Optimal defect position in a DFB fiber laser

Fiber lasers with compact cavity have numerous potential applications in sensing, communications, and medicine. Distributed feedback (DFB) rare-earth doped fiber lasers based on Bragg gratings with a phase shift are the most promising in this aspect. In this paper, we theoretically study such lasers and carry out a complex-frequency analysis of the DFB cavity modes. Our approach is based on the study of poles of open cavity response function and on the laser rate equations. An optimal defect position in the Bragg grating, which maximizes an output power towards one side, was found with this approach. We show that the optimal defect position depends on the pump power. At the pump level close to the lasing threshold, the defect should preferably appear in the middle of the grating to maximize the one-side output power. At higher pumping, the optimal position of the defect becomes asymmetric. We have found specific variables, which allow for determination of optimal defect position for a large variety of DFB laser configurations.