Nonlinear dynamics of modulational instability in optical fibers.

Abstract

Modulational instability (MI), as a phenomenon in dispersive nonlinear mediums has been a recent interest from the fundamental as well as technological standpoint. There has been great effort to understand the MI dynamics. The goal of this thesis is to extend our understanding in the following five aspects. First, we investigate parametric four-wave mixing process (FWM) among the pump, the Stokes and the anti-Stokes waves in dispersive optical fibers through the simulation of a set of coupled nonlinear Schrodinger equations. The numerical results show that the exiting Stokes is a soliton-like pulse. Second, we give a proof of the equivalence between MI and FWM. The proof process indicates that the third-order dispersion should have its influence on the MI process. We then examine in detail such influence. It is found that the third-order dispersion introduces a detailed phase-matching phenomenon, a phenomenon first addressed by us in this thesis. This phenomenon leads to an asymmetric pump power depletion, asymmetric locations of the sidebands about the central pump frequency, and saturation of the critical modulation frequency. Third, we have a study on the extended nonlinear Schrodinger equation including the third-order dispersion with high nonlinearity. In the study we investigate the evolutions of two kinds of inputs separately. A quasiperiodic input is shown to develop into temporal chaos due to nonlinear phase modulation and fiber dispersion. On the other hand, Effective modelocking is shown to occur among the sidebands generated from the induced MI process by injecting two frequency pump waves into the fiber. This process can be used to generate fs pulse train. A device is suggested for such pulse trains from the visible to infrared regions. Finally, we discuss modulational instability in periodically structured optical fibers. By assuming a special steady-state, we obtain an analytical dispersion relation and the gain of modulational instability in this structure. The effects of detuning $\Delta\beta$ and coupling constant $\kappa$ are discussed. It is found that the action of $\Delta\beta$ is like the action of $\beta\sb2$, the second-order dispersion in single-mode fibers. $\kappa$ is related to a resonance state, which is unstable under modulational perturbation. The gain of MI is shown to reach maximum when the nonlinear refractive index tunes the field to a resonance state.