A moment method for analysis the gain spectrum in fiber Raman amplifier with broadband pumps

A moment method analysis of the gain spectrum in bi-directionally pumped Raman amplifiers through continuous-spectrum radiation

“…(11)) is a two-point boundary value problem. For each (M, b), the approximated governing system of finite nonlinear coupled differential equations is solved by a nonlinear shooting method [12,16,17]. To understand the convergence of the numerical solution of the moment equations, we consider two Gaussian spectrum pumps with different powers which are centered at l ¼ 1443.2 nm along the 70 km SMF-28.…”

“…In [12] the result of full numerical modeling of backwardpumped Raman amplifier with continuous-spectrum pump was presented. The continuous pump spectrum was approximated by 31 monochromatic sources within the 80 nm bandwidth, and their frequencies being spaced by 14 cm À1 .…”

“…Here n s is the number of signal channels and a(n) is the attenuation coefficient for a wave with frequency n. The gain coefficient g(n, n 0 ) describes the energy transferred by stimulated Raman scattering (in stokes direction) between n and n 0 waves and is given by [12]:…”

“…In our previous work [12], the moment method was employed for one directional pumped FRA to reduce the system of uncountable governing equations into a set of countable coupled nonlinear differential equations. Here the moment method is adopted to solve the governing equations of the bi-directionally pumped Raman amplifiers with continuous-spectrum pump.…”

A perturbation method for analysis of TDM-pumped fiber Raman amplifier

“…The Picard iterative method is employed to investigate the steady state behavior of the conventional Raman amplifier and high power semiconductor amplifiers by previous authors [23][24][25]. Authors previously employed the variational and moment methods for minimization of the gain ripple in conventional FRAs [28][29][30]. In this paper a time dependent solution based on the Picard iterative method is presented and it is employed to minimize the gain ripple of the TDM fiber Raman amplifier.…”