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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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In the paper
“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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In the paper
“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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In the paper
“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
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesThe 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
“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
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesA 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 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
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes- Also stated in: § Abstract · plain
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
“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
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesThe 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
“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
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIn the paper
“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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- It may state two separate claims as one. 8
- Probably not a substantial claim. 4
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
“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
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt 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
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt 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
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
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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
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes? Load-bearing: unclear✓ Based: passesIt may state two separate claims as one.
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
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
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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
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
- Also stated in: § Abstract · plain
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.
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesProbably not a substantial claim.
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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.
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
- Not matched
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
“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
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt 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.
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
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably 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 .”
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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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Hajivandi, J., Pakarzadeh, H., & Kurt, H. (2021) · Optical and Quantum Electronics · doi:10.1007/s11082-021-02745-x · Cited by 14
Topologically Protected Photonic Edge States in the Visible in Plasmo‐Gyroelectric Metamaterials
Wu, X., Ye, F., Merlo, J. M., Naughton, M. J., & Kempa, K. (2018) · Advanced Optical Materials · doi:10.1002/adom.201800119 · Cited by 13
One-way surface states due to nonreciprocal light-line crossing
Abbasi, F., Davoyan, A. R., & Engheta, N. (2015) · New Journal of Physics · doi:10.1088/1367-2630/17/6/063014 · Cited by 13
Yannopapas, V., & Vanakaras, A. G. (2011) · Physical Review B · doi:10.1103/physrevb.84.045128 · Cited by 13
Local density of states of chiral Hall edge states in gyrotropic photonic clusters
Asatryan, A. A., Botten, L. C., Fang, K., Fan, S., & McPhedran, R. C. (2013) · Physical Review B · doi:10.1103/physrevb.88.035127 · Cited by 13
Coexistence of Chiral and Antichiral Edge States in Photonic Crystals
Wang, H., Xie, B., & Ren, W. (2023) · Laser & Photonics Review · doi:10.1002/lpor.202300764 · Cited by 14
Shen, S.-L., Li, J., Wu, J.-F., & Li, C. (2022) · The European Physical Journal Plus · doi:10.1140/epjp/s13360-021-02313-y · Cited by 12
Magnetically Induced Topological Evolutions of Exceptional Points in Photonic Bands
Zhao, X., Wang, J., Liu, W., Shi, L., & Zi, J. (2025) · Physical Review Letters · doi:10.1103/wv2n-51qg · Cited by 17
All‐Optical Digital Logic Based on Unidirectional Modes
Xu, J., Luo, Y., Xiao, S., Kang, F., & Tsakmakidis, K. L. (2022) · Advanced Optical Materials · doi:10.1002/adom.202201836 · Cited by 13
Topological Photonics for Optical Communications and Quantum Computing
Manzalini, A. (2020) · Quantum Reports · doi:10.3390/quantum2040040 · Cited by 14
“, who provided realistic material designs [30] and experimental observations [31].”
BackgroundRealization of a quadrupole topological insulator phase in a gyromagnetic photonic crystal
Zhou, P., Liu, G.-G., Wang, Z., Li, S., Xie, Q., Zhang, Y., Mandal, S., Xi, X., Gao, Z., Deng, L., et al. (2024) · National Science Review · doi:10.1093/nsr/nwae121 · Cited by 19
Self-citationFernandes, D. E., & Silveirinha, M. G. (2023) · Physical Review Applied · doi:10.1103/physrevapplied.20.054028 · Cited by 13
Design of second-order phoxonic topological insulators with customized bandgaps
Chen, Y., Wen, X., Lan, Z., Gu, Z., Zhu, J., & Su, Z. (2024) · International Journal of Mechanical Sciences · doi:10.1016/j.ijmecsci.2024.109329 · Cited by 12
Plasmon-induced transparency in a reconfigurable composite valley photonic crystal
Liu, Y., Wang, J., Yang, D., Wang, Y., Zhang, X., Hassan, F., Li, Y., Zhang, X., & Xu, J. (2022) · Optics Express · doi:10.1364/oe.447946 · Cited by 13
Revealing photonic Lorentz force as the microscopic origin of topological photonic states
Chen, J., Liang, W., & Li, Z. (2018) · Nanophotonics · doi:10.1515/nanoph-2019-0428 · Cited by 14
“Next, we use the physical concept of PLF to construct the basic physical images for topological photonic states and understand their unique transmission behaviors in much more complicated magneto-optical photonic crystal (MOPC) [16, 17].”
BackgroundMethodInfluentialManipulating Second Harmonic Generation in Higher‐Order Topological Photonic Crystals
Ma, J., Guo, K., Chen, F., Zhou, K., Liu, S., & Guo, Z. (2021) · Annalen der Physik · doi:10.1002/andp.202100191 · Cited by 13
One-Way Rotating Photonic Crystal Ring Resonator With High Quality Factor
Zhang, Q., & Li, X. (2018) · IEEE photonics journal · doi:10.1109/jphot.2018.2838324 · Cited by 12
“[12], [13] who presented realistic material designs and experimental verifications.”
