Orbital Angular Momentum Transfer and Beam-Quality Limits in Fork-Grating Electron Diffraction

Abstract:We analyze fork-grating generation of electron vortex beams beyond the ideal single-mode approximation. The incident beam is described as a paraxial Gaussian ensemble with finite transverse momentum spread and a first electromagnetic Hartree phase accumulated before the grating. Within Fresnel propagation we derive an analytical expression for each diffraction order and determine the corresponding orbital-angular-momentum statistics. The mean OAM of a selected order remains fixed by the topological rule, $\langle L_z\rangle_m=mp\hbar$, while its variance is set by the residual transverse momentum spread of the beam prepared at the grating. For the Gaussian mixture, the transverse purity is $\mathcal P_{\perp,m}=[1+2(\Delta L_{z,m}/\hbar)^2]^{-1}$. The observed annular profile is governed by a separate propagation-dependent blurring scale, so a beam can retain well-defined mean OAM while having low transverse purity or a partially filled vortex minimum. Within the radial phase-screen approximation, the Hartree self-field modifies the propagated profile while preserving the full-plane OAM moments and transverse purity.

Optics (physics.optics); Quantum Physics (quant-ph)

arXiv:2610.18401 [physics.optics]

(or arXiv:2610.18401v1 [physics.optics] for this version)

https://doi.org/10.48550/arXiv.2610.18401 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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