Electron Beam Shaping
Electron microscopy has, for many years, been related to two concepts: creating approximate plane waves to obtain a sample snapshot or producing very tiny probes to scan the sample for imaging and advanced spectroscopy.
Yet, there is much more to this than simple electron optics, and hints of this have been derived from experiments in light optics, starting from the idea of vortex beams as introduced by M. Berry. Beam shaping is the art of controlling the electron wavefunction before and/or after the sample. We have been among the pioneers of this idea, with early works on phase holograms and MEMS-based electron optics. Holograms are structured pieces of electron-transparent material that modulate the phase of electrons through their thickness. They are typically created using FIB or EBL structuring techniques.
By using holograms, we are able to control both the amplitude and phase of the electron beam.
In the figure, we show:
- a) the CNR logo created as the diffraction pattern of the hologram above,
- b) a combination of two Laguerre-Gaussian beams,
- c) a vortex beam.
All these beams are examples of the nearly unlimited possibilities that this technique offers, with applications in spectroscopy, diffraction, and imaging.
Holograms can also be used for the correction of spherical aberrations.
The problem with holograms is that:
- 1. They are not programmable or tunable.
- 2. They become charged under the electron beam, and this charging can distort their effect.
A solution we found is to work with MEMS electrostatic technology.
We specialize in harmonic phase plates that introduce nearly no obstruction to the electron beam’s path. Using accurate analytical and numerical models, we are able to predict the smooth phase landscape produced by a few electrodes.
Some examples of the possible applications of these phase plates are shown here.
The implementation of this technology has been made possible thanks to a close collaboration with Thermo Fisher, with whom we developed our unique, specialized aperture holder featuring pass-through fields to control the beam.
One of the most important results of MEMS technology has been the creation of the first OAM (Orbital Angular Momentum) sorter.
The OAM sorter is a new electron optical element, inspired by light optics, capable of creating on the screen a spectroscopic representation of the angular momentum components of the electron beam after elastic or inelastic interactions with the sample.
The importance of this element can only be fully appreciated when considering that energy, momentum, and angular momentum are the most important conserved quantities of an electron’s motion, and only now can angular momentum finally be measured.
The technique for this measurement is based on optical conformal mapping of the wavefunction. It uses MEMS phase elements to produce, in the stationary phase approximation, a transformation into log-polar coordinates, such that an azimuthal phase gradient is converted into a linear gradient.
In the figure, we can see in the middle column the initial beam and its transformation into polar coordinates through the sorter. The result, shown on the right, produces an OAM spectrum. The peaks at ±4 indicate the beam’s fourfold symmetry.
The concept of geometrical transformation is so revolutionary that it has the potential to transform the very idea of measurement in microscopy, extending far beyond conventional imaging.