BackgroundThe tunable one-way transmission of Lamb waves by using giant magnetostrictive materials
Xue, X., Li, P., & Jin, F. (2021) · Applied Physics Express · doi:10.35848/1882-0786/abdcd7 · Cited by 12
Classification of Chern numbers based on high-symmetry points
Wan, Y.-H., Liu, P., & Sun, Q. (2025) · Physical review. B./Physical review. B · doi:10.1103/physrevb.111.l161410 · Cited by 13
Wide-mode-area slow light waveguides in valley photonic crystal heterostructures
Zhang, C., Ota, Y., & Iwamoto, S. (2024) · Optical Materials Express · doi:10.1364/ome.525349 · Cited by 14
Extraordinary Coupling Into One-Way Magneto-Optical Photonic Crystal Waveguide
Zhu, H., & Jiang, C. (2010) · Journal of Lightwave Technology · doi:10.1109/jlt.2010.2101050 · Cited by 12
One-Way Valley-Robust Transport in Edge-Tailored Photonic Crystals
Chen, J., Yidong, Z., Yang, S., Shi, F., Li, Z., & Qiu, C. (2025) · Physical Review Letters · doi:10.1103/physrevlett.134.203803 · Cited by 14
Yuan, L., Wang, D., & Fan, S. (2017) · Physical Review A · doi:10.1103/physreva.95.033801 · Cited by 12
Polariton vortex Chern insulator [Invited]
Harrison, S. L., Nalitov, A. V., Lagoudakis, P. G., & Sigurðsson, H. (2023) · Optical Materials Express · doi:10.1364/ome.494448 · Cited by 12
Han, N., Liu, J., Gao, Y., Zhou, K., & Liu, S. (2021) · Physical review. B./Physical review. B · doi:10.1103/physrevb.104.205403 · Cited by 12
Nonlinear Photonic Diode Behavior in Energy-Graded Core–Shell Quantum Well Semiconductor Rod
Ko, S., Gong, S., & Cho, Y. (2014) · Nano Letters · doi:10.1021/nl5007905 · Cited by 12
One-way edge modes in a photonic crystal of semiconductor at terahertz frequencies
He, L., Shen, Q., Xu, J., et al. (2018) · Scientific Reports · doi:10.1038/s41598-018-26395-4 · Cited by 12
Photonic topological phases in dispersive metamaterials
Yu, Y.-Z., & Chern, R.-L. (2018) · Scientific Reports · doi:10.1038/s41598-018-36170-0 · Cited by 11
Lattice topological edge and corner modes of photonic crystal slabs
Zhang, Z., You, J. W., Lan, Z., & Panoiu, N. C. (2021) · Journal of Optics · doi:10.1088/2040-8986/ac1832 · Cited by 12
Flat Landau levels and interface states in two-dimensional photonic crystals with a nodal ring
Jin, M., Chen, Z., Lu, M., Zhan, P., & Chen, Y. (2024) · Physical review. B./Physical review. B · doi:10.1103/physrevb.109.054108 · Cited by 13
Monolithic integration of broadband optical isolators for polarization-diverse silicon photonicsPreprint
Zhang, Y., Du, Q., Wang, C., et al. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1902.01236 · Cited by 12
Weyl singularities in polaritonic multiterminal Josephson junctions
Septembre, I., Meyer, J. S., Solnyshkov, D. D., & Malpuech, G. (2023) · Physical review. B./Physical review. B · doi:10.1103/physrevb.107.165301 · Cited by 12
Disorder‐Driven Collapse of Topological Phases in Photonic Topological Insulator
Zhang, H., Sui, W., Zhang, Y., Liu, G., Shi, Q., Lv, Z., Zhang, D., Rong, C., & Yang, B. (2022) · physica status solidi (b) · doi:10.1002/pssb.202200214 · Cited by 11
Fang, Y., Wang, Z.-X., Fan, E.-P., et al. (2020) · Acta Physica Sinica · doi:10.7498/aps.69.20200415 · Cited by 12
Self-citationReconfigurable Light Imaging in Photonic Higher-Order Topological Insulators
Zhang, X., Zhou, Y., Sun, X., Zhang, X., Lu, M.-H., & Chen, Y. (2022) · Nanomaterials · doi:10.3390/nano12050819 · Cited by 14
“The permittivity of YIG can be taken as ε = 15 while its permeability is described by a tensor [7] μ = μr iμk 0 −iμk μr 0 0 0 1 .”
Topologically protected edge transport of sound in coupled cavities of a modified honeycomb lattice
Geng, Z.-G., Peng, Y., Shen, Y., Zhao, D., & Zhu, X. (2018) · Journal of Physics Condensed Matter · doi:10.1088/1361-648x/aad398 · Cited by 12
Asymmetric transmission of surface plasmon polaritons on planar gratings
Kuzmiak, V., & Maradudin, A. A. (2015) · Physical Review A · doi:10.1103/physreva.92.053813 · Cited by 12
High-Performance Asymmetric Optical Transmission Based on a Dielectric–Metal Metasurface
Liu, W., Huang, L., Ding, J., Xie, C., Luo, Y., & Hong, W. (2021) · Nanomaterials · doi:10.3390/nano11092410 · Cited by 11
“Since then, various AT devices based on artificial structures have been proposed which use photonic crystals [19,20], subwavelength asymmetric gratings [21–24], chiral metamaterials [25–27] and metasurfaces [28–30], and the operation wavelengths have been covered from microwave to visible light [31–33].”
