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REVIEW 2 major objections 1 minor 29 references

Unidirectional Guided Resonances Enabled by Competing Fourier Harmonics near the Fourth Stop Band

T0 review · 2 major / 1 minor · reviewed 2026-06-30 · grok-4.3

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Pith's one-line read Unidirectional guided resonances emerge from one-way cancellation of radiation from the first and second Fourier harmonics near the fourth stop band in photonic lattices.

desk verdict The paper offers a two-channel Fourier cancellation route to UGRs near the fourth stop band without symmetry breaking, but the claim of independent tuning looks vulnerable because the amplitudes share the same eigenmode. read the letter →

arxiv 2606.27920 v2 pith:GWXJHLBD submitted 2026-06-26 physics.optics

Sun-Goo Lee , Wook-Jae Lee This is my paper · ORCID
classification physics.optics
keywords unidirectionalguidedresonancesboundstatesinthecontinuumFourierharmonicsphotoniclatticesstopbandsradiationcancellation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper proposes a new mechanism for unidirectional guided resonances (UGRs) in single-layer planar photonic lattices. It shows that radiation near the fourth stop band is mediated by two channels from the first and second Fourier harmonics. When these components cancel in both directions, bound states in the continuum form, but when cancellation is directional, UGRs result. This approach avoids the need for broken in-plane symmetry or interband coupling by tuning lattice parameters to control the UGR positions, including merging them at the Gamma point. The model simplifies device design and relaxes lithographic constraints while providing a framework for higher-order bands.

What carries the argument

The two-channel radiation-cancellation model, where radiation components from the first and second Fourier harmonics cancel directionally.

What would settle it

If experiments show bidirectional radiation when lattice parameters are set for one-directional cancellation between the two harmonics, or if UGRs vanish without symmetry breaking even under that tuning.

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Extended reading notes

Core claim

Out-of-plane radiation near the fourth stop band is mediated by two distinct channels associated with the first and second Fourier harmonics. Full cancellation in both directions produces nonradiative bound states in the continuum, whereas UGRs arise when cancellation occurs only in one direction. The positions of these UGRs can be controlled by tuning lattice parameters, allowing them to merge at the Γ point.

Load-bearing premise

The radiation amplitudes associated with the first and second Fourier harmonics can be tuned independently via lattice parameters to produce directional cancellation without additional interfering effects or coupling to other modes.

Editorial extensions

If this is right

  • UGRs can be realized without broken C2 symmetry or interband coupling.
  • Lattice parameters can be tuned to position UGRs and merge them at the Gamma point.
  • The model enables control of topological singular states in higher-order photonic bands.
  • Device design is simplified by relaxing lithographic constraints.
  • Nonradiative BICs emerge from bidirectional cancellation.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • This two-channel cancellation could extend to other stop bands or lattice geometries.
  • Merging at the Gamma point may connect to topological transitions in photonic bands.
  • The approach might allow engineering of multi-directional or polarization-selective resonances by adding more harmonics.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 1 minor

Summary. The manuscript claims that unidirectional guided resonances (UGRs) near the fourth stop band in single-layer planar photonic lattices arise from competing out-of-plane radiation channels associated with the first and second Fourier harmonics of the Bloch mode. When these components cancel in one direction only, UGRs result; full cancellation in both directions produces nonradiative bound states in the continuum. Lattice parameters can be tuned to position the UGRs, including merging at the Γ point, without requiring broken in-plane C₂ symmetry or interband coupling.

