Abstract

We consider propagating bound states in the continuum in dielectric gratings. The gratings consist of a slab with ridges periodically arranged either on top or on both sides of the slab. Based on the Fourier modal approach, we recover the leaky zones above the line of light to identify the geometries of the gratings supporting Bloch bound states propagating in the direction perpendicular to the ridges. Most importantly, it is demonstrated that if a two-sided grating possesses either mirror or glide symmetry, the Bloch bound states are stable to variation of parameters as long as the above symmetries are preserved.

© 2018 Optical Society of America

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  33. Z. Hu and Y. Y. Lu, “Resonances and bound states in the continuum on periodic arrays of slightly noncircular cylinders,” J. Phys. B 51, 035402 (2018).
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  34. 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).
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  35. X. Cui, H. Tian, Y. Du, G. Shi, and Z. Zhou, “Normal incidence filters using symmetry-protected modes in dielectric subwavelength gratings,” Sci. Rep. 6, 36066 (2016).
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  36. Z. Wang, H. Zhang, L. Ni, W. Hu, and C. Peng, “Analytical perspective of interfering resonances in high-index-contrast periodic photonic structures,” IEEE J. Quantum Electron. 52, 1–9 (2016).
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    [Crossref]
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    [Crossref]
  42. Y. Yang, C. Peng, Y. Liang, Z. Li, and S. Noda, “Analytical perspective for bound states in the continuum in photonic crystal slabs,” Phys. Rev. Lett. 113, 037401 (2014).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  49. M. Pisarenco, J. Maubach, I. Setija, and R. Mattheij, “Aperiodic fourier modal method in contrast-field formulation for simulation of scattering from finite structures,” J. Opt. Soc. Am. A 27, 2423–2431 (2010).
    [Crossref]
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    [Crossref]

2018 (2)

Z. Hu and Y. Y. Lu, “Resonances and bound states in the continuum on periodic arrays of slightly noncircular cylinders,” J. Phys. B 51, 035402 (2018).
[Crossref]

T. Wang and S. Zhang, “Large enhancement of second harmonic generation from transition-metal dichalcogenide monolayer on grating near bound states in the continuum,” Opt. Express 26, 322–337 (2018).
[Crossref]

2017 (13)

J. Li, J. Ren, and X. Zhang, “Three-dimensional vector wave bound states in a continuum,” J. Opt. Soc. Am. B 34, 559–565 (2017).
[Crossref]

Z. Hu and Y. Y. Lu, “Propagating bound states in the continuum at the surface of a photonic crystal,” J. Opt. Soc. Am. B 34, 1878–1883 (2017).
[Crossref]

L. Yuan and Y. Y. Lu, “Bound states in the continuum on periodic structures: perturbation theory and robustness,” Opt. Lett. 42, 4490–4493 (2017).
[Crossref]

E. N. Bulgakov and D. N. Maksimov, “Bound states in the continuum and polarization singularities in periodic arrays of dielectric rods,” Phys. Rev. A 96, 063833 (2017).
[Crossref]

E. Penzo, S. Romano, Y. Wang, S. Dhuey, L. D. Negro, V. Mocella, and S. Cabrini, “Patterning of electrically tunable light-emitting photonic structures demonstrating bound states in the continuum,” J. Vac. Sci. Technol. B 35, 06G401 (2017).
[Crossref]

A. Taghizadeh and I.-S. Chung, “Quasi bound states in the continuum with few unit cells of photonic crystal slab,” Appl. Phys. Lett. 111, 031114 (2017).
[Crossref]

F. Monticone and A. Alù, “Bound states within the radiation continuum in diffraction gratings and the role of leaky modes,” New J. Phys. 19, 093011 (2017).
[Crossref]

L. Yuan and Y. Y. Lu, “Propagating Bloch modes above the lightline on a periodic array of cylinders,” J. Phys. B 50, 05LT01 (2017).
[Crossref]

Z. F. Sadrieva, I. S. Sinev, K. L. Koshelev, A. Samusev, I. V. Iorsh, O. Takayama, R. Malureanu, A. A. Bogdanov, and A. V. Lavrinenko, “Transition from optical bound states in the continuum to leaky resonances: role of substrate and roughness,” ACS Photon. 4, 723–727 (2017).
[Crossref]

Y.-X. Xiao, G. Ma, Z.-Q. Zhang, and C. Chan, “Topological subspace-induced bound state in the continuum,” Phys. Rev. Lett. 118, 166803 (2017).
[Crossref]

