Analytic optimization of P-doped cascaded Raman fiber lasers

Optimization of P-doped cascaded Raman fiber lasers is discussed analytically. The differential equations depicting the distribution of pump and Stokes radiations along Raman fiber are simplified to the algebraic equations by introducing variables: average powers, gain factors and effective fiber length. An approximate analytic solution is obtained while supposing that pump beam propagates linearly along fiber. The proposed analytic solution shows excellent agreement with numerical simulation. Moreover, optimal design of the laser is discussed using the proposed solution. The optimal values of fiber length, reflectivity of output fiber Bragg grating and power conversion efficiency are obtained under different pump power. The optimal fiber length and reflectivity of output FBG decrease with increasing pump power.