pith. sign in

arxiv: 1907.04113 · v1 · pith:KTIBDB7Mnew · submitted 2019-07-09 · ⚛️ physics.optics

Integrated flat-top reflection filters operating near bound states in the continuum

Leonid L. Doskolovich , Evgeni A. Bezus , Dmitry A. Bykov This is my paper

Pith reviewed 2026-05-25 00:12 UTC · model grok-4.3

classification ⚛️ physics.optics
keywords bound states in the continuumButterworth filtersoptical filtersslab waveguidedielectric ridgesintegrated opticsFabry-Perot BIC
0
0 comments X

The pith

A small number of identical resonant ridges on a slab waveguide realize flat-top Butterworth reflection filters by tuning distances near bound states in the continuum.

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

The paper shows that composite structures made from a few identical resonant dielectric ridges on a single-mode slab waveguide can produce flat-top reflectance spectra with steep edges and almost no sidelobes when operated near a bound state in the continuum. Proper choice of the distances between ridges allows two ridges to implement a second-order Butterworth filter and larger numbers to approximate higher-order Butterworth responses. Because the ridges support a BIC, the width of the flat-top reflection band can be reduced to arbitrarily small values without any increase in the overall length of the device. The same structures also exhibit Fabry-Pérot BICs that create sharp transmittance peaks inside a broad transmittance dip, resembling electromagnetically induced transparency.

Core claim

Composite structures of identical resonant dielectric ridges on a single-mode dielectric slab waveguide, when operated near a bound state in the continuum, produce flat-top reflectance profiles with steep slopes and virtually no sidelobes by appropriate choice of inter-ridge distances; two ridges optically implement the second-order Butterworth filter while more ridges approximate higher-order Butterworth filters, and the BIC property permits the flat-top reflection band to be made arbitrarily narrow without enlarging the structure size. The structures additionally support Fabry-Pérot BICs that give rise to electromagnetically induced transparency-like sharp transmittance peaks on a wide dip

What carries the argument

The bound state in the continuum supported by each resonant dielectric ridge on the slab waveguide, whose coupling strengths are set by geometric distances to synthesize the target Butterworth filter response.

If this is right

  • Two ridges optically implement the second-order Butterworth filter.
  • Larger numbers of ridges achieve excellent approximations to higher-order Butterworth filters.
  • The flat-top reflection band can be made arbitrarily narrow while the physical size of the structure remains fixed.
  • The structures also support Fabry-Pérot BICs that produce electromagnetically induced transparency-like transmittance peaks.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The BIC mechanism decouples the achievable bandwidth from the device footprint, allowing high spectral selectivity inside a compact integrated component.
  • Multiple filter sections could be placed sequentially along the same waveguide to realize more complex spectral responses without proportional growth in length.

Load-bearing premise

The ridges support bound states in the continuum on the slab waveguide and the couplings controlled only by distances can be made to match the exact Butterworth filter shape.

What would settle it

A numerical or experimental reflectance spectrum for two ridges at the predicted distances that deviates substantially from the ideal second-order Butterworth profile would falsify the central claim.

Figures

Figures reproduced from arXiv: 1907.04113 by Dmitry A. Bykov, Evgeni A. Bezus, Leonid L. Doskolovich.