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

E. N. Bulgakov and D. N. Maksimov, “Topological bound states in the continuum in arrays of dielectric spheres,” Phys. Rev. Lett. 118, 267401 (2017).
[Crossref]

E. N. Bulgakov and A. F. Sadreev, “Bound states in the continuum with high orbital angular momentum in a dielectric rod with periodically modulated permittivity,” Phys. Rev. A 96, 013841 (2017).
[Crossref]

2016 (10)

L. Ni, Z. Wang, C. Peng, and Z. Li, “Tunable optical bound states in the continuum beyond in-plane symmetry protection,” Phys. Rev. B 94, 245148 (2016).
[Crossref]

L. Li and H. Yin, “Bound states in the continuum in double layer structures,” Sci. Rep. 6, 26988 (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]

X. Gao, C. W. Hsu, B. Zhen, X. Lin, J. D. Joannopoulos, M. Soljačić, and H. Chen, “Formation mechanism of guided resonances and bound states in the continuum in photonic crystal slabs,” Sci. Rep. 6, 31908 (2016).
[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]

X. Cui, H. Tian, Y. Du, G. Shi, and Z. Zhou, “Normal incidence filters using symmetry-protected modes in dielectric subwavelength gratings,” Sci. Rep. 6, 36066 (2016).
[Crossref]

Z. Wang, H. Zhang, L. Ni, W. Hu, and C. Peng, “Analytical perspective of interfering resonances in high-index-contrast periodic photonic structures,” IEEE J. Quantum Electron. 52, 1–9 (2016).
[Crossref]

Y. H. Ko, M. Niraula, K. J. Lee, and R. Magnusson, “Properties of wideband resonant reflectors under fully conical light incidence,” Opt. Express 24, 4542–4551 (2016).
[Crossref]

E. N. Bulgakov and D. N. Maksimov, “Light guiding above the light line in arrays of dielectric nanospheres,” Opt. Lett. 41, 3888–3891 (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]

2015 (5)

F. Monticone and A. Alu, “Leaky-wave theory, techniques, and applications: from microwaves to visible frequencies,” Proc. IEEE 103, 793–821 (2015).
[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]

E. N. Bulgakov and A. F. Sadreev, “Light trapping above the light cone in a one-dimensional array of dielectric spheres,” Phys. Rev. A 92, 023816 (2015).
[Crossref]

V. Mocella and S. Romano, “Giant field enhancement in photonic resonant lattices,” Phys. Rev. B 92, 155117 (2015).
[Crossref]

R. A. Vicencio, C. Cantillano, L. Morales-Inostroza, B. Real, C. Meja-Cortés, S. Weimann, A. Szameit, and M. I. Molina, “Observation of localized states in Lieb photonic lattices,” Phys. Rev. Lett. 114, 245503 (2015).
[Crossref]

2014 (5)

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]

B. Zhen, C. W. Hsu, L. Lu, A. D. Stone, and M. Soljačić, “Topological nature of optical bound states in the continuum,” Phys. Rev. Lett. 113, 257401 (2014).
[Crossref]

F. Monticone and A. Alù, “Embedded photonic eigenvalues in 3D nanostructures,” Phys. Rev. Lett. 112, 213903 (2014).
[Crossref]

Y. Yang, C. Peng, Y. Liang, Z. Li, and S. Noda, “Analytical perspective for bound states in the continuum in photonic crystal slabs,” Phys. Rev. Lett. 113, 037401 (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]

2013 (2)

S. Weimann, Y. Xu, R. Keil, A. E. Miroshnichenko, A. Tünnermann, S. Nolte, A. A. Sukhorukov, A. Szameit, and Y. S. Kivshar, “Compact surface fano states embedded in the continuum of waveguide arrays,” Phys. Rev. Lett. 111, 240403 (2013).
[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]

2012 (1)

2011 (3)

2010 (4)

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, “Flat dielectric grating reflectors with focusing abilities,” Nat. Photonics 4, 466–470 (2010).
[Crossref]

R. F. Ndangali and S. V. Shabanov, “Electromagnetic bound states in the radiation continuum for periodic double arrays of subwavelength dielectric cylinders,” J. Math. Phys. 51, 102901 (2010).
[Crossref]

F. Lu, F. G. Sedgwick, V. Karagodsky, C. Chase, and C. J. Chang-Hasnain, “Planar high-numerical-aperture low-loss focusing reflectors and lenses using subwavelength high contrast gratings,” Opt. Express 18, 12606–12614 (2010).
[Crossref]

M. Pisarenco, J. Maubach, I. Setija, and R. Mattheij, “Aperiodic fourier modal method in contrast-field formulation for simulation of scattering from finite structures,” J. Opt. Soc. Am. A 27, 2423–2431 (2010).
[Crossref]

