NONLINEAR OPTICAL PULSE PROPAGATION IN MULTIMODE WAVEGUIDES

123 pagesSoliton solutions of the (1+1)D nonlinear Schrödinger equation have long been the focus of immense research effort, and have provided us with the foundation for a large portion of our current understanding of nonlinear optical phenomena, particularly in single-mode optical fiber. Today, single-mode fiber has entrenched itself as the primary workhorse in many applications, from fiber lasers to imaging techniques to telecommunications. However, as these technologies approach fundamental limits, multimode fiber has presented itself as a promising route toward further advances. Supporting many spatial eigenmodes, multimode fiber provides a method of achieving higher capacities in data transmission through space-division multiplexing, as well as larger mode areas for higher energy fiber laser sources and amplifiers. They are also interesting from a purely scientific point of view, as an ideal testbed for rich spatiotemporal nonlinear dynamics. In single mode fiber, solitons of the (1+1)D nonlinear Schrödinger equation occur when linear dispersion and the Kerr nonlinearity balance to produce localized pulses. While the literature on (1+1)D soliton dynamics is extensive, nonlinear dynamics in multimode fiber have been far less explored. Multiple spatial eigenmodes are supported, with intra- and intermodal contributions to the dispersion, and propagation involving both spatial and temporal degrees of freedom. Knowledge of multimode soliton properties would provide a basis for understanding complex nonlinear dynamics in multimode fiber in the same way that knowledge of (1+1)D solitons does for single-mode fiber. Although some prior such work exists, the observed solitons were either dominated by the fundamental mode, or were highly multimode, resulting in the measurements being obfuscated by the sheer complexity of the system. Thus, experiments that add systematic understanding of multimode solitons are needed. In particular, the study of solitons in a small number of modes is a natural step from single-mode to many-mode, and ultimately, bulk spatiotemporal systems. Few-mode fiber is the perfect platform for such studies. Here, results from pulse-propagation experiments designed to isolate multimode solitons in graded-index fiber that supports only 3 spatial eigenmodes are presented. By varying the input energy and modal composition of the launched pulses, we observe a continuous variation of multimode solitons with different spatiotemporal properties. Due to their degrees of freedom, they exhibit an energy-volume relation that is distinct from those of single-mode and fully spatiotemporal solitons. From a theoretical standpoint, while multimode fibers can be modelled as a single (3+1)D system, they can also be described by a system of coupled modes. While theory and simulations have exploited this modal picture for insight, experiments have not been able to take advantage of this, instead indirectly inferring modal dynamics from full-field measurements. Steps have been previously taken toward full modal control and measurement, but have all lacked generality. If possible, modal decomposition provides greater efficiency, especially in few-mode fibers, allowing all the tools used for single-mode measurements (autocorrelation, FROG, dispersive Fourier transform, spectrum, etc.) to be directly applied to multimode measurements. Here we demonstrate full modal control over nonlinear multimode fiber optics experiments. Using spatial light modulators at the fiber input and output, we are able to excite specific modes or combinations of modes at will, and directly perform mode-resolved measurements. We present a thorough description and tutorial for these spatial light modulators, and demonstrate mode-resolved measurements of Raman beam-cleanup in a few-mode fiber. Using this capability, nonlinear pulse propagation in multicore fiber with strong random coupling is investigated. Motivated by increasing consumer demand for data capacity, space-division multiplexing has emerged as a prime candidate to address this demand - multicore fibers have shown particular promise as a potential platform for this technology. It has been found that random coupling, caused by physical perturbations to the fiber such as bending, twisting, micro-bending, and variations in core and fiber diameters, is helpful towards mitigating nonlinear signal impairment and increasing overall signal capacity. As such, there is tremendous technological value in studying the physics of nonlinear pulse propagation in the presence of random mode coupling. Scientifically, nonlinear pulse propagation in the presence of random mode coupling is still a relatively unexplored subject. There has been a number of theoretical works, but no one to date has experimentally explored nonlinear pulse propagation in settings where random mode coupling is present and relevant. Here, we conduct nonlinear pulse propagation experiments in a 3-core multicore fiber (each core single-mode) designed to exhibit strong random coupling and explore the interplay of linear and nonlinear pulse propagation dynamics. By using different pulse durations and energies, we vary the dispersion and nonlinear lengths of the pulse relative to the coupling length of the fiber and thus observe different pulse propagation regimes dominated by the various individual effects. This is the first study that investigates nonlinear pulse evolution with considerations for random mode coupling. Finally, future directions and the extension of the work in the thesis are discussed