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 structure size. In addition to the filtering properties, the investigated structures support another type of BIC—the Fabry–Perot BIC—arising when the distances between adjacent ridges meet the Fabry–Perot resonance condition. In the vicinity of the Fabry–Perot BIC, an effect similar to electromagnetically induced transparency is observed, namely, sharp transmittance peaks against the background of a wide transmittance dip.

© 2019 Chinese Laser Press

Full Article  |  PDF Article
OSA Recommended Articles
Analytical design of flat-top transmission filters composed of several resonant structures

Leonid L. Doskolovich, Nikita V. Golovastikov, Dmitry A. Bykov, and Evgeni A. Bezus
Opt. Express 27(19) 26786-26798 (2019)

Resonant properties of composite structures consisting of several resonant diffraction gratings

Leonid L. Doskolovich, Evgeni A. Bezus, Dmitry A. Bykov, Nikita V. Golovastikov, and Victor A. Soifer
Opt. Express 27(18) 25814-25828 (2019)

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

Evgeni A. Bezus, Dmitry A. Bykov, and Leonid L. Doskolovich
Photon. Res. 6(11) 1084-1093 (2018)

References

  • View by:
  • |
  • |
  • |

  1. H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, 1984).
  2. T. Mossberg, “Planar holographic optical processing devices,” Opt. Lett. 26, 414–416 (2001).
    [Crossref]
  3. 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, e203 (2014).
    [Crossref]
  4. 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, 041105 (2009).
    [Crossref]
  5. 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, 695–697 (2012).
    [Crossref]
  6. 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, 888–896 (2011).
    [Crossref]
  7. L. L. Doskolovich, E. A. Bezus, and D. A. Bykov, “Two-groove narrowband transmission filter integrated into a slab waveguide,” Photon. Res. 6, 61–65 (2018).
    [Crossref]
  8. 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, 651–652 (1974).
    [Crossref]
  9. 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, 276–278 (1977).
    [Crossref]
  10. L. A. Weller-Brophy and D. G. Hall, “Analysis of waveguide gratings: application of Rouard’s method,” J. Opt. Soc. Am. A 2, 863–871 (1985).
    [Crossref]
  11. R. Zengerle and O. Leminger, “Phase-shifted Bragg grating filters with improved transmission characteristics,” J. Lightwave Technol. 13, 2354–2358 (1995).
    [Crossref]
  12. J. N. Damask and H. A. Haus, “Wavelength-division multiplexing using channel-dropping filters,” J. Lightwave Technol. 11, 424–428 (1993).
    [Crossref]
  13. 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, 1084–1093 (2018).
    [Crossref]
  14. 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, 25156–25165 (2018).
    [Crossref]
  15. 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, 114–119 (2015).
    [Crossref]
  16. 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, 493–496 (2016).
    [Crossref]
  17. T. G. Nguyen, G. Ren, S. Schoenhardt, M. Knoerzer, A. Boes, and A. Mitchell, “Ridge resonance: a new resonance phenomenon for silicon photonics harnessing bound states in the continuum,” arXiv:1810.06734 (2018).
  18. C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, and M. Soljačić, “Bound states in the continuum,” Nat. Rev. Mater. 1, 16048 (2016).
    [Crossref]
  19. D. C. Marinica, A. G. Borisov, and S. V. Shabanov, “Bound states in the continuum in photonics,” Phys. Rev. Lett. 100, 183902 (2008).
    [Crossref]
  20. C. W. Hsu, B. Zhen, J. Lee, S. L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Observation of trapped light within the radiation continuum,” Nature 499, 188–191 (2013).
    [Crossref]
  21. J. W. Yoon, S. H. Song, and R. Magnusson, “Critical field enhancement of asymptotic optical bound states in the continuum,” Sci. Rep. 5, 18301 (2015).
    [Crossref]
  22. Y. Wang, J. Song, L. Dong, and M. Lu, “Optical bound states in slotted high-contrast gratings,” J. Opt. Soc. Am. B 33, 2472–2479 (2016).
    [Crossref]
  23. C. Blanchard, J.-P. Hugonin, and C. Sauvan, “Fano resonances in photonic crystal slabs near optical bound states in the continuum,” Phys. Rev. B 94, 155303 (2016).
    [Crossref]
  24. D. A. Bykov, E. A. Bezus, and L. L. Doskolovich, “Coupled-wave formalism for bound states in the continuum in guided-mode resonant gratings,” Phys. Rev. A 99, 063805 (2019).
    [Crossref]
  25. E. N. Bulgakov and A. F. Sadreev, “Bloch bound states in the radiation continuum in a periodic array of dielectric rods,” Phys. Rev. A 90, 053801 (2014).
    [Crossref]
  26. J. M. Foley, S. M. Young, and J. D. Phillips, “Symmetry-protected mode coupling near normal incidence for narrow-band transmission filtering in a dielectric grating,” Phys. Rev. B 89, 165111 (2014).
    [Crossref]
  27. J. M. Foley and J. D. Phillips, “Normal incidence narrowband transmission filtering capabilities using symmetry-protected modes of a subwavelength, dielectric grating,” Opt. Lett. 40, 2637–2640 (2015).
    [Crossref]
  28. E. N. Bulgakov and A. F. Sadreev, “Bound states in the continuum in photonic waveguides inspired by defects,” Phys. Rev. B 78, 075105 (2008).
    [Crossref]
  29. Y. H. Ko and R. Magnusson, “Flat-top bandpass filters enabled by cascaded resonant gratings,” Opt. Lett. 41, 4704–4707 (2016).
    [Crossref]
  30. E. Silberstein, P. Lalanne, J.-P. Hugonin, and Q. Cao, “Use of grating theories in integrated optics,” J. Opt. Soc. Am. A 18, 2865–2875 (2001).
    [Crossref]
  31. J. P. Hugonin and P. Lalanne, “Perfectly matched layers as nonlinear coordinate transforms: a generalized formalization,” J. Opt. Soc. Am. A 22, 1844–1849 (2005).
    [Crossref]
  32. L. Li, “Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings,” J. Opt. Soc. Am. A 13, 1024–1035 (1996).
    [Crossref]
  33. N. A. Gippius, S. G. Tikhodeev, and T. Ishihara, “Optical properties of photonic crystal slabs with an asymmetrical unit cell,” Phys. Rev. B 72, 045138 (2005).
    [Crossref]
  34. 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, 105703 (2013).
    [Crossref]
  35. 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, 13–21 (2017).
    [Crossref]
  36. H.-C. Liu and A. Yariv, “Synthesis of high-order bandpass filters based on coupled-resonator optical waveguides (CROWs),” Opt. Express 19, 17653–17668 (2011).
    [Crossref]
  37. V. Liu, M. Povinelli, and S. Fan, “Resonance-enhanced optical forces between coupled photonic crystal slabs,” Opt. Express 17, 21897–21909 (2009).
    [Crossref]

