All-­bands-­flat Floquet topological photonic insulator and its application in programmable photonic waveguide lattices
Creators: Song, Hanfa
Publisher: name: University of Alberta Library
Year: 2024

<p>Coupled microring lattices are versatile photonic systems that can be used to realize various topological phases of matter. In two-dimensional microring lattices, the periodic and unidirectional circulation of light in each microring gives rise to a time-like dimension, so that the lattice emulates a (2+1)D system with much richer topological behaviors than static 2D lattices. In this thesis, we demonstrated a (2+1)D Floquet topological photonic insulator based on a microring lattice as a platform for potential application in robust programmable photonic integrated circuits. Particular focus is placed on the microring Lieb lattice with perfect couplings, which emulates an anomalous Floquet insulator with all flat bands. Such a system exhibits some unique properties, including wide edge mode continuum exceeding a Floquet-Brillouin zone, super-robustness to lattice disorder, photon caging and compact localized flat-band states that can be used to realize high-quality factor topological resonators. We first propose the theory and design of (2+1)D topological systems based on microring lattices. Accurate treatment of such a system must necessarily depart from the static 2D tight binding model and take into account the periodic coupling sequence of the network. Unlike the tight binding model which is only valid for weakly-coupled microring systems, our treatment of the microring lattices is based on the coupling of waveguide modes in space, which can fully capture the micromotion of light circulating in each microring. We focus on the Floquet-Lieb insulator (FLI) microring lattice since it provides the simplest and most compact nontrivial Floquet TPI. Of particular interest is the special case when the coupling is perfect, for which the lattice has all flat bands. Such all-bands-flat (ABF) systems exhibit some unique properties, including wide edge mode continuum in principle extending indefinitely and super-robustness to lattice disorder. Next, we realize the ABF-FLI using 2D microring resonator lattices with perfect nearest-neighbor couplings on an SOI platform. Transmission measurements and direct imaging of the scattered light distributions showed an edge mode supercontinuum spanning more than three microring free spectral ranges. Such experimental observations validate our theoretical proposals of the ABF-FLI microring lattice. In addition, we theoretically prove that the three flat bands of an ABF-FLI microring lattice originates from Aharonov-Anandan (AA) caging effect, where constructive interference occurs when both dynamic phase and AA phase are taken into consideration in the system. We experimentally demonstrate AA caging effect by observing the flat-band resonance mode from microring lattices for both the cases of large and negligible disorders. As a potential application, we propose that the ABF-FLI microring lattice can be used to construct robust programmable photonic integrated circuits (PICs). We show that by exploiting the natural hopping sequence of light in the ring lattice, we can form a new type of robust line defect modes by selectively tuning only certain coupling elements. General circuits can be implemented using a combination of the line defect modes and flat-band modes. Finally we develop an efficient and analytical method to evaluate the robustness of integrated photonic devices and circuits in the presence of random variations in the device parameters, which allows us to efficiently quantify the robustness of arbitrary photonic circuits including topological photonic circuits.</p>