An arrangement based on a degenerate cavity laser for forming an array of non-linearly coupled lasers with an intra-cavity saturable absorber is presented. More than 30 lasers were spatially phase locked and temporally Q-switched. The arrangement with nonlinear coupling was found to be 25 times more sensitive to loss differences and converged 5 times faster to the lowest loss phase locked state than with linear coupling, thus providing a unique solution to problems that have several near-degenerate solutions.Phase locking of lasers corresponds to a state where all the lasers have the same frequency and the same constant relative phase, leading to a coherent superposition of their fields [1,2]. Accordingly, the total brightness of the lasers is high and allows focusing of all the lasers to a sharp spot [3][4][5]. Phase locking of lasers has been incorporated in many investigations, including simulating spin systems [6][7][8], finding the ground-state solution of complex landscapes [6,9], observing dissipative topological defects [10,11] and solving hard computational problems [9,12].Phase locking of laser arrays can be achieved with dissipative coupling that leads to a stable state of minimal loss, which is the phase locked state [6,10,11]. Dissipative coupling involves mode competition whereby modes of different losses compete for the same gain [2,6,9,13]. Only modes with the lowest loss survive and are amplified by the gain medium. Accordingly, by inserting amplitude and phase linear optical elements into a laser cavity that minimize the loss of the phase locked states, it is possible to achieve phase locking with mode competition [2][3][4]14].While phase locking with such linear optical elements has yielded many exciting results [4-6, 10, 12-17], it suffers from inherent limitations. It is very sensitive to imperfections, such as positioning errors, mechanical vibrations, thermal effects and other types of aberrations associated with these intra-cavity elements. Moreover, in many cases, especially for spin simulations and computational problem solving [6,9,12], there are two or more states with nearly degenerate minimal loss that cannot be distinguished from each other.In this letter, we resort to nonlinear coupling between lasers by means of a saturable absorber (SA). A SA is a nonlinear optical element that block light until it saturates, where its optical loss decreases sharply [18]. It can thus affect the temporal modes within the laser so as to obtain passive Q-switching and (longitudinal) mode locking, for generating short pulses and high output peak powers [1] and studying nonlinear laser dynamics [1,3,[19][20][21]. We show that a SA can also affect the spatial phase distribution within the laser and phase lock many individual lasers. Specifically, inserting a SA at the far-field plane of a laser array ensures that the phase locked state (that has sharp and strong intensity peaks there [3-6]) corresponds to the minimal loss state, to be selected by optical feedback (mode competition) [17].We show experim...