Broadband transverse multimode nonlinear optics in strongly coupled waveguides

The thesis explores broadband transverse multimode nonlinear optical phenomena within integrated, multimode silicon nitride waveguides. It exploits spatially transverse degrees of freedom present as distinct supermodes for broadband nonlinear generation. The nonlinear conversion process is fundamentally governed by the universal third-order nonlinearity, employing supercontinuum generation as the undelying nonlinear dynamics. Our study focuses on a simplest prototype structure supporting two fundamental spatial supermodes, which is a dual-core waveguide. The fundamental, supported modes are a spatially symmetric mode and an anti-symmetric mode. With controlled excitation of these supermodes via separate single-mode input and output waveguides, we theoretically and experimentally explore new opportunities for dispersion management and nonlinear interactions to generate coherent light with broad spectral bandwidth. The thesis shows that a dual-core waveguide provides an additional degree of freedom in dispersion engineering for the supermodes, which is advantageous for controlling cascaded nonlinear optical processes or controlling the spectral location of dispersive waves. The dispersion of supermodes can also be engineered to be significantly different from each other, such that rather different output spectra are generated in parallel or separately. Furthermore, by arranging for measurement of the light from each core individually as well as collectively, a physical mode decomposition is facilitated to aid the analysis of multimode nonlinear and cascaded processes. The results and findings presented in this thesis, achieved through the use of integrated photonic circuits, provide progress in the field of multimode nonlinear optics, advancing capabilities in control, deepening understanding, and improving analysis of complex multimode interactions. Despite the advances presented in the thesis, it also shows that multimode nonlinear optics remains a vast and largely unexplored space, offering considerable opportunities for future research.