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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13 Sources not found · 12 Own interpretation · 10 Own result · 6 No basis given · 1 Own method
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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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It may state two separate claims as one.
- Rests on an assumption: In realistic gyroelectric materials, the strength of time-reversal breaking (the Voigt parameter) is at most 10^-3.
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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
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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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Self-citationTopological Protection of Quantum States in Silicon
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“Previous experiments in topological photonics have used either classical radiation [2-8], or quantum walks of single photons [9], but never used entangled states.”
BackgroundElectromagnetic wave scattering by an array of axially magnetized parallel plasma columns
Es’kin, V. A., Kudrin, A. V., Zaboronkova, T. M., et al. (2013) · International Conference Days on Diffraction (DD) · doi:10.1109/dd.2013.6712802 · Cited by 1
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Reconfigurable Topological Power Router Based on Interferometric Edge States
Zhang, X., Li, S., Yu, C., Gao, W., & Chen, M. L. N. (2026) · IEEE Transactions on Antennas and Propagation · doi:10.1109/tap.2026.3661630 · Cited by 1
“This has led to the demonstration of photonic analogs including the quantum Hall [6], [7], [8], [9], [10], [11], [12], quantum spin Hall [13], [14], [15], [16], [17], and quantum valley Hall e ff ects (QVHEs) [18], [19], [20], [21], [22], [23].”
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Unidirectional propagation control of helical edge states in topological spin photonic crystals
Sui, W., Zhang, Y., Zhang, Z.-R., Wang, X., Zhang, H., Shi, Q., & Yang, B. (2022) · Acta Physica Sinica · doi:10.7498/aps.71.20220353 · Cited by 1
Integrated topological photonics in one dimension
Hotte-Kilburn, A., & Bianucci, P. (2025) · Advances in Physics X · doi:10.1080/23746149.2025.2476417 · Cited by 2
“Later on, a consensus was formed that topological effects are present in wave theories such as electromagnetism [2,3], and mechanical vibrations [4].”
Asynchronous topological phase transition in trimer lattices
Dang, Y., Zhang, J., Jiang, T., Xin, G., Yang, J., Zhang, W., & Qi, X. (2023) · Journal of the Optical Society of America B · doi:10.1364/josab.509952 · Cited by 1
Basics of the photonic crystal gratings
Serebryannikov, A. E. (2012) · InTech eBooks · doi:10.5772/34685 · Cited by 1
Far-field detection of two-dimensional terahertz topological photonic crystals
Ma, J., Ouyang, C., Chen, X., Xu, Q., ShaoXian, L. I., Feng, X., Li, N. I. U., Yi, L. I. U., Han, J., & Zhang, W. (2021) · Zhongguo kexue. Wulixue Lixue Tianwenxue · doi:10.1360/sspma-2020-0242 · Cited by 1
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Topological Metal‐Insulator Phase Transition in A Square Lattice Model
Liu, L., Hu, K., Zhang, Z., Cao, J., Cui, W., Zhang, S., & Wang, H. (2025) · Advanced Quantum Technologies · doi:10.1002/qute.202500381 · Cited by 1
RelativisticZitterbewegungin non-Hermitian photonic waveguide systems
Wang, G., Xu, H., Huang, L., & Lai, Y.-C. (2017) · New Journal of Physics · doi:10.1088/1367-2630/aa5127 · Cited by 1
Parity anomaly and its transport signatures in three-dimensional chiral topological phases
Wan, Y., Han, Y., Zhao, R., & Sun, Q. (2026) · Physical review. B./Physical review. B · doi:10.1103/p7dw-19m2 · Cited by 2
Li, Y., Sun, Y., Zhu, W., Guo, Z., Jiang, J., Kariyado, T., Chen, H., & Hu, X. (2018) · arXiv (Cornell University) · doi:10.48550/arxiv.1801.04395 · Cited by 2
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Topology of Bloch impedance: traveling waves, dispersive media, and electromagnetic energy
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Symbolic Learning of Topological Bands in Photonic Crystals
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“Such edge channels enable slow light with a large bandwidth and can be used for optical isolation [51–55].”
