Bulk-edge correspondence for topological photonic continua

TL;DR

This paper rigorously establishes the bulk-edge correspondence in topological photonic continua, demonstrating that unidirectional edge states correspond to bulk Chern number differences and providing practical implementation insights.

Contribution

It extends the bulk-edge correspondence principle to electromagnetic continua with well-behaved responses, including detailed examples and practical imitations using air gaps.

Findings

Number of edge modes equals bulk Chern number difference

Spatial cut-off effects are crucial for accurate predictions

Air gap can mimic spatial cut-off in realistic systems

Abstract

Here, building on our previous work [Phys. Rev. B, 92, 125153, (2015)], it is shown that the propagation of unidirectional gapless edge states at an interface of two topologically distinct electromagnetic continua with a well-behaved asymptotic electromagnetic response is rigorously predicted by the bulk-edge correspondence principle. We work out detailed examples demonstrating that when the spatial-cut off of the nonreciprocal part of the material response is considered self-consistently in the solution of the relevant electromagnetic problem, the number of unidirectional gapless edge modes is identical to the difference of the Chern numbers of the bulk materials. Furthermore, it is shown how the role of the spatial cut-off can be imitated in realistic systems using a tiny air gap with a specific thickness. This theory provides a practical roadmap for the application of topological concepts to photonic platforms formed by nonreciprocal electromagnetic continua.