Abstract: Under the influence of a magnetic field, at low temperatures, charged particles confined in two-dimensional systems exhibit a remarkable range of macroscopic quantum phenomena such as the quantum Hall effects. A hallmark of these phenomena is the presence of unidirectional, topologically robust edge states - states which are confined to the edge of the system. It is, in principle, possible to engineer a synthetic magnetic field for photons and hence achieve photonic analogs of the robust electronic edge states. Investigating photonic edge states is interesting from a fundamental perspective of studying photonic transport in the presence of a gauge field and also for its application in classical and quantum information processing. In this thesis, we present the implementation of a synthetic magnetic field for photons and our observation of topological edge states in a two-dimensional lattice of coupled ring resonators, fabricated using CMOS-compatible silicon-on-insulator technology. We qualitatively show the robustness of edge states against deliberately induced lattice defects. We then analyze the statistics of transport measurements (transmission and delay) made on a number of different devices and quantitatively verify the robustness of edge states against lattice disorder. Using Wigner delay-time distribution, we show that localization is suppressed in the edge states. Furthermore, to unequivocally establish the non-trivial topological nature of edge states, we compare their transmission to a topologically trivial one dimensional system of coupled ring resonators and demonstrate that the edge states achieve higher transmission. Moreover, for photonic analogs of the quantum Hall effect, the winding number - a topologically invariant integer which characterizes edge states - is quantized, analogous to quantization of conductivity in electronic systems. We measure the winding number of the edge states in our system. Finally, we investigate the effect of nonlinear interactions in silicon ring resonators, on the stability of edge states. We show that the presence of a strong pump can result in a significant decrease in the transmission through edge states.
Keywords: Edge states,Photonics,Quantum hall effect, Topological