Frequency selectivity and resonator losses in a waveguide laser with a diffraction grating

Theoretical and experimental investigations were made of the frequency-selective and nonselective properties of a waveguide laser resonator with a circular channel and a diffraction grating. A study was made of the fundamental waveguide mode EH₁₁ corresponding to a resonator with "mode filtering," for example, when one of the reflectors is a spherical mirror matched to the waveguide. It was found that losses in a waveguide laser with a diffraction grating can be described quite accurately as the losses in an equivalent resonator with a tilted plane mirror. The grating formula was found to relate the angle of tilt of the mirror to the frequency detuning. General scaling relationships were obtained for the tilt angles and the distances between the end of the waveguide and the diffraction grating mirror. An analytic method was proposed and developed for the calculation of the losses in a waveguide laser with a diffraction grating, and with a plane or a spherical reflector in the Gaussian mode approximation. Investigations were made of lasers with a diffraction grating, with a grating and an intracavity lens, and with a grating and collimator. These cases covered practically all the important types of gas lasers emitting the fundamental waveguide mode.