Injection-locking optimization in unstable resonators

The problem of transverse-mode matching between the lowest-loss mode of a confocal unstable resonator and a Gaussian beam, which is injected into the resonator through a coupling hole in its back mirror, is analyzed. It is found that in resonators having equivalent Fresnel number greater than 0.5, there is a value of the coupling hole diameter for which a mode transition occurs. Below this value the coupling coefficient between the mode and the injected signal increases with the hole diameter. The optimal coupling hole diameter for injection locking lies somewhat below the transition value, where the low-order mode is still dominant and the coupling coefficient is high (about 0.25-0.30). The power loss through the coupling hole is negligible (about 2%) compared to the output coupling, which is about 50-70%.