Cavity design is crucial for single-mode semiconductor lasers such as the ubiquitous distributed feedback and vertical-cavity surface-emitting lasers. By recognizing that both of these optical resonators feature a single mid-gap mode localized at a topological defect in the one-dimensional lattice, we upgrade this topological cavity design concept into two dimensions using a honeycomb photonic crystal with a vortex Dirac gap by applying the generalized Kekulé modulations. We theoretically predict and experimentally show on a silicon-on-insulator platform that the Dirac-vortex cavities have scalable mode areas, arbitrary mode degeneracies, vector-beam vertical emission and compatibility with high-index substrates. Moreover, we demonstrate the unprecedentedly large free spectral range, which defies the universal inverse relation between resonance spacing and resonator size. We believe that our topological micro-resonator will be especially useful in applications where single-mode behaviour is required over a large area, such as the photonic-crystal surface-emitting laser.
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We thank L. Gan, Y. Liang and G. Li for helpful discussions. L.L. acknowledges his PhD advisor J. D. O’Brien (1969–2017) for his teaching of photonic crystal lasers. L.L. was supported by the National Key R&D Program of China (2017YFA0303800, 2016YFA0302400), the Natural Science Foundation of China (11721404), the Strategic Priority Research Program of the the Chinese Academy of Sciences (XDB33000000) and the Beijing Natural Science Foundation (Z200008). F.B. was supported by NSFC under grant nos 11734009 and 11674181.
The authors declare no competing interests.
Peer review informatio Nature Nanotechnology thanks Yidong Chong and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.
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Gao, X., Yang, L., Lin, H. et al. Dirac-vortex topological cavities. Nat. Nanotechnol. 15, 1012–1018 (2020). https://doi.org/10.1038/s41565-020-0773-7
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