111 research outputs found
Local orbital angular momentum revealed by spiral phase plate imaging in transmission electron microscopy
The orbital angular momentum (OAM) of light and matter waves is a parameter
that is getting increasingly more attention over the past couple of years.
Beams with a well defined OAM, the so-called vortex beams, are applied already
in e.g. telecommunication, astrophysics, nanomanipulation and chiral
measurements in optics and electron microscopy. Also the OAM of a wave induced
by the interaction with a sample, shows great potential of interest. In all
these experiments it is crucial to measure the exact (local) OAM content of the
wave, whether it is an incoming vortex beam or an exit wave after interacting
with a sample. In this work we investigate the use of spiral phase plates as an
alternative to the programmable phase plates used in optics to measure OAM. We
derive analytically how these can be used to study the local OAM components of
any wave function. By means of numerical simulations we illustrate how the OAM
of a pure vortex beam can be measured. We also look at a sum of misaligned
vortex beams and show how using SPPs the position and the OAM of each
individual beam can be detected. Finally we look at the OAM induced by a
magnetic dipole on a free electron wave and show how the SPP can be used to
localize the magnetic poles and measure their "magnetic charge".
Although our findings can be applied to study the OAM of any wave function,
they are of particular interest for electron microscopy where versatile
programmable phase plates do not yet exist.Comment: 7 pages, 5 figure
Extension of Friedel's law to Vortex Beam Diffraction
Friedel's law states that the modulus of the Fourier transform of real
functions is centrosymmetric, while the phase is antisymmetric. As a
consequence of this, elastic scattering of plane wave photons or electrons
within the first-order Born-approximation as well as Fraunhofer diffraction on
any aperture, is bound to result in centrosymmetric diffraction patterns.
Friedel's law, however, does not apply for vortex beams, and centrosymmetry in
general is not present in their diffraction patterns. In this work we extend
Friedel's law for vortex beams by showing that the diffraction patterns of
vortex beams with opposite topological charge, scattered on the same two
dimensional potential, always are centrosymmetric to one another, regardless of
the symmetry of the scattering object. We verify our statement by means of
numerical simulations and experimental data. Our research provides deeper
understanding in vortex beam diffraction and can be used to design new
experiments to measure the topological charge of vortex beams with diffraction
gratings, or study general vortex beam diffraction.Comment: 7 pages, 3 figure
Inelastic electron-vortex-beam scattering
Recent theoretical and experimental developments in the field of electron
vortex beam physics have raised questions on what exactly this novelty in the
field of electron microscopy (and other fields, such as particle physics)
really provides. An important part in the answer to those questions lies in
scattering theory. The present investigation explores various aspects of
inelastic quantum scattering theory for cylindrically symmetric beams with
orbital angular momentum. The model system of Coulomb scattering on a hydrogen
atom provides the setting to address various open questions: How is momentum
transferred? Do vortex beams selectively excite atoms, and how can one employ
vortex beams to detect magnetic transitions? The analytical approach presented
here provides answers to these questions. OAM transfer is possible, but not
through selective excitation; rather, by pre- and post-selection one can filter
out the relevant contributions to a specific signal
Rutherford scattering of electron vortices
By considering a cylindrically symmetric generalization of a plane wave, the
first Born approximation of screened Coulomb scattering unfolds two new
dimensions in the scattering problem: transverse momentum and orbital angular
momentum of the incoming beam. In this paper, the elastic Coulomb scattering
amplitude is calculated analytically for incoming Bessel beams. This reveals
novel features occurring for wide angle scattering when the incoming beam is
correctly prepared. The result successfully generalizes the well known
Rutherford formula, incorporating transverse and orbital angular momentum into
the formalism.Comment: 9 pages, 5 figure
Measuring the Orbital Angular Momentum of Electron Beams
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 knife-edge and the application of an astigmatic
lens are all experimentally demonstrated. The viability and limitations of each
are discussed with supporting numerical simulations.Comment: 5 pages, 4 figurs
Observation of the Larmor and Gouy Rotations with Electron Vortex Beams
Electron vortex beams carrying intrinsic orbital angular momentum (OAM) are
produced in electron microscopes where they are controlled and focused using
magnetic lenses. We observe various rotational phenomena arising from the
interaction between the OAM and magnetic lenses. First, the Zeeman coupling,
proportional to the OAM and magnetic field strength, produces an
OAM-independent Larmor rotation of a mode superposition inside the lens.
Second, hen passing through the focal plane, the electron beam acquires an
additional Gouy phase dependent on the absolute value of the OAM. This brings
about the Gouy rotation of the superposition image proportional to the sign of
the OAM. A combination of the Larmor and Gouy effects can result in the
addition (or subtraction) of rotations, depending on the OAM sign. This
behaviour is unique to electron vortex beams and has no optical counterpart, as
Larmor rotation occurs only for charged particles. Our experimental results are
in agreement with recent theoretical predictions.Comment: 5 pages, 5 figure
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