Measuring the orbital angular momentum of electron beams

Abstract

The recent demonstration of electron vortex beams has opened up the new possibility of studying orbital angular momentum (OAM) in the interaction between electron beams and matter. To this aim, methods to analyze the OAM of an electron beam are fundamentally important and a necessary next step. We demonstrate the measurement of electron beam OAM through a variety of techniques. The use of forked holographic masks, diffraction from geometric apertures, diffraction from a knifeedge and the application of an astigmatic lens are all experimentally demonstrated. The viability and limitations of each are discussed with supporting numerical simulations.

Origins and demonstrations of electrons with orbital angular momentum

“…An electron vortex beam with topological charge 2 breaks up into two separate vortices. This can be used as a quick way to characterize the OAM of the electron beam [61,63]. Schattschneider et al [62] used this mode conversion to prepare electron vortex beams.…”

“…Unlike the case for light, isolation of inelastically scattered electrons can be challenging, so non-interferometric methods to measure OAM may be necessary for inelastic scattering experiments with electron vortex beams. Three different non-interferometric methods have been demonstrated: diffraction grating-based phase flattening [63,64], measurements using apertures [63] and mode transformation with cylindrical lenses [61,63], yet none of these techniques are suitable for measuring mixtures of OAM in scattered electrons. Two new proposed techniques for sorting electrons based on OAM include magnetic lens-based on-axis sorting [65], and electrostatic off-axis sorting [66,67].…”

Spin-orbit states of neutron wave packets

“…This work is related to manipulating orbital angular momentum states of photons [3][4][5][6][7] and electrons [8][9][10][11]. Neutrons have also an intrinsic spin of /2, and in this work we suggest a means of coupling the neutron spin and OAM to prepare an entangled spin-orbit state of a neutron wavepacket.…”

Measuring OAM states of light beams with gradually-changing-period gratings

“…Several methods have been studied to measure the OAM states, such as amplitude diffractive optical elements including triangular slit [9], single-slit [10], double-slit [11,12], and forked grating [13,14]. When OAM beams propagate through these elements, their far-field diffractions will present particular features.…”