Theory of a rotating-mode coaxial infrared grating laser

Analysis is presented for a novel interaction that makes possible a compact infrared grating laser configuration. The laser utilizes an annular axis encircling beam that is confined by an axial magnetic field and passes along a grating blazed axially on the center conductor of a coaxial resonator. A smooth cylindrical outer conductor completes the Fabry-Perot resonator to provide the necessary feedback for sustained oscillation. Linear analysis leads to an eigenvalue equation for cavity resonance frequencies, start-oscillation currents, and a gain-bandwidth relationship. The latter permits estimation of an upper bound on the ideal-beam power extraction efficiency. The nonlinear studies make use of analytical and numerical methods to gain a detailed understanding of electron motion in the presence of both axially focusing and radio frequency fields, and to determine the nonlinear efficiency. There is significant degradation of the interaction efficiency when the beam has finite annular thickness. Efficiency enhancement by means of a down-tapered axial field is demonstrated. A point design for lasing at ~160 μm in the far-infrared, utilizing a 100-kV beam with a pitch angle of 55° is presented. The start-oscillation current is a sensitive function of the resonator quality factor (or finesse); for a well-designed resonator, it is on the order of tens of Amperes