2008 (2)

2005 (1)

S. P. Shipman and S. Venakides, “Resonant transmission near nonrobust periodic slab modes,” Phys. Rev. E 71, 026611 (2005).
[Crossref]

2003 (1)

S. Venakides and S. P. Shipman, “Resonance and bound states in photonic crystal slabs,” SIAM J. Appl. Math. 64, 322–342 (2003).
[Crossref]

2000 (1)

V. Pacradouni, W. J. Mandeville, A. R. Cowan, P. Paddon, J. F. Young, and S. R. Johnson, “Photonic band structure of dielectric membranes periodically textured in two dimensions,” Phys. Rev.B 62, 4204–4207 (2000).
[Crossref]

Alu, A.

F. Monticone and A. Alu, “Leaky-wave theory, techniques, and applications: from microwaves to visible frequencies,” Proc. IEEE 103, 793–821 (2015).
[Crossref]

Alù, A.

F. Monticone and A. Alù, “Bound states within the radiation continuum in diffraction gratings and the role of leaky modes,” New J. Phys. 19, 093011 (2017).
[Crossref]

F. Monticone and A. Alù, “Embedded photonic eigenvalues in 3D nanostructures,” Phys. Rev. Lett. 112, 213903 (2014).
[Crossref]

Bahari, B.

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

Beausoleil, R. G.

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, “Flat dielectric grating reflectors with focusing abilities,” Nat. Photonics 4, 466–470 (2010).
[Crossref]

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]

Bogdanov, A. A.

Z. F. Sadrieva, I. S. Sinev, K. L. Koshelev, A. Samusev, I. V. Iorsh, O. Takayama, R. Malureanu, A. A. Bogdanov, and A. V. Lavrinenko, “Transition from optical bound states in the continuum to leaky resonances: role of substrate and roughness,” ACS Photon. 4, 723–727 (2017).
[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]

Bulgakov, E. N.

E. N. Bulgakov and A. F. Sadreev, “Bound states in the continuum with high orbital angular momentum in a dielectric rod with periodically modulated permittivity,” Phys. Rev. A 96, 013841 (2017).
[Crossref]

E. N. Bulgakov and D. N. Maksimov, “Topological bound states in the continuum in arrays of dielectric spheres,” Phys. Rev. Lett. 118, 267401 (2017).
[Crossref]

E. N. Bulgakov and D. N. Maksimov, “Bound states in the continuum and polarization singularities in periodic arrays of dielectric rods,” Phys. Rev. A 96, 063833 (2017).
[Crossref]

E. N. Bulgakov and D. N. Maksimov, “Light guiding above the light line in arrays of dielectric nanospheres,” Opt. Lett. 41, 3888–3891 (2016).
[Crossref]

E. N. Bulgakov and A. F. Sadreev, “Light trapping above the light cone in a one-dimensional array of dielectric spheres,” Phys. Rev. A 92, 023816 (2015).
[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]

Cabrini, S.

E. Penzo, S. Romano, Y. Wang, S. Dhuey, L. D. Negro, V. Mocella, and S. Cabrini, “Patterning of electrically tunable light-emitting photonic structures demonstrating bound states in the continuum,” J. Vac. Sci. Technol. B 35, 06G401 (2017).
[Crossref]

Cantillano, C.

R. A. Vicencio, C. Cantillano, L. Morales-Inostroza, B. Real, C. Meja-Cortés, S. Weimann, A. Szameit, and M. I. Molina, “Observation of localized states in Lieb photonic lattices,” Phys. Rev. Lett. 114, 245503 (2015).
[Crossref]

Chan, C.

Y.-X. Xiao, G. Ma, Z.-Q. Zhang, and C. Chan, “Topological subspace-induced bound state in the continuum,” Phys. Rev. Lett. 118, 166803 (2017).
[Crossref]

Chang-Hasnain, C. J.

Chase, C.

Chen, H.

X. Gao, C. W. Hsu, B. Zhen, X. Lin, J. D. Joannopoulos, M. Soljačić, and H. Chen, “Formation mechanism of guided resonances and bound states in the continuum in photonic crystal slabs,” Sci. Rep. 6, 31908 (2016).
[Crossref]

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]

Chung, I.-S.

A. Taghizadeh and I.-S. Chung, “Quasi bound states in the continuum with few unit cells of photonic crystal slab,” Appl. Phys. Lett. 111, 031114 (2017).
[Crossref]

Cowan, A. R.

