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All-optical three-dimensional electron pulse compression

We propose an all-optical, three-dimensional electron pulse compression scheme in which Hermite-Gaussian optical modes are used to fashion a three-dimensional optical trap in the electron pulse's rest frame. We show that the correct choices of optical incidence angles are necessary for optimal compression. We obtain analytical expressions for the net impulse imparted by Hermite-Gaussian free-space modes of arbitrary order. Although we focus on electrons, our theory applies to any charged particle and any particle with non-zero polarizability in the Rayleigh regime. We verify our theory numerically using exact solutions to Maxwell's equations for first-order Hermite-Gaussian beams, demonstrating single-electron pulse compression factors of $>10^{2}$ in both longitudinal and transverse dimensions with experimentally realizable optical pulses. The proposed scheme is useful in ultrafast electron imaging for both single- and multi-electron pulse compression, and as a means of circumventing temporal distortions in magnetic lenses when focusing ultrashort electron pulses.