Modulation instability in waveguides with an arbitrary frequency-dependent nonlinear coefficient

Abstract

In this Letter, we present, for the first time, to the best of our knowledge, the modulation instability (MI) gain spectrum of waveguides with an arbitrary frequency-dependent nonlinear coefficient ensuring strict energy and photon-number conservation of the parametric process. This is achieved by starting from a linear stability analysis of the recently introduced photon-conserving nonlinear Schrödinger equation. The derived MI gain is shown to predict some unique features, such as a nonzero gain extending beyond a zero-nonlinearity wavelength and a complex structure of the MI gain spectrum. Analytical results are shown to be in excellent agreement with numerical simulations.