2019 (1)

D. A. Bykov, E. A. Bezus, and L. L. Doskolovich, “Coupled-wave formalism for bound states in the continuum in guided-mode resonant gratings,” Phys. Rev. A 99, 063805 (2019).
[Crossref]

2018 (3)

2017 (1)

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, 13–21 (2017).
[Crossref]

2016 (5)

C. Blanchard, J.-P. Hugonin, and C. Sauvan, “Fano resonances in photonic crystal slabs near optical bound states in the continuum,” Phys. Rev. B 94, 155303 (2016).
[Crossref]

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

Y. Wang, J. Song, L. Dong, and M. Lu, “Optical bound states in slotted high-contrast gratings,” J. Opt. Soc. Am. B 33, 2472–2479 (2016).
[Crossref]

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, 493–496 (2016).
[Crossref]

C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, and M. Soljačić, “Bound states in the continuum,” Nat. Rev. Mater. 1, 16048 (2016).
[Crossref]

2015 (3)

J. W. Yoon, S. H. Song, and R. Magnusson, “Critical field enhancement of asymptotic optical bound states in the continuum,” Sci. Rep. 5, 18301 (2015).
[Crossref]

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, 114–119 (2015).
[Crossref]

J. M. Foley and J. D. Phillips, “Normal incidence narrowband transmission filtering capabilities using symmetry-protected modes of a subwavelength, dielectric grating,” Opt. Lett. 40, 2637–2640 (2015).
[Crossref]

2014 (3)

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, e203 (2014).
[Crossref]

E. N. Bulgakov and A. F. Sadreev, “Bloch bound states in the radiation continuum in a periodic array of dielectric rods,” Phys. Rev. A 90, 053801 (2014).
[Crossref]