Figure 1
Figure 1. Figure 1: Geometry of a ridge on a waveguide layer (a) and of a composite structure consisting of three ridges separated by phase-shift regions (b). The red arrows indicate the propagation directions of the incident wave I, reflected wave R and transmitted wave T. As an example, [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Reflectance of an obliquely incident TE-polarized guided mode from the ridge vs. the ridge width w and the angle of incidence  . The white circle indicates the BIC position. The reflectance spectrum shown in [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Angular (a) and wavelength (b) ridge reflectance spectra at w = 355 nm (solid blue lines), w = 360 nm (dashed red lines) and w = 380 nm (dotted yellow lines). 3. Theoretical model describing the spectra of a composite structure comprising several ridges Lorentzian shape of the reflectance spectra shown in [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Transmittance (black) and reflectance (red) spectra of composite structures consisting of N = 2 (a), N = 4 (b), and N = 6 (c) ridges at the ridge width w = 380 nm and the distance between the ridges l =948 nm (solid lines). Dashed lines show the spectra of a single ridge. The shape of the spectra can be altered by changing the widths j l of the phase-shift regions separating the ridges. Indeed, in the gene… view at source ↗
Figure 5
Figure 5. Figure 5: Transmittance (black) and reflectance (red) spectra of the optimized composite structures consisting of N = 4 (a) and N = 6 (b) ridges at w = 380 nm (solid lines). Dashed lines show the spectra of a single ridge. Let us now consider an important advantage of the proposed composite filters operating in the near-BIC regime, which consists in the possibility of generating a near-rectangular reflectance peaks … view at source ↗
Figure 6
Figure 6. Figure 6: Transmittance (black) and reflectance (red) spectra of the optimized composite structures consisting of N = 2 (a), N = 4 (b), and N = 6 (c) ridges at w = 360 nm (solid lines). Dashed lines show the spectra of a single ridge. 5. Fabry–Pérot bound states in the continuum in the composite structure In addition to the possibility of obtaining a nearly rectangular reflectance peak with flat top, steep slopes an… view at source ↗
Figure 7
Figure 7. Figure 7: Reflectance ( ) ( ) 2 ,, R l r l NN  = (top) and transmittance ( ) ( ) 2 ,, T l t l NN  = (bottom) of the composite structures consisting of N = 2 (a), (d), N =3 (b), (e) and N = 4 (c), (f) ridges vs. the distance between the ridges l and the free-space wavelength. Vertical dashed lines show the distance lFP = 970.2 nm corresponding to the Fabry–Pérot resonance. As an additional illustration of the BIC… view at source ↗
Figure 8
Figure 8. Figure 8: Transmittance spectra of the composite structure consisting of N =3 ridges calculated at the width of the phase-shift region between the ridges ll == FP 970.2 nm corresponding to the BIC condition (solid blue line), and at the widths ll = + = FP 5 nm 975.2 nm (dashed red line) and ll = + = FP 10 nm 980.2 nm (dotted yellow line). 6. Conclusion In the present work, we investigated resonant optical properties… view at source ↗
read the original abstract

We propose and theoretically and numerically investigate narrowband integrated filters consisting of identical resonant dielectric ridges on the surface of a single-mode dielectric slab waveguide. The proposed composite structures operate near a bound state in the continuum (BIC) and enable spectral filtering of transverse-electric-polarized guided modes propagating in the waveguide. We demonstrate that by proper choice of the distances between the ridges, flat-top reflectance profiles with steep slopes and virtually no sidelobes can be obtained using just a few ridges. In particular, the structure consisting of two ridges can optically implement the second-order Butterworth filter, whereas at a larger number of ridges, excellent approximations to higher-order Butterworth filters can be achieved. Owing to the BIC supported by the ridges constituting the composite structure, the flat-top reflection band can be made arbitrarily narrow without increasing the structure size. In addition to the filtering properties, the investigated structures support another type of BICs - Fabry-P\'erot BICs arising when the distances between the adjacent ridges meet the Fabry-P\'erot resonance condition. In the vicinity of the Fabry-P\'erot BICs, an effect similar to the electromagnetically induced transparency is observed, namely, sharp transmittance peaks against the background of a wide transmittance dip.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 3 minor

Summary. The manuscript proposes narrowband integrated reflection filters consisting of identical resonant dielectric ridges on a single-mode slab waveguide, operating near bound states in the continuum (BICs). By appropriate choice of inter-ridge distances, flat-top reflectance spectra matching or approximating Butterworth filters (exact for N=2 ridges, good approximations for higher N) are obtained, with the reflection band made arbitrarily narrow via proximity to the BIC condition without increasing total device length. The structures additionally support Fabry-Pérot BICs that produce EIT-like sharp transmittance peaks within a broad dip.

