Abstract
The generation of electron vortex beams and the conversion of these beams into beams without angular momentum by means of astigmatic optical systems, or vice versa, has been pursued in the optical and the electron microscopy community, but also in the accelerator community in the past decades. Despite different conceptual approaches similar results have been achieved. By adapting the Courant-Snyder theory, which was originally developed for the description of optical properties of accelerators, to the description of laser modes it is shown, that identical mode converters have been developed for charged particle and for light beams, and that the Courant-Snyder phase and the Gouy phase are equivalent.
Highlights
Electron vortex beams, i.e., electron beams carrying an angular momentum, have gained interest in the quantum optical and the electron microscopy communities in the past decade for their intriguing theoretical properties and for their potential to enable new applications, ranging from the manipulation of molecules, clusters, and nanoparticles or the probing of chiral structures up to the exploration of fundamental interactions in high-energy collisions [1]
The apparent lack of communication and interaction between these communities finds a reason in the difference of basic concepts and notations, which obscures the equivalence of the underlying physical effects
Similar results have been obtained in both physical realms and a detailed comparison leads to new insights relevant to both communities
Summary
I.e., electron beams carrying an angular momentum, have gained interest in the quantum optical and the electron microscopy communities in the past decade for their intriguing theoretical properties and for their potential to enable new applications, ranging from the manipulation of molecules, clusters, and nanoparticles or the probing of chiral structures up to the exploration of fundamental interactions in high-energy collisions [1]. And largely unnoticed by the quantum optical and electron microscopy communities, vortex beams have been studied theoretically and experimentally in the accelerator community, where other techniques and applications have been developed. It will be shown that the Gouy phase and the Courant-Snyder phase advance are identical despite the fact that they are derived from very different conceptual approaches This discussion requires a set of basic relations from both the wave mechanical photon and from the charged particle accelerator physics world, which will be introduced . In the last paragraph it is shown that the conversion of pure modes leads to the same relations for the preservation of the beam quality as discussed in the field of accelerators, which demonstrates that the Derbenev transformation and the pure mode converter are identical
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