Smith-Purcell radiation from a charge moving above a finite-length grating with rectangular profiles.

Smith-Purcell radiation is generated by a charged particle beam passing close to the surface of a diffraction grating which has a strong dependency of the emitted radiation intensity on the form of the grating profile. For relativistic electron beam, it is important to take into account the number of grating periods in practical SPR setups. In this paper, the theoretical investigations of Smith-Purcell radiation from a three-dimensional bunch of relativistic electrons that moves at constant speed parallel to an electrically perfectly conducting grating with finite rectangular grooves are carried out by using the modal matching method. This model may offer a new efficient tool for terahertz production by SPR interaction and for nondestructive bunch-length measurements by SPR.