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Extremal transmission at the Dirac point of a photonic band structure
Open accessAbstract
We calculate the effect of a Dirac point (a conical singularity in the band structure) on the transmission of monochromatic radiation through a photonic crystal. The transmission as a function of frequency has an extremum near the Dirac point, depending on the transparencies of the interfaces with free space. The extremal transmission ${T}_{0}={\ensuremath{\Gamma}}_{0}W∕L$ is inversely proportional to the longitudinal dimension $L$ of the crystal (for $L$ larger than the lattice constant and smaller than the transverse dimension $W$). The interface transparencies affect the proportionality constant ${\ensuremath{\Gamma}}_{0}$, and they determine whether the extremum is a minimum or a maximum, but they do not affect the ``pseudodiffusive'' $1∕L$ dependence of ${T}_{0}$.
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“However, several authors have recently shown that ZB is not unique to Dirac electrons, rather it is a generic feature of wave packet dynamics in spinor systems with certain linear dispersion relations, such as those exhibiting the so-called Dirac points (DP) that describe massless fermions [3-13].”
From Photonic analog of Zitterbewegung in binary waveguide arrays (2010) · cites this paper as [7]
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In the citing paper
“We note that other intriguing wave transport properties such as pseudodiffusive transmission [17,18] and Zitterbewegung [20,33] are properties of the conical dispersion and can be observed as long as there is a cone, irrespective of whether effective parameters are retrievable or not.”
From Dirac Dispersion in Two-Dimensional Photonic Crystals (2012) · cites this paper as [17]
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“In particular, photonic graphene (a honeycomb array of evanescently coupled waveguides 14 ) has proven to be a useful tool for investigating graphene physics in various optical settings [15][16][17][18][19][20][21][22][23] .”
From Unveiling pseudospin and angular momentum in photonic graphene (2015) · cites this paper as [15]
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“Surface states are found as localized solutions to Eq.(16), near the surface z = 0, satisfying the appropriate boundary conditions, as discussed in [80].”
From Classical simulation of relativistic quantum mechanics in periodic optical structures (2011) · cites this paper as [80]
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“The relativistic extension of the Tamm model is defined by the potential (see, for instance, [70,80])”
From Classical simulation of relativistic quantum mechanics in periodic optical structures (2011) · cites this paper as [80]
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“In earlier studies, the Dirac-Kronig-Penney model also attracted some attention and caused a lively debate about the existence of so-called Dirac surface states, i.e. relativistic surface Tamm states which disappear in the nonrelativistic limit [66,70,77,78,79,80,81,82].”
From Classical simulation of relativistic quantum mechanics in periodic optical structures (2011) · cites this paper as [80]
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In the citing paper
“The corresponding energy spectrum is composed by a set of allowed energy bands E = E ( q ), which are defined by the following implicit equation (see, for instance, [80])”
From Classical simulation of relativistic quantum mechanics in periodic optical structures (2011) · cites this paper as [80]
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Metadata
- Authors
- Sepkhanov, R. A., Bazaliy, Y. B., & Beenakker, C. W. J.
- Affiliations
- Leiden University (NL)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2007-06-13
- Volume
- 75
- Issue
- 6
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W2088931175
- Semantic Scholar
- d09aa3b4f9fdc99b18e122ed4c306db047174004
- Cited by
- 250
- References
- 9
- Citations by year
- 2026: 3 · 2025: 6 · 2024: 10 · 2023: 9 · 2022: 7 · 2021: 18 · 2020: 8 · 2019: 12 · 2018: 11 · 2017: 15 · 2016: 22 · 2015: 21 · 2014: 16 · 2013: 22 · 2012: 18
- FWCI
- 7.14
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Leiden Repository (Leiden University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- Data Archiving and Networked Services (DANS) (submittedVersion, other-oa)
- arXiv (Cornell University)
- Funders
- Nederlandse Organisatie voor Wetenschappelijk Onderzoek
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Photonic Crystals and Applications
- Physical Sciences › Materials Science › Electronic, Optical and Magnetic Materials › Metamaterials and Metasurfaces Applications
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Topological Materials and Phenomena
- Keywords
- Dirac point, photonic crystals, photonic band structure, transmission, conical singularities, interface transparency
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