Semi-analytical model of Raman generation in silicon-on-insulator rib waveguide with DBR/F-P resonator

An approximate method of modelling of Raman generation in silicon-on-insulator (SOI) rib waveguide with DBR/F-P resonator including spatial field distribution and nonlinear effects such as Raman amplification and two photon absorption (TPA), is developed. In threshold analysis of steady-state Raman laser operation, an analytical formula relating threshold pump power to the system parameters is obtained. The analysis of the above threshold operation is based on an energy theorem. In exact energy conservation relation, we approximate the Stokes field distributions by that existing at the threshold, whereas the approximate pump field distributions are obtained by integrating the equations for the pump signal using the linear (threshold) pump field distributions and the threshold Stokes field distributions. An approximate, semi-analytical expression related the Raman output power to the pump power and system parameters is derived. Our calculations remain in a good agreement with the exact numerical solutions.