Improved control of electron computer-generated holographic grating groove profiles using ion beam gas-assisted etching

Principles of electron wave front modulation with two miniature electron mirrors

We have analyzed the possibilities of wave front shaping with miniature patterned electron mirrors through the WKB approximation. Based on this, we propose a microscopy scheme that uses two miniature electron mirrors on an auxiliary optical axis that is in parallel with the microscope axis. A design for this microscopy scheme is presented for which the two axes can be spatially separated by as little as 1 mm. We first provide a mathematical relationship between the electric potential and the accumulated phase modulation of the reflected electron wave front using the WKB approximation. Next, we derive the electric field in front of the mirror, as a function of a topographic or pixel wise excited mirror pattern. With this, we can relate the effect of a mirror pattern onto the near-field phase, or far field intensity distribution and use this to provide a first optical insight into the functioning of the patterned mirror. The equations can only be applied numerically, for which we provide a description of the relevant numerical methods. Finally, these methods are applied to find mirror patterns for controlled beam diffraction efficiency, beam mode conversion, and an arbitrary phase and amplitude distribution. The successful realization of the proposed methods would enable arbitrary shaping of the wave front without electron-matter interaction, and hence we coin the term virtual phase plate for this design. The design may also enable the experimental realization of a Mach-Zehnder interferometer for electrons, as well as interaction-free measurements of radiation sensitive specimen.

Experimental realization of a π/2 vortex mode converter for electrons using a spherical aberration corrector

In light optics, beams with orbital angular momentum (OAM) can be produced by employing a properly-tuned two-cylinder-lens arrangement, also called π/2 mode converter. It is not possible to convey this concept directly to the beam in an electron microscope due to the non-existence of cylinder lenses in commercial transmission electron microscopes (TEMs). A viable work-around are readily-available electron optical elements in the form of quadrupole lenses. In a proof-of-principle experiment in 2012, it has been shown that a single quadrupole in combination with a Hilbert phase-plate produces a spatially-confined, transient vortex mode. Here, an analogue to an optical π/2 mode converter is realized by repurposing a CEOS DCOR probe corrector in an aberration corrected TEM in a way that it resembles a dual cylinder lens using two quadrupoles. In order to verify the presence of OAM in the output beam, a fork dislocation grating is used as an OAM analyser. The possibility to use magnetic quadrupole fields instead of, e.g., prefabricated fork dislocation gratings to produce electron beams carrying OAM enhances the beam brightness by almost an order of magnitude and delivers switchable high-mode purity vortex beams without unwanted side-bands.

Interaction-Free Measurement with Electrons

Here, we experimentally demonstrate interaction-free measurements with electrons using a novel electron Mach-Zehnder interferometer. The flexible two-grating electron interferometer is constructed in a conventional transmission electron microscope and achieves high contrast in discrete output detectors, tunable alignment with independently movable beam splitters, and scanning capabilities for imaging. With this path-separated electron interferometer, which closely matches theoretical expectations, we demonstrate electron interaction-free measurements with an efficiency of 14±1%. Implementing this quantum protocol in electron imaging opens a path toward interaction-free electron microscopy.

Ultrafast laser ablation of 10-nm self-supporting membranes by two-beam interference processing

Ultrafast laser ablation was applied to process 10-nm self-supporting membranes. The membranes were processed over tens of square micrometers by single-shot irradiation of two visible laser pulses, followed by the realization of periodic sub-microstructures. The fabricated geometry is dependent on the intensity distribution of the superposed input pulses, providing flexibility and facilitating practical micro- and nanoengineering. Ease of designing the processing parameters and speed of processing are the significant advantages of this method compared to focused ion beam (FIB) milling.

Exact design of complex amplitude holograms for producing arbitrary scalar fields

Typical methods to holographically encode arbitrary wavefronts assume the hologram medium only applies either phase shifts or amplitude attenuation to the wavefront. In many cases, phase cannot be introduced to the wavefront without also affecting the amplitude. Here we show how to encode an arbitrary wavefront into an off-axis transmission hologram that returns the exact desired arbitrary wavefunction in a diffracted beam for phase-only, amplitude-only, or mixed phase and amplitude holograms with any periodic groove profile. We apply this to design thin holograms for electrons in a TEM, but our results are generally applicable to light and X-ray optics. We employ a phase reconstruction from a series of focal plane images to qualitatively show the accuracy of this method to impart the expected amplitude and phase to a specific diffraction order.