Analytical study of coherence in seeded modulation instability

Abstract

We derive analytical expressions for the coherence in the onset of modulation instability, in excellent agreement with thorough numerical simulations. As usual, we start by a linear perturbation analysis, where broadband noise is added to a cw pump; then, we investigate the effect of adding a deterministic seed to the cw pump, a case of singular interest as it is commonly encountered in parametric amplification schemes. Results for the dependence of coherence on parameters such as fiber type, pump power, propagated distance, and seed signal-to-noise ratio are presented. Finally, we show the importance of including higher-order linear and nonlinear dispersion when looking at longer-wavelength regions (mid IR).