We present an approximate analysis of the nonlinear operation of the hollow-waveguide laser with Gaussian reflectivity profile output mirror, including gain saturation and longitudinal- as well as transverse-field distribution of the laser mode. The model presented is general and can be applied to the study of an arbitrary configuration of the waveguide laser. In particular, the laser characteristics show the influence of the position of the output mirror and the Gaussian mirror parameter on the power efficiency of the laser system. It was shown that optimal position of the output mirror, which provides maximal power efficiency (with other parameters constant), depends on output power level and the mirror reflectivity coefficient.
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Emission and absorption spectra, lifetimes, and branching ratios in the blue spectral region have been experimentally determined for numerous oxide, fluoride and phosphate materials doped with Pr^{3+} ions. The emission cross-sections have been evaluated using the principle of reciprocity. A theoretical model allowing a prediction of the blue lasing characteristics of the praseodymium activated waveguide structures has been developed and employed to the investigated materials.
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