Dispersive decay of discontinuous pulses in optical fibers
Résumé
We study the decay of a discontinuous pulse occurring during the propagation in an optical fiber, in the normal dispersion and highly nonlinear regime. We consider step-like initial conditions for the power or the frequency chirp of the pulses, which correspond to the fluid height and velocity of the hydrodynamic analogy with the shallow water (Saint-Venant) equations, valid in the limit of vanishing dispersion. In the dispersionless limit, the step decays into a wave pair, consisting either of rarefaction or shock type connected by a constant state. The presence of dispersion regularizes the shock through fast oscillation, generating a dispersive shock wave. In this regime, the Whitham modulation theory can be applied to predict the different wave pairs configurations, separated by constant or oscillating states. We study the different regimes and characterize the phase transitions between them by means of a fiber optics experiment. As relevant examples, we consider typical problems of fluid dynamics such as the dam breaking or the piston problem, and the generation of cavitating states. The experiment also constitutes, to the best of our knowledge, the first fully quantitative test of Whitham theory.