An Improved Theoretical Model of $n$ th-Order Cascaded Raman Fiber Lasers

An improved analytical model is presented for the design of nth-order cascaded Raman fiber lasers (CRFLs) by considering the variation of Raman fiber effective core area with Stokes wavelength. Using this model, we determine the approximate optimal Raman fiber length and output-coupler (OC) reflectivity which make pump-to-Stokes conversion efficiency maximum. The output performance for a fifth-order Ge-doped CRFL calculated by our model is compared with the published experimental data, and good agreements between them have been found. Our calculated results show that losses, including gray losses of fiber Bragg gratings and splicing losses of fibers, have a significant effect on CRFLs characteristics, and the conversion efficiency is insensitive to the variation of Raman fiber length or reflectivity of OC near the optimal value.