J. M. Foley, S. M. Young, and J. D. Phillips, “Symmetry-protected mode coupling near normal incidence for narrow-band transmission filtering in a dielectric grating,” Phys. Rev. B 89, 165111 (2014).
[Crossref]

2013 (2)

C. W. Hsu, B. Zhen, J. Lee, S. L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Observation of trapped light within the radiation continuum,” Nature 499, 188–191 (2013).
[Crossref]

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, 105703 (2013).
[Crossref]

2012 (1)

2011 (2)

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

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, 888–896 (2011).
[Crossref]

2009 (2)

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, 041105 (2009).
[Crossref]

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

2008 (2)

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

E. N. Bulgakov and A. F. Sadreev, “Bound states in the continuum in photonic waveguides inspired by defects,” Phys. Rev. B 78, 075105 (2008).
[Crossref]

2005 (2)

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

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

2001 (2)

1996 (1)

1995 (1)

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

1993 (1)

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

1985 (1)

1977 (1)

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, 276–278 (1977).
[Crossref]

1974 (1)

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, 651–652 (1974).
[Crossref]

Babin, S.

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, e203 (2014).
[Crossref]

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, 695–697 (2012).
[Crossref]

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, 888–896 (2011).
[Crossref]

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, 041105 (2009).
[Crossref]

Bezus, E. A.

Blanchard, C.

C. Blanchard, J.-P. Hugonin, and C. Sauvan, “Fano resonances in photonic crystal slabs near optical bound states in the continuum,” Phys. Rev. B 94, 155303 (2016).
[Crossref]

Boes, A.

T. G. Nguyen, G. Ren, S. Schoenhardt, M. Knoerzer, A. Boes, and A. Mitchell, “Ridge resonance: a new resonance phenomenon for silicon photonics harnessing bound states in the continuum,” arXiv:1810.06734 (2018).

Bogaerts, W.

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, 493–496 (2016).
[Crossref]

Borisov, A. G.

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

Bugrov, A.

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, 041105 (2009).
[Crossref]

Bulgakov, E. N.

E. N. Bulgakov and A. F. Sadreev, “Bloch bound states in the radiation continuum in a periodic array of dielectric rods,” Phys. Rev. A 90, 053801 (2014).
[Crossref]

E. N. Bulgakov and A. F. Sadreev, “Bound states in the continuum in photonic waveguides inspired by defects,” Phys. Rev. B 78, 075105 (2008).
[Crossref]

Bykov, D. A.

D. A. Bykov, E. A. Bezus, and L. L. Doskolovich, “Coupled-wave formalism for bound states in the continuum in guided-mode resonant gratings,” Phys. Rev. A 99, 063805 (2019).
[Crossref]

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, 25156–25165 (2018).
[Crossref]

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

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, 1084–1093 (2018).
[Crossref]

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, 13–21 (2017).
[Crossref]

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, 105703 (2013).
[Crossref]

Cabrini, S.

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, e203 (2014).
[Crossref]

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, 695–697 (2012).
[Crossref]

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, 888–896 (2011).
[Crossref]

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, 041105 (2009).
[Crossref]

Calafiore, G.

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, e203 (2014).
[Crossref]

Calo, C.

Cao, Q.

Chua, S. L.

C. W. Hsu, B. Zhen, J. Lee, S. L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Observation of trapped light within the radiation continuum,” Nature 499, 188–191 (2013).
[Crossref]

Cui, J.-M.

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, 114–119 (2015).
[Crossref]

Damask, J. N.

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

Dhuey, S.

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, e203 (2014).
[Crossref]

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, 695–697 (2012).
[Crossref]

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, 888–896 (2011).
[Crossref]

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, 041105 (2009).
[Crossref]

Dong, L.

Doskolovich, L. L.

D. A. Bykov, E. A. Bezus, and L. L. Doskolovich, “Coupled-wave formalism for bound states in the continuum in guided-mode resonant gratings,” Phys. Rev. A 99, 063805 (2019).
[Crossref]

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

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, 25156–25165 (2018).
[Crossref]

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, 1084–1093 (2018).
[Crossref]

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, 13–21 (2017).
[Crossref]

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, 105703 (2013).
[Crossref]

Fan, S.

Flanders, D. C.

