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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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“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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“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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“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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“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
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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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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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“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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“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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“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).
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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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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.
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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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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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“es. These results provide strong evidence of one-way transport in such heterostructures. The TOLWSs here has a much larger and tunable transmission area than an ordinary topological one-way edge mode [7, 8, 9, 10, 11, 12, 13, 14, 15, 16], which is exponentially confined to the boundary. The TOLWSs are also very robust…”
BackgroundMethodInfluentialUnderwater acoustic metamaterials
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“Topological concepts are universal and include electromagnetic [104,105], optical [106,107] and acoustic [33,103] concepts.”
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“Assuming that the system is at rest at = t 0, a formal solution of equation (11) is”
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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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