Cavity decay rate and relaxation oscillation frequency in unconventional laser cavities

Measuring the relaxation oscillation frequency ω_r versus the normalized pumping rate r can provide a useful technique for determining either cavity or atomic parameters in many different kinds of lasers. Measurements of relaxation frequency versus pumping rate in a Nd:YAG laser using a gain-guided unstable-cavity design were recently found, however, to yield values of cavity decay rate which were unreasonably large compared to other estimates of the cavity losses. This difficulty has been resolved by a closer look at the relaxation oscillation dynamics in this type of laser. We find that in nonorthogonal laser cavities with nonuniform gain distributions the energy decay rate of the cavity oscillation mode usually employed in the relaxation frequency formula must be replaced by a different decay rate relevant to oscillation mode perturbations. A numerical simulation including this more general effect gives values very close to our experimental results, confirming the validity of this modified analysis