Significance. If the central claims hold, the work provides a compact design route for high-performance integrated filters in photonics by leveraging BIC physics for bandwidth control and coupled-mode engineering for spectral shaping. The combination of an explicit coupled-mode design procedure with full-wave numerical verification, including demonstration of exact second-order Butterworth response for two ridges, constitutes a concrete strength. The fixed-length narrowing mechanism is a notable practical advantage over conventional approaches.

minor comments (3)
  1. [Design procedure (around Eq. for coupled amplitudes)] The coupled-mode section would benefit from an explicit table or equation listing the extracted coupling coefficients versus distance for the ridge geometry used, to allow direct reproduction of the Butterworth coefficient matching.
  2. [Results figures] Figure captions for the reflectance spectra should include quantitative metrics (e.g., ripple amplitude in dB, transition bandwidth, sidelobe level) rather than qualitative descriptors such as 'virtually no sidelobes'.
  3. [Structure definition] The assumption that individual ridges support a BIC when placed on the slab is stated but the precise geometric parameters (ridge height, width, permittivity contrast) that place the BIC at the target wavelength should be stated once in a dedicated paragraph or table.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of our manuscript, the accurate summary of our central claims, and the recommendation for minor revision. No major comments requiring point-by-point rebuttal were provided in the report.

Circularity Check

1 steps flagged

Distances chosen to match Butterworth responses reduce to fitted design

specific steps
  1. fitted input called prediction [Abstract]
    "We demonstrate that by proper choice of the distances between the ridges, flat-top reflectance profiles with steep slopes and virtually no sidelobes can be obtained using just a few ridges. In particular, the structure consisting of two ridges can optically implement the second-order Butterworth filter, whereas at a larger number of ridges, excellent approximations to higher-order Butterworth filters can be achieved."

    Distances are selected specifically to produce the target Butterworth reflectance profile. The reported match is therefore enforced by the fitting procedure rather than emerging as an independent prediction from the structure equations without reference to the filter coefficients.

full rationale

The paper's central demonstration uses coupled-mode theory to select inter-ridge distances that realize exact or approximate Butterworth filter responses. This constitutes fitting geometric parameters to a target shape, after which the match is presented as a result. While the BIC physics and full-wave verification are independent, the filter-profile claim reduces to the parameter choice by construction. No self-citation load-bearing or other patterns detected.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The design treats ridge spacing as a free design parameter fitted to target filter responses and relies on the domain assumption that each ridge supports a BIC on the slab waveguide; no new physical entities are postulated.

free parameters (1)
  • distances between ridges
    Chosen to match the target Butterworth filter response; these are the primary adjustable quantities that determine the composite reflectance profile.
axioms (1)
  • domain assumption Identical resonant dielectric ridges placed on the slab waveguide support bound states in the continuum
    Invoked throughout the abstract as the operating regime that enables both the narrowband flat-top reflection and the arbitrary narrowing without size increase.

pith-pipeline@v0.9.0 · 5753 in / 1403 out tokens · 32145 ms · 2026-05-25T00:12:39.537107+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

27 extracted references · 27 canonical work pages

  1. [1]

    H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984)

    work page 1984

  2. [2]

    Planar holographic optical processing devices,

    T. Mossberg, “Planar holographic optical processing devices,” Opt. Lett. 26(7), 414–416 (2001)

    work page 2001

  3. [3]

    Holographic planar lightwave circuit for on-chip spectroscopy,

    G. Calafiore, A. Koshelev, S. Dhuey, A. Goltsov, P. Sasorov, S. Babin, V. Yankov, S. Cabrini, and C. Peroz, “Holographic planar lightwave circuit for on-chip spectroscopy,” Light: Sci. Appl. 3(9), e203 (2014)

    work page 2014

  4. [4]

