Topological Photonics in guided wave geometries: A topological toolbox for signal processing

In the past years, pledges of applications to photonic devices in terms of robustness, efficency, and ease of design have been fostering the research on topological photonics. Such research efforts shed light on the physics of time reversal nonsymmetric systems and, more in general, helped clarifying to the broader physics community concepts such as topological insulators, Chern numbers and others. Further than that, the perspective of an experimental implementation of topological models bolstered the development of several platforms. Among those, waveguide arrays, photonic lattices, and many more cutting-edge experimental setups are now characterized by an unprecedented control, paving the way to the experimental verification of various wave mechanical features. Only recently, topological photonics evolved from a fundamental field aimed at understanding the physics of non-trivial Hamiltonians, to a design methodology for obtaining tailored effects in photonic systems. In this thesis we present a toolbox of topological effects in photonic platforms, drawing inspiration from classical problems in signal processing. We focus on the use of topological states for the frequency conversion of photons, and on the interplay between counterproagating edge states. Rather than the fundamental physics of edge states, the focus is the exploration of topological photonics as a design method for empowering current technologies.