Explicit solution for Raman fiber laser using Lambert W function.

In this paper, an approximate explicit solution for the first-order Raman fiber laser is obtained by using Lambert W function. Good agreement between the explicit solution and numerical simulation is demonstrated. Furthermore, the optimal design of Raman fiber laser is discussed using the proposed solution. The optimal values of fiber length, reflectivity of output fiber Bragg grating and power transfer efficiency are obtained under different pump power. There exists a certain tolerance of the optimal parameters, in which the output power decreases only slightly. The optimal fiber length and reflectivity of output FBG decrease with increasing pump power.