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, 651–652 (1974).
[Crossref]

Foley, J. M.

J. M. Foley and J. D. Phillips, “Normal incidence narrowband transmission filtering capabilities using symmetry-protected modes of a subwavelength, dielectric grating,” Opt. Lett. 40, 2637–2640 (2015).
[Crossref]

J. M. Foley, S. M. Young, and J. D. Phillips, “Symmetry-protected mode coupling near normal incidence for narrow-band transmission filtering in a dielectric grating,” Phys. Rev. B 89, 165111 (2014).
[Crossref]

Gippius, N. A.

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

Golovastikov, N. V.

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, 13–21 (2017).
[Crossref]

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, 105703 (2013).
[Crossref]

Goltsov, A.

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, e203 (2014).
[Crossref]

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, 695–697 (2012).
[Crossref]

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, 888–896 (2011).
[Crossref]

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, 041105 (2009).
[Crossref]

Guo, G.-C.

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, 114–119 (2015).
[Crossref]

Hall, D. G.

Han, Z.-F.

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, 114–119 (2015).
[Crossref]

Harteneck, B.

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, 888–896 (2011).
[Crossref]

Haus, H. A.

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

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

Hong, C. S.

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, 276–278 (1977).
[Crossref]

Hope, A. P.

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, 493–496 (2016).
[Crossref]

Hsu, C. W.

C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, and M. Soljačić, “Bound states in the continuum,” Nat. Rev. Mater. 1, 16048 (2016).
[Crossref]

C. W. Hsu, B. Zhen, J. Lee, S. L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Observation of trapped light within the radiation continuum,” Nature 499, 188–191 (2013).
[Crossref]

Hugonin, J. P.

Hugonin, J.-P.

C. Blanchard, J.-P. Hugonin, and C. Sauvan, “Fano resonances in photonic crystal slabs near optical bound states in the continuum,” Phys. Rev. B 94, 155303 (2016).
[Crossref]

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

Ishihara, T.

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

Ivonin, I.

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, 695–697 (2012).
[Crossref]

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, 888–896 (2011).
[Crossref]

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, 041105 (2009).
[Crossref]

Joannopoulos, J. D.

C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, and M. Soljačić, “Bound states in the continuum,” Nat. Rev. Mater. 1, 16048 (2016).
[Crossref]

C. W. Hsu, B. Zhen, J. Lee, S. L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Observation of trapped light within the radiation continuum,” Nature 499, 188–191 (2013).
[Crossref]

Johnson, S. G.

C. W. Hsu, B. Zhen, J. Lee, S. L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Observation of trapped light within the radiation continuum,” Nature 499, 188–191 (2013).
[Crossref]

Katzir, A.

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, 276–278 (1977).
[Crossref]

Kley, E.-B.

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, 041105 (2009).
[Crossref]

Knoerzer, M.

T. G. Nguyen, G. Ren, S. Schoenhardt, M. Knoerzer, A. Boes, and A. Mitchell, “Ridge resonance: a new resonance phenomenon for silicon photonics harnessing bound states in the continuum,” arXiv:1810.06734 (2018).

Ko, Y. H.

Kopyatev, S.

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, 888–896 (2011).
[Crossref]

Koshelev, A.

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, e203 (2014).
[Crossref]

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, 695–697 (2012).
[Crossref]

Lalanne, P.

Lee, J.

C. W. Hsu, B. Zhen, J. Lee, S. L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Observation of trapped light within the radiation continuum,” Nature 499, 188–191 (2013).
[Crossref]

Leminger, O.

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

Li, L.

Liu, H.-C.

Liu, V.

Livanos, A. C.

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, 276–278 (1977).
[Crossref]

Lu, M.

Magnusson, R.

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

J. W. Yoon, S. H. Song, and R. Magnusson, “Critical field enhancement of asymptotic optical bound states in the continuum,” Sci. Rep. 5, 18301 (2015).
[Crossref]

Marinica, D. C.

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

Mitchell, A.

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, 493–496 (2016).
[Crossref]

T. G. Nguyen, G. Ren, S. Schoenhardt, M. Knoerzer, A. Boes, and A. Mitchell, “Ridge resonance: a new resonance phenomenon for silicon photonics harnessing bound states in the continuum,” arXiv:1810.06734 (2018).

Mossberg, T.

Nguyen, T. G.

