Accurate description of the beam from a coherently combined fiber laser array

By expanding the fundamental mode of a step-index fiber in terms of Laguerre-Gaussian modes, an accurate expression for the beam emitted by a fiber laser in free space has been obtained. Based on this, the coherently combined beam from a fiber laser array has been theoretically investigated. The results are compared with those obtained by the Gaussian approximation for different distances between adjacent elements, different numbers of elements, and different values of the normalized frequency V. The study shows that the errors introduced by the Gaussian approximation decrease with increasing distance between adjacent elements and increase with the number of elements. For V, the error first decreases and then increases with increasing V. These results indicate that an expansion in terms of Laguerre-Gaussian modes can be used for an accurate description of a coherently combined beam from a fiber laser array.