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Cited by 250Photonic Crystals and ApplicationsMetamaterials and Metasurfaces ApplicationsTopological Materials and Phenomena

Extremal transmission at the Dirac point of a photonic band structure

Open access
Sepkhanov, R. A., Bazaliy, Ya. B., Beenakker, C. W. J.·2007·Physical Review A
DOI 10.1103/physreva.75.063813
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Abstract

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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Integrity signals

Registry

Crossref · 10.1103/physreva.75.063813

Cites

9 of 9 references verified0 citation errors · 0 not checkable

Statistics

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Claims other papers make about this one

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  • ZB is not unique to Dirac electrons; it is a generic feature of wave packet dynamics in spinor systems with certain linear dispersion relations, such as those exhibiting Dirac points.

    “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]

    The Introduction and Section II describe Dirac points in a photonic crystal, with linearly splitting bands governed by a two-component spinor equation. But the paper analyzes transmission of monochromatic radiation, not Zitterbewegung or wave-packet dynamics, so it does not support the claim that ZB is a generic feature of such systems. The available passages have no page labels. (LLM, conf=0.81)

    Experimental — accuracy not yet measured

  • Pseudodiffusive transmission and Zitterbewegung are properties of conical dispersion and can be observed as long as there is a cone, irrespective of whether effective parameters are retrievable.

    “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]

  • Photonic graphene, a honeycomb array of evanescently coupled waveguides, is a useful tool for investigating graphene physics in various optical settings.

    “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]

  • Surface states are found as localized solutions to Eq. (16) near the surface z = 0, satisfying appropriate boundary conditions.

    “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]

    Section II (Wave Equations) describes a two-dimensional photonic crystal in the x-y plane, and the boundary-matching discussion around Eq. (3.5) concerns an interface at x = 0. Searches for surface states and localized solutions found no passage describing states near z = 0 or solutions to the citing paper’s Eq. (16). (LLM, conf=0.76)

    Experimental — accuracy not yet measured

  • The relativistic extension of the Tamm model is defined by the potential Eq. (28).

    “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]

    The passages on boundary matching and transfer matrices (§3.5–3.8) and transmission probability (§4.9) do not define a Tamm-model potential. Searches for “Tamm model,” its relativistic extension, and potential (28) found no passage addressing the claim. (LLM, conf=0.75)

    Experimental — accuracy not yet measured

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Cites

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Research works printed but not linked: 8

  1. [1]1. ͓1͔ F. D. M. Haldane and S. Raghu, e-print arXiv:cond-mat/ 0503588;
  2. [2]2. S. Raghu and F. D. M. Haldane, e-print arXiv:cond- mat/0602501.
  3. [5]5. ͓4͔ H. Schomerus, e-print arXiv:cond-mat/0611209. · arXiv
  4. [6]6. ͓5͔ Ya. M. Blanter and I. Martin, e-print arXiv:cond-mat/0612577. · arXiv
  5. [13]13. ͓13͔ A. H. Castro Neto and E.-A. Kim, e-print arXiv:cond-mat/ 0702562.
  6. [14]14. ͓14͔ M. Titov, e-print arXiv:cond-mat/0611029. · arXiv
  7. [15]15. ͓15͔ A. Rycerz, J. Tworzydło, and C. W. J. Beenakker, e-print arXiv:cond-mat/0612446. · arXiv
  8. [16]16. ͓16͔ P. M. Ostrovsky, I. V. Gornyi, and A. D. Mirlin, e-print arXiv:cond-mat/0702115. · arXiv

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Related

Authors
Sepkhanov, R. A., Bazaliy, Y. B., & Beenakker, C. W. J.
Affiliations
Leiden University (NL)
ORCID
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
DOI
10.1103/physreva.75.063813
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
Licence
link.aps.org/licenses/aps-default-license (vor)
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 › Atomic and Molecular Physics, and Optics › Topological Materials and Phenomena
Keywords
Dirac point, photonic crystals, photonic band structure, transmission, conical singularities, interface transparency

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