Phase locking of a laser array in the case of different types of multibeam intracavity interaction in nonlinear media

A theoretical investigation is made of the phase locking of a laser array in the case of different types of multibeam intracavity interaction in nonlinear media. The conditions are found under which a long-range coupling of the "all with all" type is established between the lasers and also when only the nearest neighbors interact (short-range coupling). The influence of the number of lasers, frequency offsets of their resonators, and of the coupling coefficients on the phase-locking band is considered. Expressions are obtained for determination of the threshold values of the gain and of the frequency characteristics of cophasal and noncophasal operation of a laser array under long-range and short-range coupling conditions. A study is made of the influence of the parameters of a resonantly absorbing medium on phase locking of a set of lasers and it is shown that in the case of the optimal long-range coupling the phase-locking band is independent of the number of lasers.