Dielectric laser accelerators

The use of infrared lasers to power optical-scale lithographically fabricated particle accelerators is a developing area of research that has garnered increasing interest in recent years. The physics and technology of this approach is reviewed, which is referred to as dielectric laser acceleration (DLA). In the DLA scheme operating at typical laser pulse lengths of 0.1 to 1 ps, the laser damage fluences for robust dielectric materials correspond to peak surface electric fields in the $\mathrm{GV}/\mathrm{m}$ regime. The corresponding accelerating field enhancement represents a potential reduction in active length of the accelerator between 1 and 2 orders of magnitude. Power sources for DLA-based accelerators (lasers) are less costly than microwave sources (klystrons) for equivalent average power levels due to wider availability and private sector investment. Because of the high laser-to-particle coupling efficiency, required pulse energies are consistent with tabletop microJoule class lasers. Combined with the very high (MHz) repetition rates these lasers can provide, the DLA approach appears promising for a variety of applications, including future high-energy physics colliders, compact light sources, and portable medical scanners and radiative therapy machines.

Figure 1

Four different configurations of dielectric acceleration structures. (a), (c) The beam is cylindrical, whereas in (b), (d) the beam may be elliptical or flat (high aspect ratio). The characteristic parameters are also presented.

Figure 2

Laser to electron coupling efficiency vs the number of electron microbunches per laser pulse. Adapted from [137].

Figure 3

(a) Axial electric field strengths in a 2D hexagonal lattice and (b) the optimized photonic 2D quasicrystal cavity. From [15].

Figure 4

Cross section of a biperiodic dielectric laser accelerator based on photonic confinement and optimized for strong second-order focusing. From [139].

Figure 5

Longitudinal phase space showing stable accelerating bucket and unbound trajectories.

Figure 6

Longitudinal phase space during adiabatic capture and bunching.

Figure 7

Longitudinal phase space after strong acceleration.

Figure 8

Fundamental mode of the longitudinal wakefield (left axis, solid curve) generated by a Gaussian bunch (right axis, dashed curve) in the Lin fiber accelerator.

Figure 9

The laser damage threshold of a variety of optical materials, as well as copper, for comparison. Each of these measurements were conducted with a 1 ps, 800 nm, 600 Hz Ti:sapphire laser. The data indicate a strong positive correlation between the damage threshold, the material band gap, and the material’s lattice binding energy. From [196].

Figure 10

Observed values of laser damage threshold at 1053 nm for fused silica (circle) and ${\mathrm{CaF}}_2$ (diamond). Solid lines are ${\tau }^{1/2}$ fits to long pulse results. Estimated uncertainty in the absolute fluence is about 15%. From [206].

Figure 11

Laser damage threshold of silicon for picosecond laser pulses in the near to short wavelength infrared. The damage model (solid curve) is superimposed on top of the experimental data. From [197].

Figure 12

Snapshots of the longitudinal field ($E_x$) in the grating structure at five points in time across one period, showing its principle of operation: each grating pillar provides a $\pi$ phase delay such that a correctly phased particle experiences net acceleration. From [150].

Figure 13

FDTD optimization of acceleration gradient (solid curves, left axis) with corresponding net deflection force (dashed curves, right axis) as a function of (a) grating pillar height with a fixed gap of 400 nm, (b) grating-to-grating gap with an optimal pillar height, (c) grating pillar width with a fixed gap of 400 nm and pillar height of 620 nm, and (d) grating-to-grating longitudinal misalignment with a fixed gap of 400 nm, pillar height of 620 nm, and pillar width of 480 nm.

Figure 14

Fabrication process for the (a) dual-layer grating structure, and cross-sectional SEM images of resulting (b) 400 nm and (c) 1200 nm gap structures. Adapted from [150].

Figure 15

(a) The experimental setup and (b) measured accelerating gradient as a function of laser electric field for the dual-grating acceleration experiment at SLAC. Each data point in (b) corresponds to a fitted curve of energy modulation vs relative timing of the laser and electron beam. From [151].

Figure 16

First layer width for Bragg TM and TE modes with speed-of-light phase velocity, normalized by ${\mathrm{\Delta }}_q={\lambda }_0/4\sqrt{{ϵ}_1-1}$. The layer adjacent to the core has a refractive index of 1.6 and the other material has an index of 4.6. From [126].

Figure 17

Planar TM profiles for vacuum core Bragg structures. (a) $k_x{D}_{\text{int}}=0$ and low refractive index first. (b) $k_x{D}_{\text{int}}=0$ and high refractive index first. (c) $k_x{D}_{\text{int}}=\pi /3$. (d) $k_x{D}_{\text{int}}=3\pi /4$. (e) $k_x{D}_{\text{int}}=\pi /2$ (metallic-like walls). (f) $k_x{D}_{\text{int}}=\pi$ (magnetic-like walls). The normalized decay parameter ${\alpha }^{\prime }=\alpha {\lambda }_0/\tan \delta$, and $\xi$ is the ratio of the power flowing in the core to the total power. From [126].

