Multiple Four-Wave Mixing Processes in Single - Optical Fiber

This thesis presents an investigation of multiple four-wave mixing (FWM) processes that occur when two pump lasers interact nonlinearly in single-mode optical fiber. The focus of this investigation has been the study of the nonlinear dynamics of multiple FWM processes. The equations that describe the nonlinear interaction of six frequency components (two pump lasers and two pairs of FWM sidebands) by seven FWM processes are derived starting with Maxwell's equations with a cubic term included in the material polarization. The conserved quantities, in terms of linear combinations of the power in each frequency component, are also derived for this set of differential equations. Numerical solution of these equations reveal that the six frequency components can exchange energy periodically or chaotically as they propagate down the fiber. Comparison with an analytic solution which neglects the phase mismatch for the FWM processes illustrates the critical role of the mismatch in the dynamics of multiple FWM. The experimental investigation of multiple FWM depends critically on the availability of two tuneable lasers and a computer interfaced spectral acquisition system. Experiments investigating the dependence of the FWM sideband power on the pump power and frequency detuning are in good agreement with the predictions of numerical calculations for a reasonable range of pump powers and detunings. By performing FWM experiments with fluctuating pump lasers, the nonlinear dynamics of the energy exchange between the six frequencies is investigated. The statistics of the FWM sidebands at the output of a fixed length of optical fiber are shown to depend on the nature of this energy exchange. The same qualitative trends predicted by the model are seen in experiments for a range of pump powers that include periodic and chaotic behavior of the model. The quantitative agreement is also good for many of the measurements. The limits of validity of the theoretical model is discussed, and possible means of extending the region of agreement between experiment and model are suggested. Future directions for investigating these multiple FWM processes are also suggested.