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Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials

Nature Materials volume 10, pages 582–586 (2011)Cite this article

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Abstract

A zero-refractive-index metamaterial is one in which waves do not experience any spatial phase change, and such a peculiar material has many interesting wave-manipulating properties1,2,3,4,5,6,7,8,9,10. These materials can in principle be realized using man-made composites comprising metallic resonators7 or chiral inclusions11,12, but metallic components have losses that compromise functionality at high frequencies. It would be highly desirable if we could achieve a zero refractive index using dielectrics alone. Here, we show that by employing accidental degeneracy, dielectric photonic crystals can be designed and fabricated that exhibit Dirac cone dispersion at the centre of the Brillouin zone at a finite frequency. In addition to many interesting properties intrinsic to a Dirac cone dispersion13,14,15,16,17,18,19, we can use effective medium theory to relate the photonic crystal to a material with effectively zero permittivity and permeability. We then numerically and experimentally demonstrate in the microwave regime that such dielectric photonic crystals with reasonable dielectric constants manipulate waves as if they had near-zero refractive indices at and near the Dirac point frequency.

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Figure 1: The band structure of a two-dimensional photonic crystal with a square lattice.
Figure 2: Accidental degeneracy conditions and effective parameters from effective medium theory.
Figure 3: Simulations demonstrating that waves can turn through a bent waveguide with and without embedded obstacles.
Figure 4: Microwave experiment to illustrate the cloaking effect.
Figure 5: Simulations and microwave experiment demonstrating waves passing through the PC with almost zero phase change.

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Acknowledgements

This work is supported by Hong Kong RGC grant 600209. We thank W. J. Wen for providing microwave equipment.

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Author notes

  1. Xueqin Huang, Yun Lai and Zhi Hong Hang: These authors contributed equally to this work

Authors and Affiliations

  1. Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China

    Xueqin Huang, Yun Lai, Zhi Hong Hang, Huihuo Zheng & C. T. Chan

  2. Department of Physics, Soochow University, 1 Shizi Street, Suzhou 215006, China

    Yun Lai

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  1. Xueqin Huang
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Contributions

X.H. and Y.L. did the calculations, Z.H.H. designed and performed all the experimental measurements, H.Z. helped with the calculations, and C.T.C. conceived the idea and wrote the manuscript.

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Correspondence to C. T. Chan.

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Huang, X., Lai, Y., Hang, Z. et al. Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials. Nature Mater 10, 582–586 (2011). https://doi.org/10.1038/nmat3030

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