Theoretical analysis on phase-locking properties of a laser diode array facing an external cavity

External coupling model has been used to describe the output field of a laser diode array (LDA) phase-locked with an external cavity. The analytical solution for the coupling matrix equation of the phase-locked system has been obtained. The dependencies of the threshold gain, g_j of the system mode on the residue reflection of the front facet, r_f and round trip external cavity lengths, L have been discussed. The working lengths of the external cavity for stably phase-locking the LDA of different residual reflectivities have been calculated.