Investigation of frequency-selective losses of a reflecting grating in a laser resonator

An analysis is made of the selective properties of a resonator formed by a reflecting diffraction grating and a mirror. The frequency-selective loss function (FSLF) of this resonator is determined. If the grating is considered to be an equivalent plane mirror with angular dispersion, the problem of losses due to misalignment of the grating is reduced to the problem of losses for a tilted-mirror resonator. An integral equation derived for this case was solved by computer. By using Gaussian quadrature formulas for numerical integration and an efficient algorithm, all the highest-Q oscillation modes can be determined directly with a low usage of computer time. The grating FSLF is obtained and it is found to be determined by the dependence of the increase in the insertion losses on the angular misalignment of the grating. Initially the dependence is parabolic and then increases linearly. Experimental measurements were made of the FSLF for a CO₂ laser with 100 and 150 lines/mm intracavity gratings for various values of the confocal parameter 1–0.56 and the degree of stopping down 0.55–0.35. The results agree with the calculations.