FIGS. 20A-20B show ponderomotive deflection of electrons, pushing them away from the graphene surface. FIG. 20A shows the electric field threshold for significant ponderomotive deflection as a function of electron energy. Each red cross corresponds to a line in FIG. 20B, where the trajectory of a 100 eV electron 1 nm away from the graphene surface (n=180) is plotted for different values of peak electric field amplitude at the graphene surface E0s (the value in the labels). For reference, the GP field is displayed in the background.
An important implication of the results in FIGS. 20A-20B is that for strong electric fields the distance of interaction is limited by the ponderomotive force, in addition to limitations imposed by the graphene size and the electron beam divergence. For small electron beam energies (less than a few hundred eVs), the ponderomotive force becomes the dominant factor limiting the interaction length. This practically limits the amplitudes of useful GPs in cases of low-energy electron beams. Nevertheless, the onset of significant radiation pressure for electron energies around 50 keV is already 20 GV/m, which is about the graphene breakdown field strength. This implies that the constraints imposed by the ponderomotive force are already negligible at the upper end of scanning electron microscope energies, and become even more negligible at higher electron energies (e.g., on the scale of transmission electron microscope and radiofrequency gun energies).
