| This thesis is devoted to a thorough investigation of various nonlinear phenomena in optical fibers over a variety of length, time, and power scales. It presents a unified theoretical description of fiber nonlinearities, their applications, existing problems, and possible solutions, particularly focusing on the polarization dependence of nonlinearities. The thesis begins with an investigation of quantum-correlated photon pair generation in the extremely low-power regime, and fundamental quantum noise properties of dual-pump parametric amplfiers in the very high gain regime. It then focuses on two experimental demonstrations of applications based on four-wave mixing: an ultrafast all-optical switching scheme with the capability of multi-band wavelength casting, and a subpicosecond parametric oscillator with broadband tunability. The thesis next deals with the theoretical and experimental investigation of a novel phenomenon of vector soliton fission during supercontinuum generation in a tapered fiber in the femtosecond regime. The vectorial nature of Raman scattering is discussed next. In particular, I propose a vector form of the Raman response function to descibe accurately the Raman-related phenomena during ultrashort pulse propagation inside optical fibers. The thesis also presents a unified theory to describe nonlinearities in long fibers with random birefringence and polarization-mode dispersion. It focuses on the statistical nature of the interactions between random polarization-mode disperion and various nonlinear effects like stimulated Raman scattering, cross-phase modulation, four-wave mixing, and self-phase modulation. In particular, I quantify their impacts on various nonlinear photonic functionalities such as Raman amplification, nonlinear optical switching, parametric amplfication, wavelength conversion, soliton stability, etc. |
