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Principles of electron wave front modulation with two miniature electron mirrors.

M A R Krielaart1, P Kruit1

  • 1Delft University of Technology, Faculty of Applied Sciences, Department of Imaging Physics, Lorentzweg 1, 2628 CJ Delft, The Netherlands.

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|December 5, 2021
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Summary

We present a novel microscopy technique using patterned electron mirrors for precise wave front shaping. This method enables arbitrary control over electron beams without material interaction, acting as a "virtual phase plate".

Keywords:
Beam shapingElectron mirrorsElectron wave front modulationWKB approximation

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Area of Science:

  • Electron optics
  • Wavefront shaping
  • Microscopy

Background:

  • Electron wave front manipulation is crucial for advanced microscopy.
  • Existing methods often involve electron-matter interactions, limiting precision.

Purpose of the Study:

  • To propose and design a microscopy scheme for arbitrary electron wave front shaping.
  • To introduce miniature patterned electron mirrors as a 'virtual phase plate'.

Main Methods:

  • Utilizing the WKB approximation to analyze wave front modulation by patterned electron mirrors.
  • Deriving electric fields and relating mirror patterns to phase modulation and intensity distributions.
  • Employing numerical methods to determine optimal mirror patterns.

Main Results:

  • Established a mathematical framework linking electric potential to phase modulation.
  • Derived electric fields based on mirror topography for near-field and far-field analysis.
  • Identified mirror patterns for controlled diffraction efficiency, mode conversion, and arbitrary phase/amplitude distributions.

Conclusions:

  • The proposed 'virtual phase plate' enables precise, non-interactive electron wave front shaping.
  • This technology could facilitate electron Mach-Zehnder interferometry and interaction-free measurements.