Spontaneous and stimulated radiative emission of modulated free-electron quantum wavepackets—semiclassical analysis

Here we present a semiclassical analysis of spontaneous and stimulated radiative emission from unmodulated and optically-modulated free-electron quantum wavepackets. We show that the radiative emission/absorption and corresponding deceleration/acceleration of the wavepackets depend on the controllable ‘history-dependent’ wavepacket size. The characteristics of the radiative interaction when the wavepacket size (duration) is short relative to the radiation wavelength, are close to the predictions of the classical point-particle modelling. On the other hand, in the long-sized wavepacket limit, the interaction is quantum-mechanical, and it diminishes exponentially at high frequency. We exemplify these effects through the scheme of Smith-Purcell radiation, and demonstrate that if the wavepacket is optically-modulated and periodically-bunched, it exhibits finite radiative emission at harmonics of the modulation frequency beyond the limit of high-frequency cutoff. Besides, the radiation analysis is further extended to the cases of superradiant emission from a beam of phase-correlated modulated electron wavepackets. The features of the wavepacket-dependent radiative emission explain the classical-to-quantum transition, and indicate a way for measuring the quantum electron wavepacket size. This suggests a new direction for exploring light–matter interaction.