Extraction characteristics of a cw double-hexagonal Talbot cavity with stochastic propagation phase

We solve the coupled cw electric field differential equations for an hexagonal array of fiber gain elements all sharing a common monolithic Talbot cavity mirror. A threshold analysis shows that the lowest gains are nearly equal, within 10% of one another, and that one of these corresponds to an in-phase supermode. Above threshold we study the extraction characteristics as a function of the Talbot cavity length, and we also determine the optimum outcoupling reflectivity. These simulations show that the lasing mode is an in-phase solution. Lastly, we study extraction when random linear propagation phases are present by using Monte Carlo techniques. This shows that the coherence function decreases as $\exp(-\sigma;2)$, and that the near-field intensity decreases faster as the rms phase $\sigma;2$ increases. All of the above behaviors are strongly influenced by the hexagonal array rotational symmetry.