Inverse design of multi-point gain-clamped C + L-band discrete Raman amplifiers using a physics-informed neural network

Ultra-wideband C+L Raman amplification is a promising solution for multi-band optical transmission, but stable broadband operation is challenged by strong pump–signal coupling and non-uniform pump depletion arising from the frequency dependence of the Raman gain coefficient. In this work, we propose a gain-clamped Raman amplification architecture that leverages multi-point spectral stabilization to enable robust C+L-band operation. Three clamping-control waves are placed at the short-edge (C), center, and long-edge (L) of the C+L band, such that the amplifier simultaneously suppresses spectral fluctuations across the full bandwidth and improves tolerance to input-power variations. To efficiently solve the high-dimensional inverse design involving multiple pump powers and clamping-loop VOA settings, we further develop a manifold-adaptive sampling physics-informed neural network (MAS-PINN) that unifies physics-informed learning, manifold regularization, and adaptive anchor sampling, enabling rapid and accurate generation of globally optimized configurations under user-defined gain profiles. Experiments verify both the independent and cross-coupled responses of the three clamping signals and demonstrate tunable clamped gain levels across the C+L band; at an 18-dB operating point, the proposed scheme achieves a 17.3% reduction in C+L-band flatness error (root-mean-square error, RMSE) compared with a conventional pump-only baseline. Dynamic surviving-channel add/drop tests further confirm transient stabilization, suppressing power surges from 1.3 dB to 0.45 dB under abrupt channel perturbations. The proposed architecture and MAS-PINN controller provide a practical route toward stable, flexible, and scalable ultra-wideband Raman amplification for advanced optical networks.