381 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
Quantitative measurement of orbital angular momentum in electron microscopy
Electron vortex beams have been predicted to enable atomic scale magnetic
information measurement, via transfer of orbital angular momentum. Research so
far has focussed on developing production techniques and applications of these
beams. However, methods to measure the outgoing orbital angular momentum
distribution are also a crucial requirement towards this goal. Here, we use a
method to obtain the orbital angular momentum decomposition of an electron
beam, using a multi-pinhole interferometer. We demonstrate both its ability to
accurately measure orbital angular momentum distribution, and its experimental
limitations when used in a transmission electron microscope.Comment: 6 pages, 5 figure
Symmetry-constrained electron vortex propagation
Electron vortex beams hold great promise for development in transmission
electron microscopy, but have yet to be widely adopted. This is partly due to
the complex set of interactions that occur between a beam carrying orbital
angular momentum (OAM) and a sample. Herein, the system is simplified to focus
on the interaction between geometrical symmetries, OAM and topology. We present
multiple simulations, alongside experimental data to study the behaviour of a
variety of electron vortex beams after interacting with apertures of different
symmetries, and investigate the effect on their OAM and vortex structure, both
in the far-field and under free-space propagation.Comment: 11 page
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
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
Exploiting lens aberrations to create electron vortex beams
A model for a new electron vortex beam production method is proposed and
experimentally demonstrated. The technique calls on the controlled manipulation
of the degrees of freedom of the lens aberrations to achieve a helical phase
front. These degrees of freedom are accessible by using the corrector lenses of
a transmission electron microscope. The vortex beam is produced through a
particular alignment of these lenses into a specifically designed astigmatic
state and applying an annular aperture in the condensor plane. Experimental
results are found to be in good agreement with simulations.Comment: 5 pages, 4 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
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