The use of metal gratings inside laser resonators is limited to medium power because of a low damage threshold. High-re¯ectivity (HR) dielectric layer systems commonly used as laser mirrors o er a damage threshold signi®cantly above that of metals. A di raction grating on top of a HR system combines high re¯ectivity with spectral properties. We describe a special HR grating used in a Littrow mounting as a wavelength selective resonator mirror in a 1.44 mm neodymium-doped yttrium aluminium garnet laser. The necessary restrictions lead to conditions with four transmission orders, making it more di cult to reach high e ciency, than found by Perry and co-workers. The design of the binary di raction grating on a dielectric layer system is based on a new ®nite-element method. Also for the more di cult con®guration, a di raction e ciency of nearly 100% is theoretically possible. Because of the new conditions in contrast with these in the work of Perry and co-workers, other materials have to be used. For two di erent material combinations, HR gratings are fabricated. The limiting factors in realizing 100% e ciency, are the material parameters and fabrication tolerances. First examples of gratings o er fairly good agreement with the theoretical values.
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