48 research outputs found
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
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
HAADF-STEM block-scanning strategy for local measurement of strain at the nanoscale
Lattice strain measurement of nanoscale semiconductor devices is crucial for
the semiconductor industry as strain substantially improves the electrical
performance of transistors. High resolution scanning transmission electron
microscopy (HR-STEM) imaging is an excellent tool that provides spatial
resolution at the atomic scale and strain information by applying Geometric
Phase Analysis or image fitting procedures. However, HR-STEM images regularly
suffer from scanning distortions and sample drift during image acquisition. In
this paper, we propose a new scanning strategy that drastically reduces
artefacts due to drift and scanning distortion, along with extending the field
of view. The method allows flexible tuning of the spatial resolution and
decouples the choice of field of view from the need for local atomic
resolution. It consists of the acquisition of a series of independent small
subimages containing an atomic resolution image of the local lattice. All
subimages are then analysed individually for strain by fitting a nonlinear
model to the lattice images. The obtained experimental strain maps are
quantitatively benchmarked against the Bessel diffraction technique. We
demonstrate that the proposed scanning strategy approaches the performance of
the diffraction technique while having the advantage that it does not require
specialized diffraction cameras
Topological analysis of paraxially scattered electron vortex beams
We investigate topological aspects of sub-nm electron vortex beams upon
elastic propagation through atomic scattering potentials. Two main aspects can
be distinguished: (i) Significantly reduced delocalization compared to a
similar non-vortex beam if the beam centers on an atomic column and (ii) site
symmetry dependent splitting of higher-order vortex beams. Furthermore, the
results provide insight into the complex vortex line fabric within the
elastically scattered wave containing characteristic vortex loops predominantly
attached to atomic columns and characteristic twists of vortex lines around
atomic columns.Comment: 10 pages, 6 figure
Prospects for versatile phase manipulation in the TEM: beyond aberration correction
In this paper we explore the desirability of a transmission electron
microscope in which the phase of the electron wave can be freely controlled. We
discuss different existing methods to manipulate the phase of the electron wave
and their limitations. We show how with the help of current techniques the
electron wave can already be crafted into specific classes of waves each having
their own peculiar properties. Assuming a versatile phase modulation device is
feasible, we explore possible benefits and methods that could come into
existence borrowing from light optics where so-called spatial light modulators
provide programmable phase plates for quite some time now. We demonstrate that
a fully controllable phase plate building on Harald Rose's legacy in aberration
correction and electron optics in general would open an exciting field of
research and applications.Comment: 9 pages, 4 figures, special Ultramicroscopy issue for PICO2015
conferenc
Asymmetry and non-dispersivity in the Aharonov-Bohm effect
Decades ago, Aharonov and Bohm showed that electrons are affected by
electromagnetic potentials in the absence of forces due to fields. Zeilinger's
theorem describes this absence of classical force in quantum terms as the
"dispersionless" nature of the Aharonov-Bohm effect. Shelankov predicted the
presence of a quantum "force" for the same Aharonov-Bohm physical system as
elucidated by Berry. Here, we report an experiment designed to test Shelankov's
prediction and we provide a theoretical analysis that is intended to elucidate
the relation between Shelankov's prediction and Zeilinger's theorem. The
experiment consists of the Aharonov--Bohm physical system; free electrons pass
a magnetized nanorod and far--field electron diffraction is observed. The
diffraction pattern is asymmetric confirming one of Shelankov's predictions and
giving indirect experimental evidence for the presence of a quantum "force".
Our theoretical analysis shows that Zeilinger's theorem and Shelankov's result
are both special cases of one theorem.Comment: 16 pages, 5 figure
Shaping electron beams for the generation of innovative measurements in the (S)TEM
In TEM, a typical goal consists of making a small electron probe in the
sample plane in order to obtain high spatial resolution in scanning
transmission electron microscopy. In order to do so, the phase of the electron
wave is corrected to resemble a spherical wave compensating for aberrations in
the magnetic lenses. In this contribution we discuss the advantage of changing
the phase of an electron wave in a specific way in order to obtain
fundamentally different electron probes opening up new application in the
(S)TEM. We focus on electron vortex states as a specific family of waves with
an azimuthal phase signature and discuss their properties, production and
applications. The concepts presented here are rather general and also different
classes of probes can be obtained in a similar fashion showing that electron
probes can be tuned to optimise a specific measurement or interaction