Engineered <inline-formula> <tex-math notation="LaTeX">$\pi$ </tex-math> </inline-formula>-Phase-Shifted Fiber Bragg Gratings for Efficient Distributed Feedback Raman Fiber Lasers

Distributed feedback Raman fiber lasers with π-phase-shifted uniform gratings are modeled and simulated in the steady state, to optimize their performance. Using the parameters of realistic devices, it is found that the position change of the π-phase-shift in a constant-strength uniform grating has a significant impact on the laser performance including right and left-hand-side output power and emission frequency, and linewidth. Also, it is shown that the optimum phase-shift position to maximize the laser uni-directionality is dependent on pump power and fiber loss value. A new design approach based on an engineered π-phase-shifted step-like-strength uniform grating is presented demonstrating that even for a high-loss fiber (0.1 dB/m), the laser power and linewidth can be efficiently increased and decreased by ~25% and ~15%, respectively, for the same total device length and pumping condition, just by the proper choices of the phase-shift position and two coupling coefficients.