A geometrical view of scalar modulation instability

TL;DR

This paper introduces a geometric method to analyze scalar modulation instability by relating MI gain to dispersion profiles, enabling tailored design of devices like parametric amplifiers and supercontinuum sources.

Contribution

It presents a new geometric framework for understanding and designing modulation instability based on power and frequency relationships, linking MI gain to dispersion characteristics.

Findings

Derived explicit expressions for maximum MI gain power.

Linked MI gain shape to arbitrary dispersion profiles.

Provided a tool for designing MI-based devices.

Abstract

We present a novel approach to the analysis of a full model of scalar modulation instability (MI) 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. As a result, we derive a straightforward explanation of the non-trivial dependence of the cutoff power on high-order dispersion and obtain explicitly the power that maximizes the gain. Our approach puts forth a powerful tool to synthesize a desired MI gain with the potential application to a vast number of parametric-amplification and supercontinuum-generation devices whose functioning relies upon modulation instability.