Figure 18

Symmetric TM mode dispersion diagram. Left frame: Planar waveguide with $D_{\text{int}}=0.3{\lambda }_0$. Right frame: Cylindrical waveguide with $R_{\text{int}}=0.3{\lambda }_0$. In both cases the dashed curves are obtained with no design procedure (first layer identical to the remainder of the structure), and the solid curves correspond to a $v_{\text{ph}}=c$ design procedure. From [126].

Figure 19

Quarter cross section of the Lin PBG fiber accelerator, consisting of a lattice of vacuum holes (light gray) in a glass substrate (dark gray) with lattice period $a$ and hole radii $r=0.35a$. The periodic lattice holes serve to confine the accelerating mode, and the particle beam is accelerated within the central defect, radius $R=0.52a$, propagating perpendicular to the page. From [140].

Figure 20

Photographs showing (a) 700-μm-wide cross section of a hollow-core PBG fiber drawn from borosilicate glass, and (b) magnified view of the 12-μm central defect hole, where the air holes show up as black against the light gray of the glass matrix.

Figure 21

The lowest band gaps near the light line ($v=c$) for the Lin fiber plotted on the frequency vs wave-number dispersion plane as calculated with R-Soft BandSolve photonics software ([170]). When a defect hole of the correct size is introduced, a TM mode with dispersion line crossing the light line appears in the band gap. From [143].

Figure 22

(a) Longitudinal and (b) radial electric field intensities of the defect mode crossing the light line in the PBG fiber, as calculated with a multipole solver ([103]). The white circles indicate the hole boundaries. A rainbow color scheme (the legend) is used to represent linear magnitude of the relative field intensity with the different colors being the maximum (1) and minimum (0). From [143].

Figure 23

The geometry of a woodpile accelerating waveguide structure. From [42].

Figure 24

The accelerating field seen by a speed-of-light particle, averaged over a lattice period, normalized to the accelerating field on axis, shown with structure contours for a transverse slice at $z=0$. The inner rectangle denotes the interface between free space and the absorbing boundary in the simulation. From [44].

Figure 25

Visual outline of the woodpile fabrication process. From [119].

Figure 26

Front and back images of an aligned and bonded structure. A slight transverse offset can be seen, corresponding to approximately one-third of a lattice period. Angular alignment of this structure was very accurate. From [119].

Figure 27

A single period of the focusing structure design, with optimizable parameters labeled. From [195].

Figure 28

Four independent electron bunches (left) traversing the grating BPM structure at four unique positions along the BPM, as viewed from the top, and the resulting radiation spectrum (right) from each of the four electron bunches. The inset demonstrates the resolvability of the two closely separated spectral distributions. From [194].

Figure 29

Schematics of lateral taper designs. From [130].

Figure 30

Schematics of the grating coupler with bottom metal mirror. From [186].

Figure 31

Poynting flux distribution from the accelerating mode radiating from the end of a PBG fiber accelerator (located at origin $x=y=z=0$) on a hemispherical surface of radius $80\lambda$. From [140].

Figure 32

Simulation geometry for high-efficiency transverse power coupling to the woodpile structure from a TE mode silicon guide to a TM mode accelerating channel where the electron beam (ellipse) travels.

Figure 33

Schematics of the waveguide network with waveguide splitters and optical delay lines. From [150].

Figure 34

Schematics of (a) conventional SOI waveguides: channel and ridge waveguides; (b) monolithic silicon waveguide in standard silicon.

Figure 35

Schematics of the power distribution network using ARROW structure. From [231].

Figure 36

Plot of Eq. (71) with $\eta /{\sigma }_{\gamma }=2.5$ and ${\beta }_b=1$. Density is relative to the initial density (${\rho }_0=1$). From [184].

Figure 37

Layout of a multicolor IFEL microbuncher and resulting longitudinal phase space. From [56].

Figure 38

The laser system baseline design. The outlined boxes highlight the challenging portions of the system. A total of $M$ local oscillators will be built and split $N$ times, giving a total of $M\times N$ laser coupled accelerator structures. From [18].

Figure 39

A laser undulator employing a laser side-coupled (a) slanted grating ([152]) or (b) Bragg waveguide to derive the undulator deflecting force with an undulator period much longer than the laser wavelength. From [214].

Figure 40

(a) Undulator period for 1 nm (dashed) and 0.1 nm (solid) radiation wavelengths vs electron energy subject to a 1-$\mathrm{GV}/\mathrm{m}$ laser damage field on a dielectric laser undulator. Quantum (white) and classical (colored) regimes on the current vs gamma plane for an XFEL radiating at (b) 0.1 nm and (c) 1 nm. Constant-gain-length curves are also shown with their values marked in units of millimeters (leftmost section: $\overline{\rho }<1$, second from left section: $1<\overline{\rho }<10$, third from left section: $10<\overline{\rho }<100$, rightmost section: $\overline{\rho }>100$).

Figure 41

Schematic of a self-contained DLA encapsulated as a fiber endoscope.