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, 493–496 (2016).
[Crossref]

T. G. Nguyen, G. Ren, S. Schoenhardt, M. Knoerzer, A. Boes, and A. Mitchell, “Ridge resonance: a new resonance phenomenon for silicon photonics harnessing bound states in the continuum,” arXiv:1810.06734 (2018).

Peroz, C.

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, e203 (2014).
[Crossref]

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, 695–697 (2012).
[Crossref]

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, 888–896 (2011).
[Crossref]

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, 041105 (2009).
[Crossref]

Phillips, J. D.

J. M. Foley and J. D. Phillips, “Normal incidence narrowband transmission filtering capabilities using symmetry-protected modes of a subwavelength, dielectric grating,” Opt. Lett. 40, 2637–2640 (2015).
[Crossref]

J. M. Foley, S. M. Young, and J. D. Phillips, “Symmetry-protected mode coupling near normal incidence for narrow-band transmission filtering in a dielectric grating,” Phys. Rev. B 89, 165111 (2014).
[Crossref]

Povinelli, M.

Ren, G.

T. G. Nguyen, G. Ren, S. Schoenhardt, M. Knoerzer, A. Boes, and A. Mitchell, “Ridge resonance: a new resonance phenomenon for silicon photonics harnessing bound states in the continuum,” arXiv:1810.06734 (2018).

Sadreev, A. F.

E. N. Bulgakov and A. F. Sadreev, “Bloch bound states in the radiation continuum in a periodic array of dielectric rods,” Phys. Rev. A 90, 053801 (2014).
[Crossref]

E. N. Bulgakov and A. F. Sadreev, “Bound states in the continuum in photonic waveguides inspired by defects,” Phys. Rev. B 78, 075105 (2008).
[Crossref]

Sasorov, P.

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, e203 (2014).
[Crossref]

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, 695–697 (2012).
[Crossref]

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, 888–896 (2011).
[Crossref]

Sauvan, C.

C. Blanchard, J.-P. Hugonin, and C. Sauvan, “Fano resonances in photonic crystal slabs near optical bound states in the continuum,” Phys. Rev. B 94, 155303 (2016).
[Crossref]

Schmidt, H.

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, 041105 (2009).
[Crossref]

Schmidt, R. V.

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, 651–652 (1974).
[Crossref]

Schoenhardt, S.

T. G. Nguyen, G. Ren, S. Schoenhardt, M. Knoerzer, A. Boes, and A. Mitchell, “Ridge resonance: a new resonance phenomenon for silicon photonics harnessing bound states in the continuum,” arXiv:1810.06734 (2018).

Shabanov, S. V.

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

Shank, C. V.

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, 651–652 (1974).
[Crossref]

Shellan, J. B.

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, 276–278 (1977).
[Crossref]

Silberstein, E.

Soifer, V. A.

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, 25156–25165 (2018).
[Crossref]

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, 105703 (2013).
[Crossref]

Soljacic, M.

C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, and M. Soljačić, “Bound states in the continuum,” Nat. Rev. Mater. 1, 16048 (2016).
[Crossref]

C. W. Hsu, B. Zhen, J. Lee, S. L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Observation of trapped light within the radiation continuum,” Nature 499, 188–191 (2013).
[Crossref]

Song, J.

Song, S. H.

J. W. Yoon, S. H. Song, and R. Magnusson, “Critical field enhancement of asymptotic optical bound states in the continuum,” Sci. Rep. 5, 18301 (2015).
[Crossref]

Standley, R. D.

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, 651–652 (1974).
[Crossref]

Stone, A. D.

C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, and M. Soljačić, “Bound states in the continuum,” Nat. Rev. Mater. 1, 16048 (2016).
[Crossref]

Sun, F.-W.

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, 114–119 (2015).
[Crossref]

Tikhodeev, S. G.

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

Wang, Y.

Weller-Brophy, L. A.

Xiong, X.

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, 114–119 (2015).
[Crossref]

Yankov, V.

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, e203 (2014).
[Crossref]

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, 695–697 (2012).
[Crossref]

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, 888–896 (2011).
[Crossref]

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, 041105 (2009).
[Crossref]

Yariv, A.

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

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, 276–278 (1977).
[Crossref]

Yoon, J. W.

