Time-delayed optical feedback is known to trigger a wide variety of complex dynamical behavior in semiconductor lasers. Adding a second optical feedback loop is naturally expected to further increase the complexity of the system and its dynamics, but due to interference between the two feedback arms, it was also quickly identified as a way to improve the laser stability. While these two aspects have already been investigated, the influence of the feedback phases, i.e., sub-wavelength changes in the mirror positions, on the laser behavior still remains to be thoroughly studied, despite indications that this parameter could have a significant impact. Here, we analyze the effect of the feedback phase on the laser stability in a dual-feedback configuration. We show an increased sensitivity of the laser system to feedback phase changes when two-feedback loops are present and clarify the interplay between the frequency shift induced by the feedback and the interferometric effect between the two feedback arms.
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