Three Dimensional Alternating-Phase Focusing for Dielectric-Laser Electron Accelerators

The concept of dielectric-laser acceleration (DLA) provides the highest gradients among breakdown-limited (nonplasma) particle accelerators and thus the potential of miniaturization. The implementation of a fully scalable electron accelerator on a microchip by two-dimensional alternating phase focusing (APF), which relies on homogeneous laser fields and external magnetic focusing in the third direction, was recently proposed. In this Letter, we generalize the APF for DLA scheme to 3D, such that stable beam transport and acceleration is attained without any external equipment, while the structures can still be fabricated by entirely two-dimensional lithographic techniques. In the new scheme, we obtain significantly higher accelerating gradients at given incident laser field by additionally exploiting the new horizontal edge. This enables ultralow injection energies of about 2.5 keV ($\beta =0.1$) and bulky high voltage equipment as used in previous DLA experiments can be omitted. DLAs have applications in ultrafast time-resolved electron microscopy and diffraction. Our findings are crucial for the miniaturization of the entire setup and pave the way towards integration of DLAs in optical fiber driven endoscopes, e.g., for medical purposes.

Figure 1

Top: 3D APF DLA based on SOI dual pillars. Bottom: cross sections and $|e_1(x,y)|$ therein for in-phase APF (left) and counterphase APF (right, with approximation of $n_{\text{Si}{\mathrm{O}}_2}\approx 1$) and the beam channel $w\times h$ in green.

Figure 2

Relation of $i{k}_x$ and $i{k}_y$. The black dot represents the two-dimensional APF scheme ($k_x=0$) as introduced in [26]. The red and blue dots are examples of the in-phase and counterphase APF scheme, respectively.

Figure 3

Comparison of peak acceleration gradient and focusing strength of counterphase structures: (top panel) low energy for simplified vs full pillars and (bottom panel) high energy 3D vs 2D ($k_x=0$).

Figure 4

Height scan for a free-floating dual pillar (counterphase) setup at $\beta =0.31$. Periodically reoccurring vertical eigenmodes make the 2D case (dashed lines) exceptional.

Figure 5

Maximum of each $\widehat{\beta }$ function for different APF cell lengths. The bar indicates the Pareto front of the multiminimization, where the minimum of the arithmetic average is taken as initial guess for every cell length in the design.

Figure 6

Upper panel (design): envelopes for ${ϵ}_n=2.5\mathrm{pm}$ and kinetic energy ramp. Lower panel (3D analysis): complex electric field $E_z(0,0,z)$ and spatial Fourier coefficients $e_{10}^{(n)}$ calculated from the full field windowed in each DLA cell $n$. The dashed lines represent the individually computed values of $e_{10}$ under periodic boundary conditions, which were used for the design.

Figure 7

Comparison of the final energy spectrum and throughput from a DLAtrack6D [23] simulation vs tracking simulation in the full laser fields using CST [45]. The dashed vertical line is the design top energy.