Significance. If the two-channel cancellation model holds with verifiable independent directional tuning, the work would offer a symmetry-independent route to UGRs that relaxes fabrication constraints relative to conventional approaches and supplies a framework for topological states in higher-order bands. The approach could simplify design of directional emitters in photonic lattices.

major comments (2)
  1. [Abstract] Abstract and model description: The claim that radiation amplitudes from the first and second Fourier harmonics can be tuned independently via lattice parameters (hole radius, period, fill factor) to produce one-sided cancellation rests on an unproven decoupling. Both amplitudes are Fourier coefficients of the identical Bloch mode; parameter changes reshape the entire eigenmode profile, correlating the coefficients and potentially activating higher-order harmonics or interband mixing near the fourth stop band. Explicit mode-profile calculations or far-field decompositions are needed to confirm the vector-sum cancellation occurs without these additional effects.
  2. [Model description] Two-channel radiation-cancellation model: The central derivation must demonstrate that the radiation components cancel directionally while remaining consistent with the underlying Maxwell eigenproblem, without implicit reliance on symmetry breaking or mode hybridization. Quantitative evidence (e.g., amplitude ratios or phase conditions derived from the mode expansion) should be provided to show the model is not undermined by the shared eigenmode constraint.
minor comments (1)
  1. Figure captions and far-field plots should explicitly label upward versus downward directions and identify the contributing Fourier harmonics for each resonance to aid reader verification of the directional cancellation.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on our manuscript. We address the two major comments point by point below, clarifying the basis of the two-channel model while acknowledging where additional explicit evidence will strengthen the presentation.

read point-by-point responses

  1. Referee: [Abstract] Abstract and model description: The claim that radiation amplitudes from the first and second Fourier harmonics can be tuned independently via lattice parameters (hole radius, period, fill factor) to produce one-sided cancellation rests on an unproven decoupling. Both amplitudes are Fourier coefficients of the identical Bloch mode; parameter changes reshape the entire eigenmode profile, correlating the coefficients and potentially activating higher-order harmonics or interband mixing near the fourth stop band. Explicit mode-profile calculations or far-field decompositions are needed to confirm the vector-sum cancellation occurs without these additional effects.

    Authors: We agree that the Fourier coefficients originate from the same Bloch mode and that parameter changes affect the full eigenmode. Our numerical results indicate that, near the fourth stop band, the relative amplitudes and phases of the first and second harmonics can nevertheless be adjusted via fill factor and hole radius to produce one-sided cancellation, with higher-order harmonics remaining negligible. To address the concern directly, the revised manuscript will include explicit far-field decompositions and mode-profile slices confirming the vector-sum mechanism. revision: partial

  2. Referee: [Model description] Two-channel radiation-cancellation model: The central derivation must demonstrate that the radiation components cancel directionally while remaining consistent with the underlying Maxwell eigenproblem, without implicit reliance on symmetry breaking or mode hybridization. Quantitative evidence (e.g., amplitude ratios or phase conditions derived from the mode expansion) should be provided to show the model is not undermined by the shared eigenmode constraint.

    Authors: The model is obtained by projecting the eigenmode (solved from the Maxwell equations) onto its Fourier components; directional cancellation follows from the relative phase and amplitude of the first and second harmonics at the fourth stop band. We will augment the revised manuscript with quantitative plots of the extracted amplitude ratios and phase differences from the mode expansion to demonstrate consistency with the eigenproblem and the absence of required symmetry breaking or hybridization. revision: partial

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity; derivation is self-contained Fourier analysis of Bloch modes

full rationale

The paper derives UGRs from cancellation conditions on the first and second Fourier components of the out-of-plane radiation in the eigenmode expansion near the fourth stop band. This follows directly from the standard plane-wave expansion of the periodic dielectric structure and the resulting radiation amplitudes; the cancellation in one versus both directions is a direct algebraic consequence of the vector sum of those two coefficients, not a redefinition or a fit renamed as a prediction. No self-citations are invoked as load-bearing uniqueness theorems, no ansatz is smuggled via prior work, and no parameter is fitted to a data subset then called a prediction. The lattice-parameter tuning is presented as an external control knob on the mode profile, not an internal reparameterization of the target phenomenon. The central claim therefore remains independent of its own outputs.

