Comment on "nonlinear quantum effects in electromagnetic radiation of a vortex electron"

This comment on the paper by Karlovets and Pupasov-Maksimov [Phys. Rev. A 103, 012214 (2021)10.1103/PhysRevA.103.012214] addresses their criticism of the combined experimental and theoretical study by Remez et al. [Phys. Rev. Lett. 123, 060401 (2019)10.1103/PhysRevLett.123.060401]. We show, by means of simple optical arguments as well as numerical simulations, that the arguments raised by Karlovets and Pupasov-Maksimov do not hold in the experimental regime reported by Remez et al. Further, we discuss a clarification for the theoretical derivations presented by Karlovets and Pupasov-Maksimov, as they hold only when the final state of the emitting electron is observed in coincidence with the emitted photon. Although this scenario is feasible and may stimulate new experimental regimes that do correspond to the predictions reported by Karlovets and Pupasov-Maksimov, it is not the common scenario in cathodoluminescence, where only the light is measured. Upon lifting the concerns regarding the experimental regime reported by Remez et al., and explicitly clarifying the electron postselection, we believe that the paper by Karlovets and Pupasov-Maksimov may constitute a valuable contribution to the problem of spontaneous emission by shaped electron wave functions, as it presents new expressions for the emission rates beyond the ubiquitous paraxial approximation.