This thesis encompasses a broad area of physics including linear and nonlinear optics, photonics and quantum physics. It combines the phenomena of nonlinearoptical frequency conversion with waveguiding and coupling, taking advantage of new opportunities presented by advances in fabrication technologies of micro- and nano-waveguides. In this dissertation an in-depth analysis of quantum and classical properties of light traveling in nonlinear optical waveguides, directional couplers and waveguide arrays is performed. The concepts of spatial and temporal dispersion, waveguiding in structures with subwavelength dimensions and nonlinear interactions between different frequencies of light are studied both theoretically and experimentally. Some sections of this thesis include development and implementation of novel physical ideas, while other sections are focused on comprehensive experimental and numerical analysis of advanced theoretical concepts. The results presented in this dissertation demonstrate new physical phenomena with potential applications in the areas of telecommunications and quantum information. The research performed in this thesis opens opportunities for frequency conversion with world-leading power efficiency, including operation with ultrashort pulses for a variety of wavelengths to suit a wide range of perspective application requirements. It also shows an approach for simple and energy efficient spatio-temporal optical signal control, which can find applications in next generation telecommunications networks. Furthermore, the results obtained in this dissertation demonstrate the possibility for flexible shaping of quantum statistics of photons generated in photonic waveguiding structures through spontaneous frequency conversion, contributing to the development of integrated quantum circuits. The new methods of frequency conversion in micro- and nano-scale waveguides and optical circuits have potential to advance the performance, energy efficiency, and security of future optical communication networks and computing systems
