Evaluating Mode Purity of Vortex Smith-Purcell Radiation

Vortex Smith-Purcell radiation (V-SPR) is a type of free-space free electron radiation with helical wavefront and orbital angular momentum, permitting flexible tunability in terms of topological charge and operation band based on chiral plasmons and harmonic diffractions. In this work, the criteria for assessing the mode purity of vortex modes are given. Besides, the relationship between mode dispersion and mode purity from the quantum point of view is derived according to the uncertainty relation between the azimuthal angle and the angular momentum. Mode purity allows effective evaluation of V-SPR performance and is expected to facilitate the design of compact vortex beam sources in hard-to-reach regimes.