The DOI matches its Crossref record; 19 of the 19 references it cites were found in a registry or an index; none of the 14 sources its claims cite is checked for support yet.
Reflection-Free One-Way Edge Modes in a Gyromagnetic Photonic Crystal
Open accessAbstract
We point out that electromagnetic one-way edge modes analogous to quantum Hall edge states, originally predicted by Raghu and Haldane in 2D photonic crystals possessing Dirac point-derived band gaps, can appear in more general settings. We show that the TM modes in a gyromagnetic photonic crystal can be formally mapped to electronic wave functions in a periodic electromagnetic field, so that the only requirement for the existence of one-way edge modes is that the Chern number for all bands below a gap is nonzero. In a square-lattice yttrium-iron-garnet crystal operating at microwave frequencies, which lacks Dirac points, time-reversal breaking is strong enough that the effect should be easily observable. For realistic material parameters, the edge modes occupy a 10% band gap. Numerical simulations of a one-way waveguide incorporating this crystal show 100% transmission across strong defects.
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“For realistic material parameters, the edge modes occupy a 10% band gap.”
- Also stated in: § Abstract · plain
“With a 1600 Gauss bias, we obtain a wide MO band gap of 10% relative size and very low dispersion, with the edge mode confined to a few lattice constants.”
§ Reflection-Free One-Way Edge Modes in a Gyromagnetic Photonic Crystal > Abstract
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“For example, Fig. 2 shows the TM band diagram for a square lattice of YIG rods in air, containing a quadratic M-point degeneracy between the second and third bands.”
§ Reflection-Free One-Way Edge Modes in a Gyromagnetic Photonic Crystal > Abstract
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“This degeneracy is lifted upon applying an external dc magnetic field, which introduces magnetic anisotropy in the high-index rods and breaks T (as well as inversion and mirror symmetries.)”
§ Reflection-Free One-Way Edge Modes in a Gyromagnetic Photonic Crystal > Abstract
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“With realistic material parameters, the one-way modes are laterally confined to a few lattice constants, and occupy a broad (10%) band gap with negligible material loss.”
§ Reflection-Free One-Way Edge Modes in a Gyromagnetic Photonic Crystal > Abstract
plain- Asserted: passes — The authors put it forward as true.
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In the paper
“With realistic material parameters, the one-way modes are laterally confined to a few lattice constants, and occupy a broad (10%) band gap with negligible material loss.”
- Also stated in: § Abstract · plain
“With a 1600 Gauss bias, we obtain a wide MO band gap of 10% relative size and very low dispersion, with the edge mode confined to a few lattice constants.”
§ Reflection-Free One-Way Edge Modes in a Gyromagnetic Photonic Crystal > Abstract
plain- Asserted: passes — The authors put it forward as true.
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In the paper
“Numerical simulations of a oneway waveguide incorporating this crystal show 100% transmission across strong defects.”
- Also stated in: § Abstract · plain
“In the one-way waveguide, a steady-state source operating at the midgap frequency 0:555 2c=a excites a one-way mode that circumvents the PEC defect, with 100% power transmission throughout the MO band gap.”
§ Reflection-Free One-Way Edge Modes in a Gyromagnetic Photonic Crystal > Abstract
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In the paper
“The MO photonic crystal exhibits strong (order unity) T breaking due to the use of gyromagnetic ferrimagnets.”
§ Reflection-Free One-Way Edge Modes in a Gyromagnetic Photonic Crystal > Abstract
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In the paper
“In the one-way waveguide, a steady-state source operating at the midgap frequency 0:555 2c=a excites a one-way mode that circumvents the PEC defect, with 100% power transmission throughout the MO band gap.”
§ Reflection-Free One-Way Edge Modes in a Gyromagnetic Photonic Crystal > Abstract
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“With a gyromagnetic linewidth of 0.3 Oe and a dieletric loss tangent of 0.0002, typical in commericially available monocrystalline YIG [17], the complex propagation constant is 0:359 0:0001i 2=a in the case of Fig. 3.”
