Effect of mutual-injection ways on phase locking of arrays of two mutually injected fiber lasers: theoretical investigation

The effect of mutual-injection ways on phase locking of arrays of two mutually injected fiber lasers is studied theoretically. The phase-locked states of arrays with different ways of mutual injection are given analytically. It is found that different ways of mutual injection will result in different phase-locked states. The relationships between phase locking and ways of mutual injection are also discussed. The results indicate that the unconditionally phase-locked states can only be formed at the reflectors (i.e., fiber Bragg gratings [FBGs] or output faces) linking directly with the couplers. It is also found that only some of these arrays can make two output laser beams phase-locked unconditionally, while the other arrays can only make two output laser beams phase-locked with some conditions satisfied.