Matrix algorithms for dynamic gain-spectrum adjustment of backward-pumped distributed fiber Raman amplifier

Two matrix algorithms aiming at a dynamic gain-spectrum adjustment in a backward-pumped distributed fiber Raman amplifier (B-DFRA) are developed based on the relation between changes in the pump power and the gain spectrum. Characteristic channels are chosen to reduce the dimension of matrices in the algorithm, which can be implemented by built-in microprocessors or DSP chips inside the B-DFRA module. Furthermore, as shown by the theoretical analysis and the numerical simulation, elements in the matrices can be directly and easily measured in deployed fiber plants without information on fiber parameters. These matrix algorithms are capable of adjusting the gain spectrum to fit the arbitrary profile desired in reality, while a wide dynamic range can be achieved by a multistage adjustment using matrices measured under several gain levels