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Dirac-vortex topological cavities

Nature Nanotechnology volume 15, pages 1012–1018 (2020)Cite this article

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Abstract

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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Fig. 1: Comparison of the Dirac-vortex cavity and the three types of commercialized semiconductor laser cavities for single-mode operation.
Fig. 2: Design of the photonic-crystal Dirac-vortex cavity in an air-clad silicon membrane (0.46a thick, n = 3.4) by three-dimensional (3D) simulations for the TE-like modes.
Fig. 3: Cavity properties as a function of the vortex size studied using 2D calculations with the effective refractive index 2.6.
Fig. 4: Cavity Q as a function of substrate index (nsub) studied by 3D finite-difference-time-domain method for two configurations.
Fig. 5: Experimental studies of silica-cladded Dirac-vortex cavities with α = 4, m0 = 50 nm and a = 490 nm.

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Acknowledgements

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.

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Author notes

  1. These authors contributed equally: Xiaomei Gao, Lechen Yang.

Authors and Affiliations

  1. Institute of Physics, Chinese Academy of Sciences/Beijing National Laboratory for Condensed Matter Physics, Beijing, China

    Xiaomei Gao, Lechen Yang, Hao Lin, Lang Zhang, Jiafang Li & Ling Lu

  2. MOE Key Laboratory of Weak-Light Nonlinear Photonics, TEDA Institute of Applied Physics and School of Physics, Nankai University, Tianjin, China

    Xiaomei Gao, Lang Zhang & Fang Bo

  3. School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, China

    Lechen Yang & Hao Lin

  4. Institute for Advanced Study, Tsinghua University, Beijing, China

    Zhong Wang

  5. Songshan Lake Materials Laboratory, Dongguan, China

    Ling Lu

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Contributions

L.L. conceived and led the project and wrote the paper. X.G. performed the simulations with help from H.L. and L.Z.; L.Y. performed device fabrication and characterization. Z.W. contributed to the analytical model. All authors discussed the results and commented on the manuscript.

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Correspondence to Ling Lu.

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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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Supplementary Information

Supplementary Figures S1–S12, Supplementary Table S1.

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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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