Threshold-less and focused Cherenkov radiations using sheet electron-beams to drive sub-wavelength hole arrays

Cherenkov radiation (CR) was one of the most famous discoveries in the last century and still has broad applications in modern physics. Recently, threshold-less and reversed CRs have attracted even more attention thanks to their unique characteristics and application prospects. Here we illustrated a threshold-less CR in vacuo by using a sheet free-electron beam (FEB) to excite an oblique-lined sub-wavelength hole array. It is achieved by setting the effective velocity of emitters-resonant modes successively excited by the sheet FEB-to be greater than the speed of light in vacuo. By letting the sub-wavelength holes line up along a designed curve, we further demonstrated a focused CR with radiation being convergent to specific focusing spots, which can be located at any designed positions in space, achieving backward (reversed) as well as forward (normal) CRs in effect. This focused CR does not have the conventional Cherenkov cone, and its intensity at the focusing spot is greatly enhanced. These newly revealed threshold-less and focused CRs may lead to broad interest and attractive applications, especially for developing integrated and focused light sources in the terahertz region.