Detailed experimental and theoretical investigations on two coupled fiber lasers, each with many longitudinal modes, reveal that the behavior of the longitudinal modes depends on both the coupling strength as well as the detuning between them. For low to moderate coupling strength only longitudinal modes which are common for both lasers phase-lock while those that are not common gradually disappear. For larger coupling strengths, the longitudinal modes that are not common reappear and phase-lock. When the coupling strength approaches unity the coupled lasers behave as a single long cavity with correspondingly denser longitudinal modes. Finally, we show that the gradual increase in phase-locking as a function of the coupling strength results from competition between phase-locked and non phase-locked longitudinal modes.
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