Without referring to specific devices, a universal discussion has been made on the high power laser diode arrays (LDAs) phase locked with external cavities (ECs). For a phase locked LDA based on the diffraction coupling between the nearest neighbor emitters, the coupling parameters have been expressed by module and argument, and the threshold conditions for different supermodes are analyzed, including the finite reflection of the front facet of the LDA facing the EC. Even though the thresholds of the super modes of LDA are affected by the residual reflection at the front facet, it can still be analytically proved that the favored mode of the LDA is either the lowest or highest order super mode. There exist some isolated EC lengths favoring the lowest order or highest order super modes, which are in consistent with the mode coupling theory.