Bulk-plasmon-mediated free-electron radiation beyond the conventional formation time

Free-electron radiation is a fundamental photon emission process that is induced by fast-moving electrons interacting with optical media. Historically, it has been understood that, just like any other photon emission process, free-electron radiation must be constrained within a finite time interval known as the "formation time", whose concept is applicable to both Cherenkov radiation and transition radiation, the two basic mechanisms describing radiation from a bulk medium and from an interface, respectively. Here we reveal an alternative mechanism of free-electron radiation far beyond the previously defined formation time. It occurs when a fast electron crosses the interface between vacuum and a plasmonic medium supporting bulk plasmons. While emitted continuously from the crossing point on the interface - thus consistent with the features of transition radiation - the extra radiation beyond the conventional formation time is supported by a long tail of bulk plasmons following the electron's trajectory deep into the plasmonic medium. Such a plasmonic tail mixes surface and bulk effects, and provides a sustained channel for electron-interface interaction. These results also settle the historical debate in Ferrell radiation, regarding whether it is a surface or bulk effect, from transition radiation or plasmonic oscillation.