Phase locked laser arrays, where all the lasers have a common frequency and a constant phase difference relative to each other, have interesting physical properties. They can be exploited as excellent tools to investigate the properties of coupled oscillators as analogue to coupled classical-spins arrays (XY model) and study the behavior of frustrated array configurations. Also, phase locking of many lasers can result in a combined powerful laser that can be highly focused. In general, most techniques for phase locking an array of lasers involve negative coupling that tends to lock lasers with a π phase shift between neighboring lasers. This leads to a super mode of out-of-phase lasers that cannot be tightly focused. Thus, it is necessary to convert these out-of-phase lasers to a super mode of in-phase lasers in order to obtain tight focusing.

We developed a method for converting an array of out-of-phase lasers into one of in-phase lasers by resorting to phase doubling with second harmonic generation (SHG). The method is presented along with experimental and calculated results for negatively coupled laser arrays formed in various geometries. These include simple geometries, such as two coupled lasers, a one dimensional ring array with an even number of lasers, and arrays of hundreds of lasers formed in square and honeycomb geometries. In addition, we present bistable geometries, which include a one dimensional ring array with an odd number of lasers and an array of hundreds of lasers formed in a triangular geometry. Finally, we consider a frustrated array of hundreds of lasers formed in kagome geometry.