A geometrical view of scalar modulation instability in optical fibers

Abstract

Full models of scalar modulation instability (MI) in optical fibers available in the literature usually involve complex formulations. In this paper, we present a novel approach to the analysis of MI in optical fibers by means of a simple geometrical description in the power vs. frequency plane. This formulation allows to relate the shape of the MI gain to any arbitrary dispersion profile of the medium, thus providing a simple insight. As a result, we derive a straightforward explanation of the non-trivial dependence of the cutoff power on high-order dispersion and derive explicitly the power that maximizes the gain. Our approach puts forth a tool to synthesize a desired MI gain with the potential application to a number of parametric-amplification and supercontinuum-generation devices whose initial-stage dynamics rely upon modulation instability.