J. W. Yoon, S. H. Song, and R. Magnusson, “Critical field enhancement of asymptotic optical bound states in the continuum,” Sci. Rep. 5, 18301 (2015).
[Crossref]

Young, S. M.

J. M. Foley, S. M. Young, and J. D. Phillips, “Symmetry-protected mode coupling near normal incidence for narrow-band transmission filtering in a dielectric grating,” Phys. Rev. B 89, 165111 (2014).
[Crossref]

Zengerle, R.

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

Zhen, B.

C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, and M. Soljačić, “Bound states in the continuum,” Nat. Rev. Mater. 1, 16048 (2016).
[Crossref]

C. W. Hsu, B. Zhen, J. Lee, S. L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Observation of trapped light within the radiation continuum,” Nature 499, 188–191 (2013).
[Crossref]

Zou, C.-L.

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, 114–119 (2015).
[Crossref]

Zou, X.-B.

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, 114–119 (2015).
[Crossref]

Appl. Phys. Lett. (3)

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, 041105 (2009).
[Crossref]

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, 651–652 (1974).
[Crossref]

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, 276–278 (1977).
[Crossref]

Comput. Opt. (1)

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, 13–21 (2017).
[Crossref]

IEEE Photon. J. (1)

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, 888–896 (2011).
[Crossref]

IEEE Photon. Technol. Lett. (1)

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, 493–496 (2016).
[Crossref]

J. Lightwave Technol. (2)

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

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

J. Opt. (1)

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, 105703 (2013).
[Crossref]

J. Opt. Soc. Am. A (4)

J. Opt. Soc. Am. B (1)

Laser Photon. Rev. (1)

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, 114–119 (2015).
[Crossref]

Light Sci. Appl. (1)

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, e203 (2014).
[Crossref]

Nat. Rev. Mater. (1)

C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, and M. Soljačić, “Bound states in the continuum,” Nat. Rev. Mater. 1, 16048 (2016).
[Crossref]

Nature (1)

C. W. Hsu, B. Zhen, J. Lee, S. L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Observation of trapped light within the radiation continuum,” Nature 499, 188–191 (2013).
[Crossref]

Opt. Express (3)

Opt. Lett. (4)

Photon. Res. (2)

Phys. Rev. A (2)

D. A. Bykov, E. A. Bezus, and L. L. Doskolovich, “Coupled-wave formalism for bound states in the continuum in guided-mode resonant gratings,” Phys. Rev. A 99, 063805 (2019).
[Crossref]

E. N. Bulgakov and A. F. Sadreev, “Bloch bound states in the radiation continuum in a periodic array of dielectric rods,” Phys. Rev. A 90, 053801 (2014).
[Crossref]

Phys. Rev. B (4)

J. M. Foley, S. M. Young, and J. D. Phillips, “Symmetry-protected mode coupling near normal incidence for narrow-band transmission filtering in a dielectric grating,” Phys. Rev. B 89, 165111 (2014).
[Crossref]

C. Blanchard, J.-P. Hugonin, and C. Sauvan, “Fano resonances in photonic crystal slabs near optical bound states in the continuum,” Phys. Rev. B 94, 155303 (2016).
[Crossref]

E. N. Bulgakov and A. F. Sadreev, “Bound states in the continuum in photonic waveguides inspired by defects,” Phys. Rev. B 78, 075105 (2008).
[Crossref]

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

Phys. Rev. Lett. (1)

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

Sci. Rep. (1)

J. W. Yoon, S. H. Song, and R. Magnusson, “Critical field enhancement of asymptotic optical bound states in the continuum,” Sci. Rep. 5, 18301 (2015).
[Crossref]

Other (2)

