The effect of radial radiation transport on intensity characteristics and oscillation frequency of homogeneously broadened lasers

In the present treatment of performance characteristics of laser systems, having homogeneous line broadening, a radial gain profile is taken into account. It will be shown that such a profile, which may be induced by the laser beam itself, changes the curvature of the phase front, so that additional radiation transport in the radial direction takes place. It turns out that for many practical systems the radial radiation transport can be comparable to the radiation gained directly from the medium and therefore may not be neglected. Furthermore, it will be shown how the additional radial radiation transport affects the oscillating frequency. Conditions are deduced in which mode competition leads to the survival of the mode having highest radiation intensity. This is not the one closest to the line center as found in systems where radial radiation transport is not taken into account. Treating this problem we approximate medium parameters by a quadratic profile so that the modes have a Gaussian structure. The oscillation frequency, determined on one side by the dispersion of the active medium and on the other side by the spontaneous decay of the upper level, is discussed. The frequency shift is not very sensitive to changes of mirror reflectivity but increases considerably with increasing thermal effects. Numerical calculations show, for instance, that for a semiconfocal system a frequency shift close to 0.5 in units of normalized frequency can be predicted.