Unified theory of parametric and Raman scattering processes in multimode fibers: coupling matrix method

Multimode photonics has raised renewed interest as a means of harnessing light states across multiple spatial, temporal, and spectral dimensions, thereby accelerating progress in applications that demand controllable multiplexing and parallel processing. Considerable advances in the manipulation of light propagation and amplification have been achieved, often interpreted through models restricted to specific interaction regimes. In this work, we develop a unified theoretical framework for multimode interactions mediated by Kerr-induced parametric and Raman scattering processes in optical fibers. Starting from the coupled multimode nonlinear Schrödinger equations, we derive a coupling matrix that captures the multimode amplification dynamics, incorporating key control parameters, such as dispersion, nonlinearity, pump power, and pump modal distribution. This framework allows for dynamic control of multimode gain and reveals three distinct regimes: Raman-only, parametric-only, and hybrid regimes where both processes interplay. We experimentally demonstrate Raman gain manipulation in a two-mode fiber, validating the theoretical predictions in the Raman-only regime. The proposed model provides a versatile platform for studying parametric and Raman phenomena in multimode systems and offers new opportunities for advancing multimode-based photonic applications.