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

T. G. Nguyen, G. Ren, S. Schoenhardt, M. Knoerzer, A. Boes, and A. Mitchell, “Ridge resonance: a new resonance phenomenon for silicon photonics harnessing bound states in the continuum,” arXiv:1810.06734 (2018).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1.
Fig. 1. Geometry of a ridge on a (a) waveguide layer and of a (b) composite structure consisting of three ridges separated by phase-shift regions. Red arrows indicate the propagation directions of the incident wave I, reflected wave R, and transmitted wave T.
Fig. 2.
Fig. 2. Reflectance of an obliquely incident TE-polarized guided mode with free-space wavelength λ0=630  nm from the ridge versus ridge width w and angle of incidence θ. The white circle indicates the BIC position. White dashed lines indicate the ridge widths, at which the angular spectra in Fig. 3(a) are plotted.
Fig. 3.
Fig. 3. (a) Angular and (b) wavelength ridge reflectance spectra at w=355  nm (solid blue lines), w=360  nm (dashed red lines), and w=380  nm (dotted yellow lines). The angular spectra are calculated at the fixed free-space wavelength of 630 nm and are the cross sections of the reflectance distribution in Fig. 2 along the white dashed lines. The wavelength spectra are calculated at the angles of incidence θ1=53.28° (w=355  nm), θ2=53.37° (w=360  nm), and θ3=53.72° (w=380  nm), at which the resonant peaks are centered at λ=λ0=630  nm.
Fig. 4.
Fig. 4. Transmittance (black) and reflectance (red) spectra of composite structures consisting of (a) N=2, (b) N=4, and (c) N=6 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.
Fig. 5.
Fig. 5. Transmittance (black) and reflectance (red) spectra of the optimized composite structures consisting of (a) N=4 and (b) N=6 ridges at w=380  nm (solid lines). Dashed lines show the spectra of a single ridge.
Fig. 6.
Fig. 6. Transmittance (black) and reflectance (red) spectra of the optimized composite structures consisting of (a) N=2, (b) N=4, and (c) N=6 ridges at w=360  nm (solid lines). Dashed lines show the spectra of a single ridge.
Fig. 7.
Fig. 7. Reflectance RN(l,λ)=|rN(l,λ)|2 (top) and transmittance TN(l,λ)=|tN(l,λ)|2 (bottom) of the composite structures consisting of (a), (d) N=2, (b), (e) N=3, and (c), (f) N=4 ridges versus the distance between the ridges l and free-space wavelength. Vertical dashed lines show the distance lFP=970.2  nm corresponding to the Fabry–Perot resonance.
Fig. 8.
Fig. 8. Transmittance spectra of the composite structure consisting of N=3 ridges calculated at the width of the phase-shift region between the ridges l=lFP=970.2  nm corresponding to the BIC condition (solid blue line), and at the widths l=lFP+5  nm=975.2  nm (dashed red line) and l=lFP+10  nm=980.2  nm (dotted yellow line).

Equations (19)

Equations on this page are rendered with MathJax. Learn more.

S1(λ)=(t1(λ)r1(λ)r1(λ)t1(λ)),
r1(λ)=exp(iφ)iImλpλλp,t1(λ)=exp(iφ)λReλpλλp,
S2(λ)=S1(λ)*L(l1)*S1(λ),
L(l1)=exp[iψ(l1)]I.
ψ(l1)=kxl1=k0nwg,TEcosθ0·l1,
S2(λ)=(t2(λ)r2(λ)r2(λ)t2(λ))=11exp(2iψ)r12(exp(iψ)t12r1[1exp(2iψ)(r12t12)]r1[1exp(2iψ)(r12t12)]exp(iψ)t12).
r2(λ)=γr,2λλz,1(λλp,1)(λλp,2),t2(λ)=γt,2(λReλp)2(λλp,1)(λλp,2),
λz,1=Reλp+tan[ψ(l1)+φ]Imλp,
λp,1,2=Reλp+i(1±σ)Imλp,
ψ(l1)+φ=π(m1/2),mN,
r2(λ)=2exp(iφ)1[(λλp)/Imλp]2,t2(λ)=(1)miexp(iφ)(λReλp)/Imλp1[(λλp)/Imλp]2.
r3(λ)=γr,3(λλz,1)(λλz,2)(λλp,1)(λλp,2)(λλp,3),t3(λ)=γt,3(λReλp)3(λλp,1)(λλp,2)(λλp,3),
λz,1,2=Reλp+i1σ21±σ+σ2Imλp,
λp,1=Reλp+i(1σ2)Imλp,λp,2,3=λp+iσ2(σ±8+σ2)Imλp,
rN(λ)=γr,Nm=1N1(λλz,m)m=1N(λλp,m),tN(λ)=γt,N(λReλp)Nm=1N(λλp,m).
RBW,N(λ)=11+[(λλ0)/σ]2N,
ψ(li)+φ=πm,mN,
λp,1=λp,2=Reλp,λp,3=Reλp+3iImλp.
Imλp,i(δ)=αiδ2+O(δ3),i=1,2,