In this paper, the array of fiber lasers coupled by bi-dimensional mutual injection is firstly, to our knowledge, investigated. Phase locking of the array is theoretically studied and the phase-locked states of the array are given. It is found that the array with bi-dimensional mutual injection can export the same amount of the phase-locked states as the array with one-dimensional mutual injection, which implies that the amount of phase-locked states does not depend on the dimension of mutual injection. The conditions needed for phase locking of the array are also studied. It is illuminated that, compared with the array with one-dimensional mutual injection, more conditions are needed for phase locking of the array with bi-dimensional mutual injection. Based on these results, the options for improving the performance of the array of fiber lasers coupled by mutual injection are discussed.
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