Abstract
Beam shaping—the ability to engineer the phase and the amplitude of massive and massless particles—has long interested scientists working on communication, imaging, and the foundations of quantum mechanics. In light optics, the shaping of electromagnetic waves (photons) can be achieved using techniques that include, but are not limited to, direct manipulation of the beam source (as in x-ray free electron lasers and synchrotrons), deformable mirrors, spatial light modulators, mode converters, and holograms. The recent introduction of holographic masks for electrons provides new possibilities for electron beam shaping. Their fabrication has been made possible by advances in micrometric and nanometric device production using lithography and focused on ion beam patterning. This article provides a tutorial on the generation, production, and analysis of synthetic holograms for transmission electron microscopy. It begins with an introduction to synthetic holograms, outlining why they are useful for beam shaping to study material properties. It then focuses on the fabrication of the required devices from theoretical and experimental perspectives, with examples taken from both simulations and experimental results. Applications of synthetic electron holograms as aberration correctors, electron vortex generators, and spatial mode sorters are then presented.
Highlights
The transmission electron microscope was developed primarily to study matter at the highest spatial resolution
Light optics has provided a broad range of applications beyond imaging, with recent progress triggered by the concept of scitation.org/journal/jap structured light waves, whereby a wave front and its spatial intensity distribution can be controlled in a manner that goes beyond the use of conventional optical elements
In order to establish the relationship between groove profile and efficiency, we begin by explaining how an incoming wave function is transformed after its interaction with an S-computer-generated holograms (CGHs)
Summary
The transmission electron microscope was developed primarily to study matter at the highest spatial resolution. Modern days nanofabrication techniques, such as Focused Ion Beam (FIB) milling and Electron Beam Lithography (EBL), allow to imprint thickness modulations on a membrane with lateral and depth scales of tens of nm Such scales are the common ones needed to fabricate a synthetic hologram whose typical total dimensions are in the range of a few micrometers with details down to tens of nm. Developments have proceeded from rough amplitude modulations of electron waves to today’s fine and precise control over amplitude and phase modulations in the form of complex patterns. This Tutorial provides an overview of the theoretical and numerical calculation, fabrication, and analysis of synthetic electron holograms. In the third chapter, we show a series of examples of the possible uses of synthetic holograms
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