    Digital optical spectrometer-on-chip,

    S. Babin, A. Bugrov, S. Cabrini, S. Dhuey, A. Goltsov, I. Ivonin, E.-B. Kley, C. Peroz, H. Schmidt, and V. Yankov, “Digital optical spectrometer-on-chip,” Appl. Phys. Lett. 95(4), 041105 (2009)

    work page 2009

  5. [5]

    Multiband wavelength demultiplexer based on digital planar holography for on-chip spectroscopy applications,

    C. Peroz, C. Calo, A. Goltsov, S. Dhuey, A. Koshelev, P. Sasorov, I. Ivonin, S. Babin, S. Cabrini, and V. Yankov, “Multiband wavelength demultiplexer based on digital planar holography for on-chip spectroscopy applications,” Opt. Lett. 37(4), 695–697 (2012)

    work page 2012

  6. [6]

    High-resolution spectrometer-on-chip based on digital planar holography,

    C. Peroz, A. Goltsov, S. Dhuey, P. Sasorov, B. Harteneck, I. Ivonin, S. Kopyatev, S. Cabrini, S. Babin, and V. Yankov, “High-resolution spectrometer-on-chip based on digital planar holography,” IEEE Photon. J. 3(5), 888–896 (2011)

    work page 2011

  7. [7]

    Two-groove narrowband transmission filter integrated into a slab waveguide,

    L. L. Doskolovich, E. A. Bezus, and D. A. Bykov, “Two-groove narrowband transmission filter integrated into a slab waveguide,” Photon. Res. 6(1), 61–65 (2018)

    work page 2018

  8. [8]

    Narrow-band grating filters for thin-film optical waveguides,

    R. V. Schmidt, D. C. Flanders, C. V. Shank, and R. D. Standley, “Narrow-band grating filters for thin-film optical waveguides,” Appl. Phys. Lett. 25(11), 651–652 (1974)

    work page 1974

  9. [9]

    Broad-band grating filters for thin film optical waveguides,

    C. S. Hong, J. B. Shellan, A. C. Livanos, A. Yariv, and A. Katzir, “Broad-band grating filters for thin film optical waveguides,” Appl. Phys. Lett. 31(4), 276–278 (1977)

    work page 1977

  10. [10]

    Analysis of waveguide gratings: application of Rouard’s method,

    L. A. Weller-Brophy and D. G. Hall, “Analysis of waveguide gratings: application of Rouard’s method,” J. Opt. Soc. Am. A 2(6), 863–871 (1985)

    work page 1985

  11. [11]

    Phase-shifted Bragg grating filters with improved transmission characteristics,

    R. Zengerle and O. Leminger, “Phase-shifted Bragg grating filters with improved transmission characteristics,” J. Lightwave Technol. 13(12), 2354–2358 (1995)

    work page 1995

  12. [12]

    Wavelength-division multiplexing using channel-dropping filters,

    J. N. Damask and H. A. Haus, “Wavelength-division multiplexing using channel-dropping filters,” J. Lightwave Technol. 11(3), 424–428 (1993)

    work page 1993

  13. [13]

    Bound states in the continuum and high-Q resonances supported by a dielectric ridge on a slab waveguide,

    E. A. Bezus, D. A. Bykov, and L. L. Doskolovich, “Bound states in the continuum and high-Q resonances supported by a dielectric ridge on a slab waveguide,” Photon. Res. 6(11), 1084–1093 (2018)

    work page 2018

  14. [14]

    Spatial integration and differentiation of optical beams in a slab waveguide by a dielectric ridge supporting high-Q resonances,

    E. A. Bezus, L. L. Doskolovich, D. A. Bykov, and V. A. Soifer, “Spatial integration and differentiation of optical beams in a slab waveguide by a dielectric ridge supporting high-Q resonances,” Opt. Express 26(19), 25156–25165 (2018)

    work page 2018

  15. [15]

    Guiding light through optical bound states in the continuum for ultrahigh-Q microresonators,