§ Reflection-Free One-Way Edge Modes in a Gyromagnetic Photonic Crystal > PRL 100, 013905 (2008) P H Y S I C A L R E V I E W L E T T E R S
What the sources say
- Not matchedcites [17] 17. E. P. Wohlfarth, in Ferromagnetic Materials (North- Holland, Amsterdam, 1986), Vol. 2, p. 293.
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In the paper
“Although embedded sources were used in these simulations, we have verified in a separate set of simulations that it is also easy to couple to the one-way mode using waves incident on the system boundary.”
§ Reflection-Free One-Way Edge Modes in a Gyromagnetic Photonic Crystal > Abstract
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In the paper
“The separated bands acquire nonzero Chern numbers, causing one-way modes to appear at the edges of the sample.”
§ Reflection-Free One-Way Edge Modes in a Gyromagnetic Photonic Crystal > Abstract
plaindirect- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“With a 1600 Gauss bias, we obtain a wide MO band gap of 10% relative size and very low dispersion, with the edge mode confined to a few lattice constants.”
§ Reflection-Free One-Way Edge Modes in a Gyromagnetic Photonic Crystal > Abstract
plaindirect- Asserted: passes — The authors put it forward as true.
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It may state two separate claims as one.
The paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Note that the regular crystal has zero Chern numbers for all its photonic bands, so there is only one forward-propagating mode at the interface.”
§ Reflection-Free One-Way Edge Modes in a Gyromagnetic Photonic Crystal > Abstract
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In the paper
“Although such reduction narrows the operational bandwidth, we find the dispersion has no impact on the backscattering suppression or the confinement of the edge mode.”
§ Reflection-Free One-Way Edge Modes in a Gyromagnetic Photonic Crystal > PRL 100, 013905 (2008) P H Y S I C A L R E V I E W L E T T E R S
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In the paper
“Hatsugai has shown that in a lattice QH system, this process creates a total of C different edge states at the system's boundary [9].”
§ Reflection-Free One-Way Edge Modes in a Gyromagnetic Photonic Crystal > Abstract
What the sources say
- Not matchedcites [9] 9. Y. Hatsugai, Phys. Rev. Lett. 71, 3697 (1993).
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
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In the paper
“When the system is tuned past this critical point, the degeneracies are lifted; a band gap opens and the band's Chern number changes by an integer C.”
§ Reflection-Free One-Way Edge Modes in a Gyromagnetic Photonic Crystal > Abstract
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In the paper
“Because of the absence of backpropagating modes, backscattering is completely suppressed.”
- Also stated in: § Abstract · plain
“One of the unusual properties of the one-way edge modes is the complete suppression of backscattering, which is an optical analog of the dissipation-free transport of edge electrons in QH systems.”
§ Reflection-Free One-Way Edge Modes in a Gyromagnetic Photonic Crystal > Abstract
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In the paper
“The key properties of the Chern number are that (i) it is always an integer, (ii) the sum of the Chern numbers over all bands is zero, and (iii) the Chern number of every band is zero if the Hamiltonian is T symmetric [13].”
§ Reflection-Free One-Way Edge Modes in a Gyromagnetic Photonic Crystal > Abstract
What the sources say
- Not matchedcites [13] 13. B. Simon, Phys. Rev. Lett. 51, 2167 (1983).
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
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In the paper
“The key properties of the Chern number are that (i) it is always an integer, (ii) the sum of the Chern numbers over all bands is zero, and (iii) the Chern number of every band is zero if the Hamiltonian is T symmetric [13].”
§ Reflection-Free One-Way Edge Modes in a Gyromagnetic Photonic Crystal > Abstract
What the sources say
- Not matchedcites [13] 13. B. Simon, Phys. Rev. Lett. 51, 2167 (1983).
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
plain- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it.
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In the paper
“As a result, the band gap is not robust against disorder, and the edge modes scatter easily into bulk modes of the crystal, leading to significant radiative loss.”
§ Reflection-Free One-Way Edge Modes in a Gyromagnetic Photonic Crystal > Abstract
plaindirect- Asserted: passes — The authors put it forward as true.
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- Rests on an assumption: In realistic gyroelectric materials, the strength of time-reversal breaking (the Voigt parameter) is at most 10^-3.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“While our analysis has thus far been limited to 2D structures at microwave frequencies, similar one-way waveguides can be realized in practical 3D structures and at higher frequencies.”
