Diffraction Theory of Two-Mirror Echelette Resonators

We develop the theory of a two-mirror resonator, in which one mirror is an echelette diffraction grating. The diffraction loss related to the finite sizes of the mirrors, the loss determined by the existence of a mirror diffraction maximum of the grating (coupling loss), and the ohmic loss are taken into account. We show the possibility of constructing a resonator with one high-Q mode in a wide frequency band. This mode can be used as the working mode of a gyrotron operated at the second gyrofrequency harmonic, which interacts efficiently with the electron beam. We also demonstrate the possibility of frequency tuning of the resonator in a frequency band of 1%, while retaining the parameters which are satisfactory for gyrotron operation, and a high degree of resonator selectivity (i.e., the presence of a single mode).