Brillouin and transverse mode instabilities in fiber amplifiers for high-energy laser systems.

High-energy fiber lasers have developed a lot of interest due to their applications in industry, medicine, and defense. Recent advances enabled an explosive growth in operating power to the scale of multi-kilowatts. However, nonlinear effects such as the Brillouin instability (BI) and the transverse mode instability (TMI) impose limits on the power of high-energy fiber amplifiers. This dissertation focuses on the theoretical modeling of these nonlinear effects. The goal is to model these effects and further propose new mitigation techniques to increase the operating powers and advance the techniques for high-energy fiber amplifiers. The nonlinear effects in optical fibers often involve mode coupling. Avoided crossings occur when two modes are strongly coupled to each other and share similar propagation constants. We start with a tutorial to study avoided crossings in one-dimensional slab waveguides in both index guiding and antiresonant waveguides. We use simple one-dimensional slab waveguides as examples to illustrate the physics and properties of avoided crossings in more complicated specialty optical fibers. We study the TMI in an Yb-doped fiber amplifier in the presence of a single higher-order mode (HOM). Current modeling techniques for TMI require that the longitudinal discretization be substantially smaller than the beat length between the fundamental mode and HOM. We formulate the phase-matched model for TMI, which only considers the phase-matched terms that contribute to the coupling between the fundamental mode and HOMs. By doing so, the number of sections in the longitudinal discretization may be greatly decreased, which leads to a large computational win with no loss of accuracy. The BI may be modeled as a three-wave mixing process where two optical modes interact with a resonant acoustic mode. We consider phase modulation of the input pump as a suppression technique for BI. We show that piecewise parabolic phase waveforms like sawtooth and triangle phase may provide larger power thresholds compared to that of the more commonly used pseudorandom bitstream (PRBS) modulation. Because of the nearly rectangular spectrum associated with piecewise parabolic phase modulation, these modulation schemes are better fitted for power scaling such as spectral beam combining. Recently, our piecewise parabolic phase idea that was published was experimentally demonstrated. We further consider a single computational model that models BI and TMI together. A multi-time-scale approach must be used since these nonlinear effects evolve over drastically different time scales. Both BI and TMI depend differently on the core diameter of the fiber. At and under the pump power threshold for the combined BI-TMI model, the pump power threshold closely follows that of the individual BI and TMI models. However, BI may trigger TMI when strong BI leads to stochastic oscillations in the fundamental mode amplitude. This feature cannot be predicted by modeling either BI or TMI alone. At the end, we discuss the future prospects for high-energy laser fiber amplifiers and give a summary.