Generalized modulational instability in multimode fibers: Wideband multimode parametric amplification

In this paper intermodal modulational instability (IM-MI) is analyzed in a multimode fiber where several spatial and polarization modes propagate. The coupled nonlinear Schr\"{o}dinger equations describing the modal evolution in the fiber are linearized and reduced to an eigenvalue problem. As a result, the amplification of each mode can be described by means of the eigenvalues and eigenvectors of a matrix that stores the information about the dispersion properties of the modes and the modal power distribution of the pump. Some useful analytical formulas are also provided that estimate the modal amplification as function of the system parameters. Finally, the impact of third-order dispersion and of absorbtion losses is evaluated, which reveals some surprising phenomena into the IM-MI dynamics. These outcomes generalize previous studies on bimodal-MI, related to the interaction between 2 spatial or polarization modes, to the most general case of $N>2$ interacting modes. Moreover, they pave the way towards the realization of wideband multimode parametric amplifiers