Effect of small misalignments and the parameter spread on the optical modes of a multicore fibre laser with a spatial filter

A multicore fibre laser is considered in which a ring waveguide (RW) of length equal to 1/2 or 1/4 of the Talbot length is used as a spatial filter separating a required collective mode. Explicit expressions are obtained for the eigenvalues of the modes in such lasers by using the Gaussian approximation for the fields of individual microcores. The effect of regular and random displacements of microcores and of the angular misalignment of a multicore fibre (MCF) relative to the RW is considered within the framework of the theory of weak perturbations. A change in the mode loss spectrum caused by a random phase incursion in the MCF is calculated using the perturbation theory. The explicit expressions derived for the perturbed eigenvalues are compared with the results of numerical simulation of the MCF laser with the RW of length equal to 1/4 of the Talbot length. Comparison of the results allows the use of these expressions for estimating the eigenvalues of Talbot resonators with the perturbed parameters of a laser set.