Assumptions & free parameters 1 free parameters · 1 assumptions · 0 invented entities

The model depends on the domain assumption that radiation near the fourth stop band is mediated by exactly two Fourier channels whose amplitudes can be balanced directionally by geometry; no explicit free parameters or invented entities are named in the abstract.

free parameters (1)
  • lattice parameters
    Tuned to position and merge UGRs
assumptions (1)
  • domain assumption Out-of-plane radiation near the fourth stop band is mediated by two distinct channels from the first and second Fourier harmonics
    Invoked to explain both bound states and UGRs

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Cite this review

Pith. "Pith review of Unidirectional Guided Resonances Enabled by Competing Fourier Harmonics near the Fourth Stop Band." pith.science (2026). https://pith.science/paper/GWXJHLBD

@misc{pith2026260627920,
  author       = {Pith},
  title        = {Pith review of: Unidirectional Guided Resonances Enabled by Competing Fourier Harmonics near the Fourth Stop Band},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GWXJHLBD}},
  note         = {Machine review of arXiv:2606.27920}
}
abstract

Unidirectional guided resonances (UGRs) have attracted considerable attention owing to their remarkable ability to radiate exclusively in one direction from single-layer planar photonic lattices without metallic components. Conventionally, UGRs have been understood to require either broken in-plane $C_2$ symmetry or interband coupling between distinct modes. Here, a new mechanism for realizing UGRs is presented, in which out-of-plane radiation near the fourth stop band is mediated by two distinct channels associated with the first and second Fourier harmonics. When the radiation components from the first and second Fourier harmonics cancel each other out in both the upward and downward directions, nonradiative bound states in the continuum emerge. By contrast, UGRs arise when such cancellation occurs only in one direction. By tuning the lattice parameters, the positions of these UGRs can be controlled, allowing them to merge at the $\Gamma$ point. The two-channel radiation-cancellation model enables UGRs without relying on in-plane symmetry breaking or interband coupling, thereby relaxing lithographic constraints and simplifying device design. It also provides a useful framework for controlling topological singular states in higher-order photonic bands.

Figures

Figures reproduced from arXiv: 2606.27920 by the authors.

Figure 1
Figure 1. FIG. 1. (a) Schematic of a 1D BDG. (b) Conceptual illustratio [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. shows the FEM-simulated η curves as a func￾tion of kx/K for several values of ǫc/ǫs at ρ = 0.4887. For ǫc/ǫs = 0.99, as shown in [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 2
Figure 2. FIG. 2. FEM results near the fourth stop band in an up-down sym [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: FIG. 4. (a) Schematic of the silicon ZCG with broken up-down m [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]
Figure 3
Figure 3. Figure 3: FIG. 3. FEM-simulated radiation ratio [PITH_FULL_IMAGE:figures/full_fig_p004_3.png]
Figure 4
Figure 4. Figure 4: FIG. 4. (a) Schematic of the silicon ZCG with broken up-down m [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

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Works this paper leans on

29 extracted references · 29 canonical work pages

  1. [1]

    P. Qiao, W. Yang, and C. J. Chang-Hasnain, ”Recent advances in high-contrast metastructures, metasurfaces, and photonic crystals,” Adv. Opt. Photon. 10, 180–245 (2018)

    work page 2018

  2. [2]

    Wideband dielectric meta- material reflectors: Mie scattering or leaky Bloch mode resonance?

    Y. H. Ko and R. Magnusson, “Wideband dielectric meta- material reflectors: Mie scattering or leaky Bloch mode resonance?” Optica 5, 289–294 (2018)

    work page 2018

  3. [3]

    Lasing action from photonic bound states in continuum,

    A. Kodigala, T. Lepetit, Q. Gu, B. Bahari, Y. Fainman, and B. Kant´ e, “Lasing action from photonic bound states in continuum,” Nature 541, 196–199 (2017)

    work page 2017

  4. [4]

    J. Yu, W. Yao, M. Qiu, and Q. Li, ”Free-space high-Q nanophotonics,” Light Sci. Appl. 14, 174 (2025)

    work page 2025

  5. [5]