§ Reflection-Free One-Way Edge Modes in a Gyromagnetic Photonic Crystal > Abstract
plain- Asserted: passes — The authors put it forward as true.
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Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.
The authors state this as an assumption.
Hatsugai's relation between edge states and Chern numbers, derived using a lattice quantum Hall model, applies to the photonic system.
“The Chern-number argument for the existence of photonic edge modes depends on a crucial assumption: that Hatsugai's relation between edge states and Chern numbers [9], which was derived using a lattice QH model, applies to the photonic system.”
The paper relies on this without support.
In realistic gyroelectric materials, the strength of time-reversal breaking (the Voigt parameter) is at most 10^-3.
“In realistic gyroelectric materials, the strength of T breaking, characterized by the ratio of (imaginary) offdiagonal to (real) on-diagonal elements of the permittivity tensor (the Voigt parameter) is at most 10 ÿ3 .”
The paper relies on this without support.
One-way edge modes in gyroelectric photonic crystals have never been observed experimentally.
“To our knowledge, these one-way edge modes have never been observed experimentally, and to do so one would desire a band gap that is orders of magnitude broader.”
The authors state this as an assumption.
The permeability tensor is frequency-independent with real-valued μ and κ, neglecting material dispersion and loss.
“For now, we neglect the effect of material dispersion and loss, assuming a frequency-independent permeability tensor with real-valued and .”
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The cited source doesn’t support the claim as written.
In the citing paper
“the idea of Haldane and Raghu was experimentally implemented using the two-dimensional magnetooptical photonic crystal structure in the microwave domain”
From Topological photonics (2019) · cites this paper as Wang et al., 2008
Checked by a reasoning model — may be wrong.
Experimental — accuracy not yet measuredThe source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“Soon after, this was followed by a realistic design of a gyromagnetic photonic crystal operating at microwave frequencies and displaying a Chern number of 1 (Chong, Wen, and Soljačić, 2008;Wang et al., 2008).”
From Topological photonics (2019) · cites this paper as Wang et al., 2008
Experimental — accuracy not yet measuredIn the citing paper
“Finally we mention that a topological phase similar to that reported here should also be observable in a wider class of bianisotropic systems with quadratic degeneracies [ 14, 46].”
From Photonic topological insulators (2013) · cites this paper as [14]
In the citing paper
“In contrast, our photonic meta-crystal structure preserves time-reversal symmetry and realizes quantum spin Hall response with spin-polarized one-way photonic edge transport.”
From Photonic topological insulators (2013) · cites this paper as [14]
In the citing paper
“Finally, the spin-orbit interaction of light and spin-to-orbit conversion of the angular momentum (which can be associated with the spin Hall effect) occurs upon the scattering of polarized plane waves on various non-planar objects, such as lenses or small scatterers, or in inhomogeneous anisotropic media [67,145 -152].”
From Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium (2009) · cites this paper as [147]
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“(1) and introducing the “wavefunction” ψ = Ez √ µ̃, the eigenvalue problem reduces to (Wang et al., 2008) − |∇+ iA(r)|2ψ + V (r)ψ = 0, (7) where A = µ̃ 2 ẑ ×∇η, V = 1 4 (|∇ ln µ̃|2 + |µ̃∇η|2)− 1 2 ∇2 ln µ̃− µ̃εω2.”
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“The one-way electromagnetic (EM) modes are theoretically topologically protected, which has been theoretically demonstrated [22,23] and experimentally proven [24,25] by many groups.”
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“In conventional way, asymmetric unidirectional propagation can be realized by many approaches, such as using magneto-optical materials [2-4], anisotropic crystals [5, 6], optics non-linear [7] and opto-acoustic effect [8].”
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“At the same time, periodic structures built by magneto-optical materials demonstrated the existence of one-way edge modes due to broken time-reversal symmetry (TRS) [12-19].”
