Experimental measurements of the origin of self-phasing in passively coupled fiber lasers

We have directly measured the intensity distribution, gain, and induced phase shift between two fiber lasers that are coherently combined by a Dammann grating. The induced phase shift between the lasers has been shown to approximately cancel out any applied phase error introduced into the cavity, allowing the combined resonator to operate at an efficient low-loss state. We show that the origin of this self-phasing stems from a redistribution of power between the two lasers. The resulting difference in circulating intensity produces a differential change in saturated gain, which in turn produces a differential Kramers-Kronig phase shift that effectively cancels the applied phase error.