Fig. 1: Enhancing both directionality and intensity of bremsstrahlung emission via shaping of electron wavefunction.

a–c illustrate the bremsstrahlung process involving 20 keV initial electron wavefunctions ((a) is unshaped, (b, c) are shaped where (b) is converging to a Bessel beam of order 0 and (c) is converging to a Bessel beam of order 1, respectively, with increasing number of momentum components \({N}_{{\rm{s}}}\)) scattering off a graphene flake (oriented in xy-plane), and emitting X-ray photons in multiple directions. Radiation patterns in (b, c) are distinctly different from (a) in terms of both magnitude and directionality, showing the significant effect of quantum interference resulting from electron waveshaping. Compared to (a), (b) generates radiation of higher intensity while (c) generates both stronger and directional radiation (on-axis). (d, e) show the linear scaling relation between the bremsstrahlung emission differential cross section \({\rm{d}}\sigma /({\rm{d}}{\omega }_{{k}^{{\prime} }}{\rm{d}}{\Omega }_{{k}^{{\prime} }})\) (15 keV photon, at emission angles \({\theta }_{{k}^{{\prime} }}\) = −0.3 [π rad], \({\phi }_{{k}^{{\prime} }}\) = 0.5 [π rad] and \({\theta }_{{k}^{{\prime} }}\) = 0 [π rad], \({\phi }_{{k}^{{\prime} }}\) = 0 [π rad], respectively) and the number of atoms \({N}_{{\rm{a}}}\) for two different shaped electron wavefunctions as mentioned in (b, c), respectively, for the cases of 6, 12 and 24 momentum states. Similarly, (f, g) show the scaling relation between the single atom bremsstrahlung differential cross section and the number of electron momentum states \({N}_{{\rm{s}}}\), as mentioned in (b, c), respectively