BackgroundInfluentialMagnetically Tunable Unidirectional Electromagnetic Devices Based on Magnetic Surface Plasmon
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“If two MM slabs have the opposite magnetization, then the EM wave reflected forward from one MM slab will also be reflected forward from the other, leading to the design of an OEMW different from those proposed recently (Fu et al., 2011; 2010; He et al., 2010; Huang & Jiang, 2009; Wang et al., 2008; 2009; Yu et al., 2…”
BackgroundMethodResultInfluentialRobust Unidirectional Surface Plasmon-Polaritons at Visible Frequencies Under Normal Magnetic Field
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“Besides,therealsoexistsanalternative waytoachieveunidirectionalEMmodesusingphotoniccrystals (PhCs) [13] with topologically nontrivial bandgaps [14], [15], [16].”
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Magnetic control of Goos-Hanchen shifts in a yttrium-iron-garnet filmPreprint
Yu, W., Sun, H., & Gao, L. (2017) · arXiv (Cornell University) · doi:10.48550/arxiv.1701.01462
“φ = + + − A B g k A B k d 2 tan( ) (34) e e y”
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BackgroundSpace-wave isolator based on remanence at microwave frequencies
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Artificial faraday rotation using active metamaterials
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“Scientifically, topologically-nontrivial phenomena, such as photonic chiral edge states[1], [2], allow for reflection-free transport even in the presence of large disorder.”
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Nonreciprocal dynamic degeneracy splitting in non-Hermitian photonic crystals
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Scattering Rates of Polariton Relaxation
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Winding coupling phase for pseudo-spin-derived topological photonics
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Emergence of Rashba Spin‐Orbit Coupling in Staggered‐Gyromagnetic Photonic Crystals
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Frequency-axis light transport and topological effects in dynamic photonic structures
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A Nonlinear Optical Benzil Single Crystal for Photonic Applications
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Chiral Surface Plasmon Polaritons on One-Dimension Nanowires
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Topological phases in Kagome and triangular photonic crystals
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Tunable directional radiation and reception based on magneto-optical photonic crystal waveguides
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“Propagation of topological edge modes was then studied in real photonic crystals [3] and concepts of the photonic analogues of the Hall states [3, 4, 5] and topological insulators [6, 7, 8, 9] were introduced.”
BackgroundValley-Hall-like second-order photonic topological insulators in Kagome latticePreprint
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“Photonic topological insulators (PTIs), as the extension of topological insulators from electronics to optics, have been realized using different mechanism such as photonic quantum anomalous Hall (QAH) [1-8], quantum spin Hall (QSH) [9- 16] or quantum valley Hall (QVH) effects [17-22].”
BackgroundObservation of Backscattering-Immune Tunnelling States Without External Magnetic Fields
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Strong Coupling: Polariton Bose Condensation
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Tunable wave localization at the Dirac frequency in a metallic photonic crystal cavity
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Nontrivial structural cells induce topologically nontrivial phases under a certain symmetry
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Coupled acoustic resonator systems with novel acoustic properties
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Two-photon quantum walks in Su-Schrieffer-Heeger lattices
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Interlayer-coupling-induced tunable topological phase transition in bilayer photonic crystals
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Photonic arbitrary Chern vectors
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Self-citationBroadband Slow Light in Topologically Protected Waveguides
Mann, S. A., & Alù, A. (2020) · Conference on Lasers and Electro-Optics · doi:10.1364/cleo_at.2020.jm4a.4
Topological Photonic Crystal of Large Valley Chern NumbersPreprint
Xi, X., Ye, K.-P., & Wu, R. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2004.00266
“degeneracy-lifting contributes a Berry flux of magnitude π in each band [2-5], leading to a peak in the Berry curvature.”
BackgroundNear-End Crosstalk Suppression in Coupled Contra-Directional Chern Topological Edge Modes
Elesawy, M. M., Santiago-Vargas, A. D., Hagag, M. F., et al. (2026) · doi:10.1109/imsrftt43070.2026.11602496
“Building on the theoretical foundations established in [2] and the first experimental demonstration in [3], Chern PToIs have since been implemented in transmission lines [3], [4], [5], couplers and power dividers [6], and antennas [7], [8], offering robust propagation even in the presence of defects.”
