Modulation Instability, Four-Wave Mixing and their Applications

This chapter presents an overview of the analysis of the nonlinear dynamics of Modulation instability (MI) by means of a simple three-mode truncation. It discusses how the coupling between two polarization modes in a birefringent optical fiber may extend the domain of MI to the normal dispersion regime. It also briefly discusses the case where the MI is induced by two pumps and occurs on top of multiple four-wave mixing. The chapter reviews the linear stability analysis of a plane wave background solution of the nonlinear Schrodinger (NLS). It generalizes the model to include pump depletion and describes a truncated three-wave model for the pump and its immediate sidebands. The chapter briefly considers an application of the four-wave mixing process in passive fiber cavities. This application relies on the fact that the growth rate of the cavity MI is purely real and can give rise to stationary periodic patterns and temporal cavity solitons.