLA/BNL rf photogun [28] is accelerated by the linear accelerator cavity (LINAC) which is tuned to reduce the energy spread to below 30 keV full width half max. The gun solenoid and a quadrupole (quad) lens triplet are used to focus the beam through the central vacuum chamber, where the DLA sample is located. After the chamber, a quad doublet is used to refocus the electrons onto a YAG screen located on the high-resolution dipole spectrometer. This final screen is viewed with an intensified camera. The optical system for the drive laser includes two achromatic lenses and a cylindrical lens to shape the intensity distribution at the DLA. A half wave plate (HWP) and polarising beam splitter (PBS) combination allow intensity control. In addition, there is a translation stage for timing alignment and tunable mirrors (M1, M2) for angle of incidence control.

Figure 2

(a) Schematic of the double grating DLA concept. A laser pulse is illuminating at angle $\theta$ with respect to the y axis the $500\mu \mathrm{m}$ long DLA structure. The electrons travel along $z$ in an 800 nm tall gap. (b) Overhead view of the sample holder used in the experiments. The sample holder serves multiple functions, accessed via translation in $x$ and $y$. A standard TEM copper grid (circled in white) is used to establish electron laser synchronization [30]. A phosphor screen (i) is mounted at 45° to check spatial overlap with the laser using an overhead camera. Outlined in red, narrow alignment channels in the DLA structure can be used to fine-tune the beam location. After insertion of the DLA sample, a signature of where the electron beam hits the sample (from the radiation emitted by the nontransmitted electrons passing in the fused silica) can also be picked up by this camera enabling a final “live” spatial alignment in grating structure, outlined in green (three grating sections). Downstream of the DLA, a featured collimator (ii) piece provides a large reference for the position of the sample holder.

Figure 3

(a) Schematic of the optical system delivering the laser to the DLA. Two achromatic lenses are used to obtain a small round spot size ($\mathrm{FWHM}=230\mu \mathrm{m}$) at the DLA plane. A cylindrical lens is then added to the transport in order to expand the laser beam along the acceleration axis. The angle of incidence is controlled by two mirrors, M1 and M2, before the reference iris, also shown. The displacement of the laser on that iris is converted to an angular offset, $\theta$, at the DLA grating. (b) Reverse ray-tracing with three example trajectories at 25, 30, and 35 mrad incidence angles. The dotted lines indicate the two achromatic lenses, and the solid vertical line is the iris position. (c) Three photos of the reference iris at different incidence angles are overlaid. There is a linear relationship between the angle of incidence at the sample $\theta$ and the displacement at the iris.

Figure 4

Two sample ICCD spectrometer images (bottom) with their corresponding lineouts (top) are shown. On the left, the unmodulated beam has a Lorenzian shape with a FWHM of 23.5 keV. A modulated spectra is shown in the right column.

Figure 5

Simulation of the energy profiles at the spectrometer (yellow lines) when the finite electron and laser spatial distributions are taken into account. The $f$ traces are obtained by convolving the intrinsic energy distribution function $g$ (red dashed) with the induced energy modulation $f_1$ (blue dotted). The top traces correspond to a small ${\sigma }_e/{\sigma }_l$ ratio and a nearly one-dimensional interaction. For a relatively small $\mathrm{\Delta }\xi$ (left column), the DLA interaction only broadens slightly the initial energy spectrum (shown in red). When the DLA peak energy modulation $\mathrm{\Delta }\xi$ is much larger than the spectrometer intrinsic resolution (right column), the characteristic double peak electron distribution is obtained. The larger ${\sigma }_e/{\sigma }_l$ ratio case is shown in the bottom row. In this case, which is the more typical case in our experimental setup, the electron beam experiences a wide range of laser intensities and the final energy profile is significantly different than the one-dimensional case.

Figure 6

Example of peak energy modulation fit for the measured energy lineout (blue points), as seen in the spectrometer image on the right of Fig. 4. In this case, the fit yields a spot size ratio ${\sigma }_e/{\sigma }_L=1.3$, and a peak energy modulation $\mathrm{\Delta }\xi =26\mathrm{keV}$. To give an idea of the sensitivity of the fit, we show what the curve would look like for a different energy modulation $\mathrm{\Delta }\xi =1\mathrm{keV}$ for which the RMSE with the data is more than doubled.

Figure 7

DLA peak energy modulation vs relative time of arrival of laser and e-beam at the DLA. The solid circles represent the mean of the three highest modulations at each delay. The black curve is a supergaussian fit which is used to extract the 2.7 ps FWHM for the temporal window of the interaction.

Figure 8

Observed gradient vs incident electric field. The solid circles are the average of the five peak modulations for each laser energy setpoint in the scan. The pink dashed curve shows the predicted energy modulation at the phase-matching condition. A small change in the angle of incidence on the structure (10 mrad offset) yields the black line which more closely matches the measured behavior. The saturation point is reached at $6\mathrm{GV}/\mathrm{m}$, with a corresponding peak acceleration gradient of $0.65\mathrm{GeV}/\mathrm{m}$. Damage threshold and available laser energy limited us in probing the structure at higher fields.

Figure 9

Peak energy modulation as a function of incident angle, with constant incident intensity. The simulated modulation curve in black matches the observed behavior and was obtained assuming an incident laser of 1 mJ and structure factor 0.18, as fit by the gradient scan. The blue dots denote the mean of the top five modulations at each angle.

Figure 10

Plot of the phase advance within the grating structure due to the angular offset of the incident laser. The observation of DLA acceleration signal up to 30 mrad incidence angle, corresponding to a phase advance of $194\mathrm{mrad}/\mathrm{period}$, confirms the large acceptance bandwidth of the double grating structure.