Universal spectral dynamics of modulation instability: theory, simulation, experiment

Abstract

A central process of nonlinear fibre optics is modulation instability (MI), where weak perturbations on a continuous wave are amplified to generate a parametric cascade of spectral sidebands. Although studied for many years, it has only been recently appreciated that MI dynamics can be described analytically by Akhmediev breather (AB) solutions to the nonlinear Schrodinger equation (NLSE) [1]. This has led to important results, including the first observation of the Peregrine Soliton [2]. AB theory has also shown that the spectral amplitudes at the peak of the MI gain curve yield a characteristic log-triangular spectrum, providing new insight into the initial phase of supercontinuum generation [3]. Here, we present a significant extension to this theory by generalising the analysis to describe spectral characteristics for arbitrary gain. Our new result also describes the dynamics of the spectral development, a process previously studied only via truncated models or numerical approaches [4]. We confirm our theory by simulations and experiments.