Dirac cones induced by accidental degeneracy in photonic crystals and zero-refractive-index materials
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 properties. These materials can in principle be realized using man-made composites comprising metallic resonators or chiral inclusions, 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 dispersion, 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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Both the focusing effect through a concave lens and the waveguiding and cloaking effect through a waveguide filled with εeff=μeff=0 photonic crystal were demonstrated.
“Both the focusing effect through a concave lens and the waveguiding and cloaking effect through a waveguide filled with ε eff = μ eff = 0 photonic crystal were demonstrated.”
From Dirac Dispersion in Two-Dimensional Photonic Crystals (2012) · cites this paper as [66]
Numerical simulations and microwave experiments demonstrated that the photonic crystal with band dispersion shown in Figure 1 has εeff(ωD)=μeff(ωD)=0 at the Dirac frequency.
“In order to demonstrate that the photonic crystal with a band dispersion shown in Figure 1 does have ε eff (ω D ) = μ eff (ω D ) = 0 at the Dirac frequency, numerical simulations, and microwave experiments were carried out [66].”
From Dirac Dispersion in Two-Dimensional Photonic Crystals (2012) · cites this paper as [66]
If the triply degenerate state is formed by monopole and dipole excitations, the system can be mapped to an effective medium with permittivity and permeability equal to zero simultaneously.
“If this triply degenerate state is formed by monopole and dipole excitations, the system can be mapped to an effective medium with permittivity and permeability equal to zero simultaneously”
From Dirac Dispersion in Two-Dimensional Photonic Crystals (2012) · cites this paper as [66]
The emergence of linear bands as a consequence of accidental degeneracy at k=0 can also be obtained using multiple scattering theory or k·p perturbation.
“We note that the emergence of linear bands as a consequence of accidental degeneracy at k = 0 can also be obtained using multiple scattering theory [66] or k • p perturbation [76,77].”
From Dirac Dispersion in Two-Dimensional Photonic Crystals (2012) · cites this paper as [66]
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Self-citation
- Authors
- Huang, X., Lai, Y., Hang, Z. H., Zheng, H., & Chan, C. T.
- Affiliations
- Hong Kong University of Science and Technology (HK)
- Corresponding author
- Chan, C. T.
- Venue
- Nature Materials
- Published
- 2011-05-29
- Volume
- 10
- Issue
- 8
- Pages
- 582-586
- ISSN
- 1476-1122 (ISSN-L)
- 1476-4660
- OpenAlex
- W1964548562
- Cited by
- 993
- References
- 30
- Citations by year
- 2026: 41 · 2025: 63 · 2024: 48 · 2023: 72 · 2022: 62 · 2021: 74 · 2020: 81 · 2019: 89 · 2018: 79 · 2017: 94 · 2016: 89 · 2015: 62 · 2014: 54 · 2013: 38 · 2012: 41
- FWCI
- 17.62
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Nature Materials (publishedVersion)
- PubMed (publishedVersion)
- Rare & Special e-Zone (The Hong Kong University of Science and Technology) (submittedVersion)
- Topics
- Physical Sciences › Materials Science › Electronic, Optical and Magnetic Materials › Metamaterials and Metasurfaces Applications
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Photonic Crystals and Applications
- Physical Sciences › Engineering › Biomedical Engineering › Acoustic Wave Phenomena Research
- Keywords
- Dirac cones, Dirac point, photonic crystals, zero refractive index, zero-index metamaterials, accidental degeneracy, dielectric photonic crystals, effective medium theory, wave manipulation, Brillouin zone
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