Self-citationTunable topological edge states based on anomalous scattering
Yang, C. G., Li, J., Liu, J., Yao, J., Wang, Y., Zhou, Z., & Yuan, C. (2025) · Optics Letters · doi:10.1364/ol.555560 · Cited by 2
Broadband Unidirectional Electromagnetic Mode along an Arbitrary Surface
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Low-symmetrical Topological Graphene Metasurfaces with Quantum Valley and Spin Hall Effects
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An experimental study of self-guided unidirectional waveguides by a chain of gyro-magnetic rods
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Valley-Hall-like photonic topological insulators with vanishing Berry curvaturePreprint
Zhang, L., & Xiao, S. (2019) · arXiv (Cornell University) · Cited by 1
Improving Topological Confinement Using Asymmetric Elements
Jin, X., Razzari, L., & Bianucci, P. (2022) · Advanced Photonics Research · doi:10.1002/adpr.202200089 · Cited by 2
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“Moreover, it provides a new perspective on wave localization, which is a central topic to many practical applications including surface plasmon resonances [5, 25, 34, 45, 53], topologically robust states in quantum Hall effect [24, 29, 50], directional optical waveguide [27, 28], photonic transport [31, 48, 51], and c…”
BackgroundStatic nonreciprocity in mechanical metamaterials enabled by symmetry breaking: a perspective
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Manipulating Electromagnetic Waves with Zero Index Materials
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“Although early designs for photonic topological one-way edge modes involved breaking the time-reversal (T-reversal) symmetry in gyromagnetic materials using an external magnetic field [4-7], it was soon discovered that a synthetic magnetic field could exhibit the same effect as a real magnetic field in producing one-w…”
BackgroundOn maximum left/right reflectance asymmetry exhibited by a gyrotropic dielectric slab
Mackay, T. G., & Lakhtakia, A. (2024) · Journal of Physics Communications · doi:10.1088/2399-6528/ad1dc7 · Cited by 1
Acoustic Metamaterials with Conical Dispersions
Huang, X., Xiao, M., Chan, C. T., & Liu, F. (2017) · World Scientific series in nanoscience and nanotechnology/World scientific series in nanoscience and nanotechnology · doi:10.1142/9789813228702_0013 · Cited by 1
Highly efficient channel drop filter based on photonic crystal one-way waveguide
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Non-reciprocal optical devices based on linear silicon photonic crystals
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Observation of localization reversal and harmonic generation in nonlinear non-Hermitian skin effect
Wu, J., Shen, R.-C., Zhang, L., Chen, F., Wang, B., Chen, H., Yang, Y., & Xue, H. (2026) · Nature Communications · doi:10.1038/s41467-026-74610-y · Cited by 2
“Since the realization of photonic Chern insulators at microwave frequencies [3, 4], various topological phases have been successfully implemented in photonics, including the quantum spin Hall phase [5–7], valley Hall phase [8– 10], Floquet topological phase [11–13], among others.”
Tang, G.-H., Ma, Z.-L., Zhang, R., Hou, B., Dong, Y.-H., Fan, R., Cai, Q., Zhu, Y., Peng, R., & Wang, M. (2025) · Physical review. B./Physical review. B · doi:10.1103/physrevb.111.195423 · Cited by 1
Realization of pure gyration coupling in an on-chip superconducting microwave device
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Magneto-optical double zero-index media and their electromagnetic properties in the bulk
Feng, F., Wang, N., & Wang, G. P. (2022) · New Journal of Physics · doi:10.1088/1367-2630/ac9f28 · Cited by 2
Terahertz Topological Photonic Integrated Transmission Line Based On Valley Spin States
Zhang, X., Wang, L., Zhang, Y., & Yang, Z. (2023) · IEEE International Vacuum Electronics Conference (IVEC) · doi:10.1109/ivec56627.2023.10157549 · Cited by 1
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A scale-invariant large-area single-mode topological photonic cavityPreprint
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Self-citationAcoustic topological one-way waveguides with tunable widths using spinning components
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Asymmetric light transmission based on coupling between photonic crystal waveguides and L1/L3 cavity
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Semiclassical description of light–matter coupling
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Dual-band dislocation modes in a topological photonic crystal
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Self-Guiding Backscattering Immune Transportation of Light in the Visible Range
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“[1] pointed out that the Voigt parameter of conventional gyroelectric materials is very small (in the order of ∼10−3), resulting in weak TRS breaking strength and the inability to form an observable topological bandgap.”
BackgroundEdge states and the Valley Hall EffectPreprint
Drouot, A., & Weinstein, M. I. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1910.03509 · Cited by 1
“The types of perturbed honeycomb operators or edge operators we consider were introduced in [22,23] to capture the essential features of theoretical and experimental work [30,45,49].”
BackgroundNonreciprocal multifunctional electromagnetic wave controller
Wang, Y., Tao, X., Pei, W., Ma, H., Li, F., & Poo, Y. (2021) · Optics Communications · doi:10.1016/j.optcom.2021.127529 · Cited by 1
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“Geometrical and topological quantities, such as the Berry curvature or Berry phase, have been introduced in the bulk of photonics models in complete analogy to their solid-state counterparts [25, 82].”
Multiple topological phases in phononic crystals
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Photonic crystal one-way ring resonator
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Goos-Hänchen shift of a normally incident beam on a magneto-optical metagrating
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Variational Quantum Algorithm for Photonic Crystals(Invited Paper)
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Continual mode transformation in a unidirectional compound waveguide
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“As is known, the YIG material has material dispersion and loss, and the material parameters are dependent on the working frequency and the applied magnetic field [6].”
BackgroundQuantum transport in coupled resonators enclosed synthetic magnetic flux
Jin, L. (2016) · Annals of Physics · doi:10.1016/j.aop.2016.03.005 · Cited by 1
Topological phases in non-Hermitian nonlinear-eigenvalue systems
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“The impact of nonlinearity on boundary states gives rise to unique topological phenomena inter-twined with the soliton [45–51] and synchronization [52– 54], and a potential realization of high-performance topological lasers [55].”
Effects of optical axis orientation on polarization singularities in anisotropic grating system
Lei, S., Zheng, Z.-H., Duan, Q., et al. (2025) · Journal of Applied Physics · doi:10.1063/5.0284473 · Cited by 1
Robust flow of light in three-dimensional dielectric photonic crystals
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Topological phase transition of photonic Chern insulators by multi-Mie-resonance inversion
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Channel switch based on the transformation of two kinds of topological edge states
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Instability of Quadratic Band Degeneracies and the Emergence of Dirac Points
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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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