Synchronization in fiber lasers arrays

We consider an array of fiber lasers coupled through the nearest neighbors. The model is a generalized nonlinear Schroedinger equation where the usual Laplacian is replaced by the graph Laplacian. For a graph with no symmetries, we show that there is no resonant transfer of energy between the different eigenmodes. We illustrate this and confirm our result on a simple graph. This shows that arrays of fiber ring lasers can be made temporally coherent.