Line selection in carbon dioxide waveguide lasers using diffraction gratings

This paper treats theoretically the coupling losses which arise in square dielectric waveguide CO ₂ lasers when one element of the optical resonator is a diffraction grating. These losses are due to imperfect coupling of the radiation which is launched from the end of the guide to the grating and returned from the grating back to the guide. The results of the calculations show that the coupling efficiency is a sensitive function of radiation wavelength. This result is then used to investigate the ability of a 150 lines/mm diffraction grating to resolve adjacent rotational-vibrational transitions in the CO ₂ emission. It is shown that "line-hopping" places a limitation on the maximum tunability which can be obtained and is a result of the poor discrimination at the grating surface especially in the case of waveguide lasers having much reduced apertures. Computations based on the scaling laws are employed to maximise the tunability as a function of waveguide aperture taking into account limitations imposed by "line-hopping", cut-off and the optical resonator frequency offset condition of c/4 L. Comparisons are made between theory and experiment, and design guidelines for the construction of widely tunable CO ₂ waveguide lasers are presented graphically.