Extremely broadband topological surface states in a photonic topological metamaterialsPreprint
Kim, M., Lee, D., Gao, W., Ha, T., Kim, T.-T., Zhang, S., & Rho, J. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1901.01482
“on implemented in photonics [4, 5, 6, 7, 8]. Besides Weyl points, other topological states, such as quantum Hall effect and quantum spin Hall effect have been also predicted and observed in photonics [9, 10, 11, 12, 13, 14, 15, 16, 17, 18]. During the last several years, photonic topological materials have developed r…”
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Novel topological phases in gyromagnetic photonic crystals
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Surface States in Topologically Trivial and Non-Trivial Photonic Crystals
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“This is a critical issue in photonic circuit technology, and the development of topological photonic materials has attracted significant attention in recent years as a potential solution [8,9].”
BackgroundNonreciprocal Transmission through Grating with Magneto-Optical Substrate
Zhu, H., Li, F., Liu, Y., et al. (2013) · International Photonics and Optoelectronics Meetings · doi:10.1364/n3.2013.nsa3a.34
Zhang, Z., Liu, C., Li, H., Yu, L., & Ruan, B. (2025) · Journal of Applied Physics · doi:10.1063/5.0275355
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Dipole and Quadrupole Topological Phases of a Simple Magneto-Optical Photonic Crystal
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Topological wireless power transferPreprint
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Physics and Applications of One-Way Magneto-Optical Photonic Crystals
Wang, Z., Chong, Y. D., Joannopoulos, J. D., & Marin Soljacic, A. (2010) · Conference on Lasers and Electro-Optics · doi:10.1364/qels.2010.qfh1
Self-citationLarge Chern number one-way waveguides
Skirlo, S. A., Igarashi, Y., Lü, L., & Marin Soljacic, A. (2015) · doi:10.1364/cleo_qels.2015.ftu2c.3
Self-citationLiao, T.-H., Tsang, L., & Tan, S. (2021) · IEEE International Symposium on Antennas and Propagation and USNC-URSI Radio Science Meeting (AP-S/URSI) · doi:10.1109/aps/ursi47566.2021.9704413
Dirac-vortex topological photonic crystal fiber
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Topological spin dynamics in 2D Bose Lattices
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Unidirectional bulk magnetoplasmons at terahertz frequencies
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Strong Magneto-Optical Response Enabled by Quantum Two-Level Systems
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Design of Non-Reciprocal Absorbing Material Based on One-Way Transmission Structure
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A scale-invariant large-area single-mode topological photonic cavityPreprint
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Self-citationPhotonic crystal antireflection coatings, surface modes, and impedances
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Nonlinear, non-Hermitian and high-dimensional classical topological systems
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Acoustic graphyne: A second-order real Chern topological insulator
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Topological Edge State Enabled Dual-Band Microwave Circulator using Photonic Crystals
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Functional Topological THz devices using Semiconductors
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A Hybrid Topological Heterostructure for Communication
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Metadata
- Authors
- Wang, Z., Chong, Y. D., Joannopoulos, J. D., & Soljačić, M.
- Affiliations
- Massachusetts Institute of Technology (US)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2008-01-10
- Volume
- 100
- Issue
- 1
- Pages
- 013905-013905
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2108731428
- Semantic Scholar
- 41ca4f0ff8b496c56fe38c84cbb7ad55532dead4
- Cited by
- 1,444
- References
- 19
- Citations by year
- 2026: 65 · 2025: 109 · 2024: 129 · 2023: 103 · 2022: 116 · 2021: 109 · 2020: 115 · 2019: 98 · 2018: 103 · 2017: 106 · 2016: 79 · 2015: 75 · 2014: 46 · 2013: 54 · 2012: 54
- FWCI
- 16.03
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- DR-NTU (Nanyang Technological University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- National Science Foundation (0213282)
- Division of Materials Research
- Army Research Office (W911NF-07-D- 0004, W911NF)
- Topics
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Topological Materials and Phenomena
- 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
- Keywords
- gyromagnetic photonic crystals, Chern number, quantum Hall edge states, Dirac point, yttrium iron garnet, time-reversal symmetry breaking, TM modes, microwave photonics, photonic waveguides, square lattice photonic crystal
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