    Fan and J

    S. Fan and J. D. Joannopoulos, ”Analysis of guided res- onances in photonic crystal slabs,” Phys. Rev. B 65, 235112 (2002)

    work page 2002

  6. [6]

    J. Jin, X. Yin, L. Ni, M. Soljaˇ ci´ c, B. Zhen, and C. Peng, ”Topologically enabled ultrahigh- Q guided reso- nances robust to out-of-plane scattering,” Nature 574, 501–504 (2019)

    work page 2019

  7. [7]

    Topological nature of optical bound states in the con- tinuum

    B. Zhen, C. W. Hsu, L. Lu, A. D. Stone, and M. Soljaˇ ci´ c, “Topological nature of optical bound states in the con- tinuum” Phys. Rev. Lett. 113(25), 257401 (2014). 6

    work page 2014

  8. [8]

    Bound states in the continuum

    C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, and M. Soljaˇ ci´ c, “Bound states in the continuum” Nat. Rev. Mater. 1, 16048 (2016)

    work page 2016

Show all 29 references
  1. [9]

    Bound states in the continuum (BIC) accompanied by avoided crossings in leaky-mode photonic lattices,

    S.-G. Lee, S. H. Kim, and C. S. Kee, “Bound states in the continuum (BIC) accompanied by avoided crossings in leaky-mode photonic lattices,” Nanophotonics 9(14), 4374–4380 (2020)

    2020

  2. [10]

    Ob- servation of topologically enabled unidirectional guided resonances,

    X. Yin, J. Jin, M. Soljaˇ ci´ c, C. Peng, and B. Zhen, “Ob- servation of topologically enabled unidirectional guided resonances,” Nature 580, 467–471(2020)

    2020

  3. [11]

    Lee, K.-J

    S.-G. Lee, K.-J. Kim, and W.-J. Lee, ”Formation and ra- diation of unidirectional guided resonances in asymmet- ric gratings with simultaneously broken up-down mirror and in-plane C2 symmetries,” Photonics Research 13(6), 1783–1791 (2025)

    2025

  4. [12]

    Zero- index bound states in the continuum,

    M. Minkov, I. A. Williamson, M. Xiao, and S. Fan, “Zero- index bound states in the continuum,” Phys. Rev. Lett. 121, 263901 (2018)

    2018

  5. [13]

    Experimental observation of a polarization vortex at an optical bound state in the con- tinuum,

    H. M. Doeleman, F. Monticone, W. Hollander, A. Al` u, and A. F. Koenderink, “Experimental observation of a polarization vortex at an optical bound state in the con- tinuum,” Nat. Photonics 12, 397–401 (2018)

    2018

  6. [14]

    Ultralow-threshold laser using super-bound states in the continuum,

    M.-S. Hwang, H.-C. Lee, K.-H. Kim, K.-Y. Jeong, S.- H. Kwon, K. Koshelev, Y. Kivshar, and H.-G. Park, “Ultralow-threshold laser using super-bound states in the continuum,” Nat. Commun. 12, 4135 (2021)

    2021

  7. [15]

    Applications of bound states in the continuum in photonics,

    M. Kang, T. Liu, C. T. Chan, and M. Xiao, “Applications of bound states in the continuum in photonics,” Nat. Rev. Phys. 5, 659–678 (2023)

    2023

  8. [16]

    Electrically- pumped compact topological bulk lasers driven by band- inverted bound states in the continuum,

    S. Han, J. Cui, Y. Chua, Y. Zeng, L. Hu, M. Dai, F. Wang, F. Sun, S. Zhu, L. Li, A. G. Davies, E. H. Linfield, C. S. Tan, Y. Kivshar, and Q. J. Wang, “Electrically- pumped compact topological bulk lasers driven by band- inverted bound states in the continuum,” Light Sci. Appl. ...

