High frequency characteristics of dielectric-loaded grating for terahertz Smith-Purcell radiation

Abstract

The research on a Smith-Purcell device becomes active since it holds promise in developing a high power, tunable, and compact terahertz radiation source. In this paper, a dielectric loaded grating for Smith-Purcell device is proposed. By investigating the interaction between the sheet electron beam and surface wave above the grating, the dispersion equation with electron beam is derived, in which the electron beam has a finite thickness. And then the growth rate of the beam-wave interaction is numerically calculated from the dispersion equation. In addition, the current threshold for oscillators, known as a start current, is carefully estimated from the dispersion equation by considering the boundary conditions of electromagnetic field. The effects of structure length, electron beam parameters and dielectric constant on start current are analyzed at length. The results reveal that the start current decreases as the structure length increases. This is because as the structure length becomes greater, the distance of the beam-wave interaction becomes longer, which can strengthen the beam-wave interaction. And with increasing beam thickness and beam-grating distance, the start current increases. Because the electric field of the surface wave decreases exponentially with the increase of distance from the grating, the electron beam far from the grating cannot be bunched by the field, which makes it harder for Smith-Purcell device to oscillate. However, as the beam voltage becomes greater, the start current decreases first quickly and then slightly. Compared with the case of metal grating, it can be seen that the use of dielectric can improve the growth rate and reduce the start current for the operation of a Smith-Purcell backward wave oscillator. The start current decreases quickly when the dielectric constant is greater than 1. Then it increases slightly when dielectric constant is between 2 and 3, and finally the start current continues to decrease. But it cannot be helpful to choose a very big value of dielectric in order to obtain a low start current, because the operation frequency decreases as dielectric constant increases. It is more appropriate to choose a dielectric constant in a required frequency range. The predictions of our theory and the results from the particle-in-cell simulation are consistent with each other, which verifies the validity and accuracy of the theory in this paper.