Operating modes of dual-grating dielectric laser accelerators

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Operating modes of dual-grating dielectric laser accelerators

Dylan S. Black, Zhexin Zhao, Kenneth J. Leedle, Yu Miao, Robert L. Byer, Shanhui Fan, and Olav Solgaard

Phys. Rev. Accel. Beams 23, 114001 – Published 10 November 2020

Abstract

In this work, we present a comprehensive theoretical description of the Lorentz force in dual-grating dielectric laser accelerators (DLA). Here we examine the dual-grating DLA under arbitrary illumination conditions, both single-side and dual-side drive. We improve upon previous descriptions of these forces by providing a unified description of all possible operating modes of these devices, and classify the modes into three categories. In particular, we predict the existence of the previously observed “line modes” and a novel “elliptical mode”, provide an experimental demonstration of this new mode, and suggest a possible application for it in improving the resolution of attosecond-scale streak cameras. Finally, we examine several complementary methods of tuning a dual-grating DLA to a desired operating mode—particularly dual-drive phase rotation and translational offset of the grating teeth.

Received 14 April 2020
Accepted 21 October 2020

DOI:https://doi.org/10.1103/PhysRevAccelBeams.23.114001

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Electromagnetic field calculations Low-energy multiple-particle dynamics Single-particle dynamics

Low- & intermediate-energy accelerators

Accelerators & Beams

Authors & Affiliations

Dylan S. Black ^1,*, Zhexin Zhao^1,*, Kenneth J. Leedle ¹, Yu Miao¹, Robert L. Byer ², Shanhui Fan¹, and Olav Solgaard ¹

¹Department of Electrical Engineering, Stanford University, 350 Serra Mall, Stanford, California 94305-9505, USA
²Department of Applied Physics, Stanford University, 348 Via Pueblo Mall, Stanford, California 94305-4090, USA

^*D. S. B. and Z. Z. contributed equally to this work.

Article Text

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Supplemental Material

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References

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Issue

Vol. 23, Iss. 11 — November 2020

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Images

Figure 1
An electron bunch travels along $z$ through a dual-grating DLA structure. The grating has periodicity $Λ$ and is assumed infinite in $x$ . Two lasers of equal amplitude with relative phase $θ_{r}$ are normally incident on the grating structure, with wave vectors $\pm k_{0} \hat{y}$ . A reference particle enters the structure traveling with speed $β c$ at some injection phase $α$ relative to the laser field, and experiences a force given by Eq. (20).
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Figure 2
The ( $Δ p_{⊥}$ , $Δ p_{∥}$ ) phase space is plotted for the three classes of modes. The (normalized) momentum kicks plotted here are derived by integration of the $n = 1$ component of Eq. (21) for an on-axis particle ( $y = 0$ ). $γ$ is set to 1 for convenience. As $α$ varies from 0 to $2 π$ , it traces out ellipses in ( $Δ p_{⊥}$ , $Δ p_{∥}$ ) space. Values of $r_{n}$ corresponding to the three mode classes are then chosen, and $θ_{r}$ is varied from 0 to $2 π$ for each mode. The rotated line (solid black) has $r_{1} = 0.1$ . The upright ellipse (dashed blue) has $r_{1} = e^{2 i}$ . The general ellipse (dashed red) has $r_{1} = 0.7 e^{i}$ . The principal modes occur when $θ_{r} = 0$ or $π$ . All other $θ_{r}$ values produce skew modes.
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Figure 3
This figure shows an elliptical profile produced by single-side illumination of a dual-pillar DLA device. The structure was originally designed for cosh mode operation, but can be made to produce elliptical beam profiles through suitable angle tuning. For a 57 keV beam, an energy gain of 500 eV corresponds to a longitudinal momentum kick of roughly $1.1 keV / c$ , and a 5 mrad deflection corresponds to a transverse momentum kick of roughly $1.2 keV / c$ . Note: The $r_{n}$ value for this ellipse was extracted by an elliptical fitting algorithm in MATLAB. The fit error is unknown due to large uncertainty in the horizontal (deflection) axis calibration. Please see the Supplemental Material [18] for experimental details.
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Figure 4
(a) Gliding one row of grating with respect to the other. The dual grating consists of two rows of rectangular silicon pillars with width $0.52 μ m$ , length $1.32 μ m$ , periodicity $1 μ m$ and electron channel width $0.4 μ m$ . The illumination laser wavelength is $2 μ m$ and electron velocity is $0.5 c$ . (b) shows the electric and magnetic field of the dual grating with glide ratio $g = 0.5$ and top-side illumination. The amplitude and phase of $r_{n}$ through tuning the glide ratio are shown in (c). (d) shows the amplitudes of the cosh and sinh modes as a function of the glide ratio.
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