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, gjgj of the system mode on the residue reflection of the front facet, rfrf 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.