Abstract
Floquet topological photonic insulators characterized by periodically varying Hamiltonians are known to exhibit much richer topological behaviors than static systems. In a Floquet insulator, the phase evolution of the Floquet–Bloch modes plays a crucial role in determining its topological behaviors. Here, we show that by perturbing the driving sequence, it is possible to manipulate the cyclic phase change in the system over each evolution period to induce self-interference of a bulk mode, leading to a resonance effect, which can be regarded as a Floquet counterpart of defect-mode resonance in static lattices. This Floquet Defect Mode Resonance (FDMR) is cavity-less since it does not require physical boundaries; its spatial localization pattern is, instead, determined by the driving sequence and is found to be different in topologically trivial and nontrivial lattices. We demonstrated excitation of FDMRs by edge modes in a Floquet octagon lattice on silicon-on-insulator, achieving extrinsic quality factors greater than 104. Imaging of the scattered light pattern directly revealed the hopping sequence of the Floquet system and confirmed the spatial localization of FDMR in a bulk-mode loop. The new Floquet topological resonator could find various applications in lasers, optical filters and switches, nonlinear cavity optics, and quantum optics.
Highlights
The ability to form robust high quality factor resonators in a topological lattice is of practical interest as it would significantly broaden the range of applications of Topological photonic insulators (TPIs) such as in lasers, filters, nonlinear cavity optics, and quantum optics
We report a new mechanism for forming resonance in a Floquet TPI by adiabatically tuning the cyclic phase of a Floquet mode to achieve constructive interference. This has the concomitant effect of shifting its quasienergy into a topological bandgap to form an isolated flat-band state that is spatially localized in a bulk-mode resonant loop, which we refer to as Floquet Defect Mode Resonance (FDMR)
We report a new method for trapping light in a Floquet TPI lattice by adiabatically tuning the cyclic phase of a Floquet mode to induce self-interference
Summary
Topological photonic insulators (TPIs) provide a rich playground for exploring both the physics of periodic systems and applications of their exotic properties. In particular, Floquet TPIs characterized by periodically varying Hamiltonians have recently gained much attention as they can exhibit richer topological behaviors than static undriven systems, such as the existence of anomalous Floquet insulator (AFI) edge modes even though the energy bands of the lattice have a trivial Chern number. In a periodically driven system, the evolution of the phase bands of the Floquet–Bloch modes, defined as the phases of the eigenvalues of the system’s evolution operator, plays a crucial role in determining its topological behaviors. Here, we investigate the possibility of manipulating the cyclic phase change in a Floquet mode to induce self-interference and resonance effects in the lattice bulk. We report a new mechanism for forming resonance in a Floquet TPI by adiabatically tuning the cyclic phase of a Floquet mode to achieve constructive interference This has the concomitant effect of shifting its quasienergy into a topological bandgap to form an isolated flat-band state that is spatially localized in a bulk-mode resonant loop, which we refer to as Floquet Defect Mode Resonance (FDMR). We note that while drive-dependent defects have been used to investigate the robustness of edge modes in 2D Floquet TPIs based on coupled waveguides, the perturbation of the Floquet–Bloch Hamiltonian to manipulate both the cyclic phase change and spatial localization of a Floquet mode to create a resonance has not been reported before. We achieved an extrinsic Q-factor of ∼1.7 × 104, which is among the highest reported to date for 2D topological photonic resonators. Our work introduces a new, versatile method for forming high-Q resonances in a Floquet lattice, which could have a wide range of applications in cavity optics
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