Efficient formulation of Raman amplifier propagation equations with average power analysis

For the first time, we derive efficient modeling equations for the average power analysis of Raman amplifiers (RAs) from the standard propagation equations. Applications of these equations to the numerical analysis of practical RA-based systems show a reduction in computation time of over two orders of magnitude compared with the direct integration approach based on ordinary coupled differential equations, while reproducing all the essential system performances precisely. In addition to enhanced computational efficiency, the derived equations also give deeper insights into the detailed dynamics of RAs.