Alternating-Phase Focusing for Dielectric-Laser Acceleration

The concept of dielectric-laser acceleration provides the highest gradients among breakdown-limited (nonplasma) particle accelerators. However, stable beam transport and staging have not been shown experimentally yet. We present a scheme that confines the beam longitudinally and in one transverse direction. Confinement in the other direction is obtained by a single conventional quadrupole magnet. Within the small aperture of 420 nm we find the matched distributions, which allow an optimized injection into pure transport, bunching, and accelerating structures. The combination of these resembles the photonics analogue of the radio frequency quadrupole, but since our setup is entirely two dimensional, it can be manufactured on a microchip by lithographic techniques. This is a crucial step towards relativistic electrons in the MeV range from low-cost, handheld devices and connects the two fields of attosecond physics and accelerator physics.

Figure 1

(Top panel) Schematic view of a dual pillar DLA structure and a particle bunch around a reference particle and (bottom panel) simulation of the longitudinal time harmonic electric field.

Figure 2

Overview of electron acceleration and focusing properties as a function of phase. The circles denote the fixed points for different ${\phi }_s$.

Figure 3

(Top panel) Contours of ${\widehat{\beta }}_{\max }=\widehat{\beta }(L/4)$ in the $(|e_1|,L)$ plane. The arrow indicates the laser amplitude dependent tuning range. (Bottom panel) The transverse phase space evolution (parameters at the black dot on top) of particles, not hitting the aperture ($\pm 0.21\mu \mathrm{m}$) within 1200 DLA cells, is shown as every two DLA cells. The blue ellipses are the linear theory, at minimum and maximum beam size.

Figure 4

Contours of ${\widehat{\beta }}_{\max }=\widehat{\beta }(L/4)$ in the $(\beta ,L)$ plane. The designed accelerator lattice is a trade-off between following the minimum and minimizing the mismatch at the jumps.

Figure 5

Analytical [Eq. (10)] and numerical (rms) beam envelopes, scaled to identical initial beam size at $ϵ=100\mathrm{pm}$. (Inset) Enlargement of the beginning.

Figure 6

(Right panels) Phase space after acceleration of a Gaussian bunch up to 1 MeV and (left panel) transmittable initial longitudinal distribution at 83 keV for $y=y^{\prime }=0$. The blue ellipse represents a linearly matched bunch with a total bunch length $4{\sigma }_z=40\mathrm{nm}$.

Figure 7

Periodic longitudinal phase space after APF bunching. The initial beam parameters for the accelerator given by the ellipses are met. The small plot shows the transverse phase space, where the particle phase is color coded.