Free-electron Brewster-transition radiation.

We reveal a mechanism to enhance particle-matter interactions by exploiting the pseudo-Brewster effect of gain materials, presenting an enhancement of at least four orders of magnitude for light emission. This mechanism is enabled by the emergence of an unprecedented phase diagram that maps all phenomena of free-electron transition radiation into three distinct phases in a gain-thickness parameter space, namely, the conventional, intermediate, and Brewster phases, when an electron penetrates a dielectric slab with a modest gain and a finite thickness. Essentially, our revealed mechanism corresponds to the free-electron transition radiation in the Brewster phase, which also features ultrahigh directionality, always at the Brewster angle, regardless of the electron velocity. Counterintuitively, we find that the intensity of this free-electron Brewster-transition radiation is insensitive to the Fabry-Pérot resonance condition and, thus, the variation of slab thickness, and moreover, a weaker gain could lead to a stronger enhancement for light emission.