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Diffractive electron optics

A sub-relativistic free electron propagating in vacuum can be accurately described as a de Broglie matter wave with a wavelength inversely proportional to its longitudinal momentum. As a result of the charge carried by the electron, electric fields, magnetic fields, or the electro-static mean inner potential of thin, weekly interacting materials can impart a phase shift to the wavefront of an electron wave ^[1]. Thickness modulated Si3N4 membranes as well and programmable phase shift devices have exploited these properties to apply spatially varying phase shifts to control the far field spatial intensity and phase of the electron wave. Devices like these have been used in experiments to arbitrarily shape the electron wavefront, correct the aberrations inherent to electron microscopes, resolve the orbital angular momentum of a free electron, as well as being used in experiments to measure dichroism in the interaction between the free electron and magnetic materials or plasmon nanostructures ^[2].

^ Pozzi, Giulio; Peter Hawkes (2016). "Particles and waves in electron optics and microscopy". Advances in imaging and electron physics. 194 (2): 1–336.
^ Shiloh, Roy; Lu, Peng-Han; Remez, Roei; Tavabi, Amir H; Pozzi, Giulio; Dunin-Borkowski, Rafal E; Arie, Ady (2019). "Nanostructuring of electron beams". Physica Scripta. 94 (3): 034004. doi:10.1088/1402-4896/aaf258. ISSN 0031-8949.

[1] Pozzi, Giulio; Peter Hawkes (2016). "Particles and waves in electron optics and microscopy". Advances in imaging and electron physics. 194 (2): 1–336.

[ShilohLu2019-2] Shiloh, Roy; Lu, Peng-Han; Remez, Roei; Tavabi, Amir H; Pozzi, Giulio; Dunin-Borkowski, Rafal E; Arie, Ady (2019). "Nanostructuring of electron beams". Physica Scripta. 94 (3): 034004. doi:10.1088/1402-4896/aaf258. ISSN 0031-8949.

[1]

[2]