BackgroundManipulating one-way space wave and its refraction by time-reversal and parity symmetry breaking
Poo, Y., He, C., Xiao, C. K., Lu, M., Wu, R., & Chen, Y. (2016) · Scientific Reports · doi:10.1038/srep29380 · Cited by 12
Topological phases and non‐Hermitian topology in photonic artificial microstructures
Liu, H., Lai, P., Wang, H., Cheng, H., Tian, J., & Chen, S. (2023) · Nanophotonics · doi:10.1515/nanoph-2022-0778 · Cited by 12
“In realistic gyroelectric materials, because the ratio of off-diagonal to diagonal elements of the permittivity tensor is small, the strength of time reversal breaking is weak [20].”
Electromagnetic Nonreciprocity in a Magnetized Plasma Circulator
Li, F., Davis, R. J., Kandil, S. M., et al. (2022) · Physical Review Applied · doi:10.1103/physrevapplied.18.064066 · Cited by 12
Hajivandi, J., & Kurt, H. (2020) · Physica B Condensed Matter · doi:10.1016/j.physb.2020.412550 · Cited by 12
Peierls-Nabarro barrier effect in nonlinear Floquet topological insulators
Ablowitz, M. J., Cole, J. T., Hu, P., & Rosenthal, P. (2021) · Physical review. E · doi:10.1103/physreve.103.042214 · Cited by 10
Shen, Y., Chen, Z., He, Y., Li, Z., & Shen, J. (2018) · Journal of the Optical Society of America B · doi:10.1364/josab.35.000607 · Cited by 11
Wiltshaw, R., Ponti, J. M. D., & Craster, R. V. (2023) · The Quarterly Journal of Mechanics and Applied Mathematics · doi:10.1093/qjmam/hbad001 · Cited by 11
“Within photonics, externally applied magnetic fields allow time-reversal-symmetry to be passively broken to generate states with a single chirality, as in [27, 28, 98, 99].”
BackgroundUnidirectional magnetoelectric-field multiresonant tunneling
Kamenetskii, E. O., Hollander, E., Joffe, R., & Shavit, R. (2015) · Journal of Optics · doi:10.1088/2040-8978/17/2/025601 · Cited by 11
Gao, Y., He, L., Xu, X., et al. (2019) · Journal of Magnetism and Magnetic Materials · doi:10.1016/j.jmmm.2019.165921 · Cited by 11
Topological properties of nearly flat bands in two-dimensional photonic crystals
Yang, B., Wu, T., & Zhang, X. (2017) · Journal of the Optical Society of America B · doi:10.1364/josab.34.000831 · Cited by 11
Wu, H., Xi, X., Li, X., Poo, Y., Liu, S., & Wu, R. (2022) · Photonics Research · doi:10.1364/prj.437552 · Cited by 12
All-Optical Control of the Photonic Hall Lattice in a Pumped Waveguide Array
Lin, S., Wang, L., Yuan, L., & Chen, X. (2022) · Physical Review Applied · doi:10.1103/physrevapplied.17.064029 · Cited by 12
1 × 2 Beam splitter with high efficiency based on nonreciprocal photonic crystal waveguide
Wang, Z., Yu, Z.-D., Zheng, X., et al. (2012) · Journal of Electromagnetic Waves and Applications · doi:10.1080/09205071.2012.703058 · Cited by 11
“[21], which means that the proposed splitter can possess a wider band.”
BackgroundSelf-citationFang, Y.-T., Chen, L., Zheng, J., et al. (2014) · IEEE photonics journal · doi:10.1109/jphot.2014.2345872 · Cited by 11
Realizing the topological rainbow based on cavity-coupled topological edge state
AbdelAll, N., Almokhtar, M., Khouqeer, G. A., & Elshahat, S. (2023) · Optics & Laser Technology · doi:10.1016/j.optlastec.2023.110351 · Cited by 11
Anomalous broadband Floquet topological metasurface with pure site rings
Guo, Z., Wu, X., Sun, Y., Jiang, H., Ding, Y., Li, Y., Zhang, Y., & Chen, H. (2023) · Advanced Photonics Nexus · doi:10.1117/1.apn.2.1.016006 · Cited by 11
Transport study of the wormhole effect in three-dimensional topological insulators
Gong, M., Lu, M., Liu, H., Jiang, H., Sun, Q., & Xie, X. (2020) · Physical review. B./Physical review. B · doi:10.1103/physrevb.102.165425 · Cited by 11
“[52] Z.”
BackgroundGao, H., Wei, G., Miao, C., Dong, P., & Zhou, Y.-S. (2019) · Journal of Optics · doi:10.1007/s12596-019-00541-1 · Cited by 11
An effective gauge potential for nonreciprocal acoustics
Dai, D.-D., & Zhu, X. (2013) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/102/14001 · Cited by 11
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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