    C.-L. Zou, J.-M. Cui, F.-W. Sun, X. Xiong, X.-B. Zou, Z.-F. Han, and G.-C. Guo, “Guiding light through optical bound states in the continuum for ultrahigh-Q microresonators,” Laser Photon. Rev. 9(1), 114–119 (2015)

    work page 2015

  16. [16]

    Quantitative analysis of TM lateral leakage in foundry fabricated silicon rib waveguides,

    A. P. Hope, T. G. Nguyen, A. Mitchell, and W. Bogaerts, “Quantitative analysis of TM lateral leakage in foundry fabricated silicon rib waveguides,” IEEE Photon. Technol. Lett. 28(4), 493–496 (2016)

    work page 2016

  17. [17]

    Flat-top bandpass filters enabled by cascaded resonant gratings,

    Y. H. Ko and R. Magnusson, “Flat-top bandpass filters enabled by cascaded resonant gratings,” Opt. Lett. 41(20), 4704–4707 (2016)

    work page 2016

  18. [18]

    Use of grating theories in integrated optics,

    E. Silberstein, P. Lalanne, J.-P. Hugonin, and Q. Cao, “Use of grating theories in integrated optics,” J. Opt. Soc. Am. A 18(11), 2865–2875 (2001)

    work page 2001

  19. [19]

    Perfectly matched layers as nonlinear coordinate transforms: a generalized formalization,

    J. P. Hugonin and P. Lalanne, “Perfectly matched layers as nonlinear coordinate transforms: a generalized formalization,” J. Opt. Soc. Am. A 22(9), 1844–1849 (2005)

    work page 2005

  20. [20]

    Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings,

    L. Li, “Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings,” J. Opt. Soc. Am. A 13(5), 1024–1035 (1996)

    work page 1996

  21. [21]

    Optical properties of photonic crystal slabs with an asymmetrical unit cell,

    N. A. Gippius, S. G. Tikhodeev, and T. Ishihara, “Optical properties of photonic crystal slabs with an asymmetrical unit cell,” Phys. Rev. B 72(4), 045138 (2005)

    work page 2005

  22. [22]

    Time-domain differentiation of optical pulses in reflection and in transmission using the same resonant grating,

    D. A. Bykov, L. L. Doskolovich, N. V. Golovastikov, and V. A. Soifer, “Time-domain differentiation of optical pulses in reflection and in transmission using the same resonant grating,” J. Opt. 15(10), 105703 (2013)

    work page 2013

  23. [23]

    Temporal differentiation and integration of 3D optical pulses using phase-shifted Bragg gratings,

    N. V. Golovastikov, D. A. Bykov, and L. L. Doskolovich, “Temporal differentiation and integration of 3D optical pulses using phase-shifted Bragg gratings,” Comput. Opt. 41(1), 13–21 (2017)

    work page 2017

  24. [24]

    Synthesis of high-order bandpass filters based on coupled-resonator optical waveguides (CROWs),

    H.-C. Liu and A. Yariv, “Synthesis of high-order bandpass filters based on coupled-resonator optical waveguides (CROWs),” Opt. Express 19(18), 17653–17668 (2011)

    work page 2011

  25. [25]

    Fano resonances in photonics,

    M. F. Limonov, M. V. Rybin, A. N. Poddubny, and Y. S. Kivshar, “Fano resonances in photonics,” Nat. Photon. 11(9), 543–554 (2017)

    work page 2017

  26. [26]

    Bound states in the continuum in photonics,

    D. C. Marinica, A. G. Borisov, and S. V. Shabanov, “Bound states in the continuum in photonics,” Phys. Rev. Lett. 100(18), 183902 (2008)

    work page 2008

  27. [27]

    Resonance-enhanced optical forces between coupled photonic crystal slabs,

    V. Liu, M. Povinelli, and S. Fan, “Resonance-enhanced optical forces between coupled photonic crystal slabs,” Opt. Express 17(24), 21897–21909 (2009)

    work page 2009