A Method for Designing Multibeam Higher Order Mode Extended Interaction Oscillators Based on Subwavelength Hole Array Smith-Purcell Radiation

Combining the radiation characteristics of a subwavelength hole array (SHA) with the resonance characteristics of higher order mode resonant cavities, a method for designing multibeam higher order mode extended interaction oscillators (EIOs) based on the SHA narrowband Smith-Purcell (SP) characteristic radiation region has been proposed. For the validation of the feasibility of this design method, first, the feasibility of the higher order mode operation was verified by cold cavity characteristics, hot cavity particle-in-cell (PIC) simulation, and cold cavity experiment, respectively. Therefore, the law of the operating modes corresponding to peak characteristic impedance <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$R/Q$ </tex-math></inline-formula> has been confirmed, and the device has been confirmed to operate at higher order modes TM<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$_{n,1}$ </tex-math></inline-formula>-<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2\pi $ </tex-math></inline-formula>(<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n = 3$ </tex-math></inline-formula>, 5, 7, 9, and 11) modes stably and show the best resonance characteristic in its corresponding mode. Second, the feasibility of the multibeam design scheme was verified by a proposed x-SHA x-beam (xSHAxB) higher order mode EIO, whose output power is more than x(<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$x = 2$ </tex-math></inline-formula>–6) times that of the 1SHA1B EIO. Consequently, this study offers a novel perspective on the design of interaction resonant cavities and provides an effective way for designing multibeam higher order mode EIOs, contributing to further improvement of output power.