Topological phases in ring resonators: recent progress and future prospects

Daniel Leykam,Luqi Yuan

doi:10.1515/nanoph-2020-0415

Abstract

AbstractTopological photonics has emerged as a novel paradigm for the design of electromagnetic systems from microwaves to nanophotonics. Studies to date have largely focused on the demonstration of fundamental concepts, such as nonreciprocity and waveguiding protected against fabrication disorder. Moving forward, there is a pressing need to identify applications where topological designs can lead to useful improvements in device performance. Here, we review applications of topological photonics to ring resonator–based systems, including one- and two-dimensional resonator arrays, and dynamically modulated resonators. We evaluate potential applications such as quantum light generation, disorder-robust delay lines, and optical isolation, as well as future research directions and open problems that need to be addressed.

Highlights

Demand for miniaturized optical components such as waveguides and lenses that can be incorporated into compact photonic devices is pushing fabricationPresent address: Daniel Leykam, Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore.One natural setting where this robustness can potentially be useful is in the design of integrated photonic circuits [3], where strong light confinement brings sensitivity to nanometre-scale fabrication imperfections
Topological photonics has emerged as a novel paradigm for the design of electromagnetic systems from microwaves to nanophotonics
While the electronic quantum Hall phase exhibits a Hall conductivity precisely quantized to 1 part in 109, in photonics, various effects such as material absorption, out-of-plane scattering, and imperfect symmetries mean that the topological protection is only approximate, so the edge modes are only protected against certain classes of perturbations

Summary

Introduction

Present address: Daniel Leykam, Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore. These exhibit either unidirectional or spin-controlled propagation along the edge The former appear in topological systems with broken time-reversal symmetry (known as quantum Hall topological phases [15]), while in photonics, where an is the annihilation operator for the nth site and J1,2 are coupling strengths. The synthetic gauge field refers to complex (direction-dependent) coupling between different sites of the photonic lattice, arising in systems with nonreciprocity or broken time-reversal symmetry, corresponding to tight binding coupling terms of the form Jeiθa†n+1an + Je−iθa†nan+1, where θ is the coupling phase. While the electronic quantum Hall phase exhibits a Hall conductivity precisely quantized to 1 part in 109, in photonics, various effects such as material absorption, out-of-plane scattering, and imperfect symmetries mean that the topological protection is only approximate, so the edge modes are only protected against certain classes of perturbations. The end states of the Su–Schrieffer–Heeger model are only protected against the “off-diagonal” disorder in the intersite coupling coefficients and are not protected against the “diagonal” disorder in the individual sites’ resonant frequencies, which leads to random variations to the end modes’ resonant frequencies

Ring resonators

Topological coupled resonator lattices

Topology of dynamically modulated resonators

Future directions

Conclusion