Design optimization of the first-order P-doped fiber Raman lasers using an explicit approach

Theoretical design optimization of the first-order P-doped fiber Raman laser (FRL) by an explicit approach was investigated. The authors derived an explicit expression for the output power of the laser without using the depleted-pump approximation. The proposed solution shows excellent agreement with numerical simulation. According to the explicit solution, one can clearly know the effects of fiber length, reflectivity of output fiber Bragg grating (FBG), Raman gain and loss of the P-doped fiber and extra losses on the output power. The solution also present a criteria by which one can determine whether the depleted-pump approximation is valid or not. It is very fast and convenient to optimize the output power of the FRL using the proposed explicit solution. The optimal values of fiber length, reflectivity of output FBG and conversion efficiency are obtained under different pump power. While increasing pump power, the optimal fiber length and reflectivity of output FBG decrease and the optimal conversion efficiency increase. There exists a certain tolerance of the optimal parameters, in which the conversion efficiency decreases only slightly. The results provide us an intuitive physical understanding to the laser and are instructive to experimental design of the laser.