    2023

  9. [17]

    Second-order dis- tributed feedback lasers with mode selection provided by first-order radiation loss,

    R. F. Kazarinov and C. H. Henry, “Second-order dis- tributed feedback lasers with mode selection provided by first-order radiation loss,” IEEE J. Quant. Electronics 21, 144–150 (1985)

    1985

  10. [18]

    Band gaps and leaky-wave effects in resonant photonic-crystal waveguides,

    Y. Ding and R. Magnusson, “Band gaps and leaky-wave effects in resonant photonic-crystal waveguides,” Opt. Express 15(2), 680–694 (2007)

    2007

  11. [19]

    Band flips and bound- state transitions in leaky-mode photonic lattices,

    S.-G. Lee and R. Magnusson, “Band flips and bound- state transitions in leaky-mode photonic lattices,” Phys. Rev. B 99(4), 045304 (2019)

    2019

  12. [20]

    Metasurfaces with Bound States in the Continuum Enabled by Eliminating First Fourier Harmonic Component in Lattice Parame- ters,

    S.-G. Lee, S. H. Kim, and C. S. Kee, “Metasurfaces with Bound States in the Continuum Enabled by Eliminating First Fourier Harmonic Component in Lattice Parame- ters,” Phys. Rev. Lett. 126(1), 013601 (2021)

    2021

  13. [21]

    Yariv and P

    A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984)

    1984

  14. [22]

    Band dynamics ac- companied by bound states in the continuum at the third- order Γ point in leaky-mode photonic lattices,

    S.-G. Lee, S.-H. Kim, and C.-S. Kee, “Band dynamics ac- companied by bound states in the continuum at the third- order Γ point in leaky-mode photonic lattices,” Photon. Res. 9, 1109–1116 (2021)

    2021

  15. [23]

    Fourier-component engi- neering to control light diffraction beyond the subwave- length limit,

    S.-G. Lee and R. Magnusson, “Fourier-component engi- neering to control light diffraction beyond the subwave- length limit,” Nanophotonics 11, 1537–1547 (2022)

    2022

  16. [24]

    Merging and band transition of bound states in the continuum in leaky-mode photonic lattices,

    S.-G. Lee, S.-H. Kim, and W.-J. Lee, “Merging and band transition of bound states in the continuum in leaky-mode photonic lattices,” Laser Photonics Rev. 17 2300550 (2023)

    2023

  17. [25]

    Wideband reflectors with zero-contrast gratings,

    R. Magnusson, “Wideband reflectors with zero-contrast gratings,” Opt. Lett. 39(15), 4337–4340 (2014)

    2014

  18. [26]

    Single-layer optical bandpass filter technology,

    M. Niraula, J. W. Yoon, and R. Magnusson, “Single-layer optical bandpass filter technology,” Opt. Lett. 40(21), 5062–5065 (2015)

    2015

  19. [27]

    Ultralow-loss optical interconnect enabled by topological unidirectional guide d resonance,

    H. Wang, Y. Zuo, X. Yin, Z. Chen, Z. Zhang, F. Wang, Y. Hu, X. Zhang, and C. Peng, “Ultralow-loss optical interconnect enabled by topological unidirectional guide d resonance,” Science Advances 10(12) eadn4372 (2024)

    2024

  20. [28]

    Topological unidi- rectional guided resonances emerged from interband cou- pling,

    X. Yin, T. Inoue, C. Peng, S. Noda, “Topological unidi- rectional guided resonances emerged from interband cou- pling,” Phys. Rev. Lett. 130, 056401 (2023)

    2023

  21. [29]

    Transition from quasi-unidirectional to unidirectional guided resonance s in leaky-mode photonic lattices,

    S.-G. Lee, S.-H. Kim, and W.-J. Lee, “Transition from quasi-unidirectional to unidirectional guided resonance s in leaky-mode photonic lattices,” Laser Photonics Rev. 18, 2301339 (2024)

    2024

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