V. Pacradouni, W. J. Mandeville, A. R. Cowan, P. Paddon, J. F. Young, and S. R. Johnson, “Photonic band structure of dielectric membranes periodically textured in two dimensions,” Phys. Rev.B 62, 4204–4207 (2000).
[Crossref]

Cui, X.

X. Cui, H. Tian, Y. Du, G. Shi, and Z. Zhou, “Normal incidence filters using symmetry-protected modes in dielectric subwavelength gratings,” Sci. Rep. 6, 36066 (2016).
[Crossref]

Dhuey, S.

E. Penzo, S. Romano, Y. Wang, S. Dhuey, L. D. Negro, V. Mocella, and S. Cabrini, “Patterning of electrically tunable light-emitting photonic structures demonstrating bound states in the continuum,” J. Vac. Sci. Technol. B 35, 06G401 (2017).
[Crossref]

Dong, L.

Dreisow, F.

Y. Plotnik, O. Peleg, F. Dreisow, M. Heinrich, S. Nolte, A. Szameit, and M. Segev, “Experimental observation of optical bound states in the continuum,” Phys. Rev. Lett. 107, 28–31 (2011).
[Crossref]

Du, Y.

X. Cui, H. Tian, Y. Du, G. Shi, and Z. Zhou, “Normal incidence filters using symmetry-protected modes in dielectric subwavelength gratings,” Sci. Rep. 6, 36066 (2016).
[Crossref]

Fainman, Y.

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S. Weimann, Y. Xu, R. Keil, A. E. Miroshnichenko, A. Tünnermann, S. Nolte, A. A. Sukhorukov, A. Szameit, and Y. S. Kivshar, “Compact surface fano states embedded in the continuum of waveguide arrays,” Phys. Rev. Lett. 111, 240403 (2013).
[Crossref]

Venakides, S.

S. P. Shipman and S. Venakides, “Resonant transmission near nonrobust periodic slab modes,” Phys. Rev. E 71, 026611 (2005).
[Crossref]

S. Venakides and S. P. Shipman, “Resonance and bound states in photonic crystal slabs,” SIAM J. Appl. Math. 64, 322–342 (2003).
[Crossref]

Vicencio, R. A.

R. A. Vicencio, C. Cantillano, L. Morales-Inostroza, B. Real, C. Meja-Cortés, S. Weimann, A. Szameit, and M. I. Molina, “Observation of localized states in Lieb photonic lattices,” Phys. Rev. Lett. 114, 245503 (2015).
[Crossref]

Wang, T.

Wang, Y.

E. Penzo, S. Romano, Y. Wang, S. Dhuey, L. D. Negro, V. Mocella, and S. Cabrini, “Patterning of electrically tunable light-emitting photonic structures demonstrating bound states in the continuum,” J. Vac. Sci. Technol. B 35, 06G401 (2017).
[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]

Wang, Z.

Z. Wang, H. Zhang, L. Ni, W. Hu, and C. Peng, “Analytical perspective of interfering resonances in high-index-contrast periodic photonic structures,” IEEE J. Quantum Electron. 52, 1–9 (2016).
[Crossref]

L. Ni, Z. Wang, C. Peng, and Z. Li, “Tunable optical bound states in the continuum beyond in-plane symmetry protection,” Phys. Rev. B 94, 245148 (2016).
[Crossref]

Weimann, S.

R. A. Vicencio, C. Cantillano, L. Morales-Inostroza, B. Real, C. Meja-Cortés, S. Weimann, A. Szameit, and M. I. Molina, “Observation of localized states in Lieb photonic lattices,” Phys. Rev. Lett. 114, 245503 (2015).
[Crossref]

S. Weimann, Y. Xu, R. Keil, A. E. Miroshnichenko, A. Tünnermann, S. Nolte, A. A. Sukhorukov, A. Szameit, and Y. S. Kivshar, “Compact surface fano states embedded in the continuum of waveguide arrays,” Phys. Rev. Lett. 111, 240403 (2013).
[Crossref]

Xiao, Y.-X.

Y.-X. Xiao, G. Ma, Z.-Q. Zhang, and C. Chan, “Topological subspace-induced bound state in the continuum,” Phys. Rev. Lett. 118, 166803 (2017).
[Crossref]

Xu, Y.

S. Weimann, Y. Xu, R. Keil, A. E. Miroshnichenko, A. Tünnermann, S. Nolte, A. A. Sukhorukov, A. Szameit, and Y. S. Kivshar, “Compact surface fano states embedded in the continuum of waveguide arrays,” Phys. Rev. Lett. 111, 240403 (2013).
[Crossref]

Yang, W.

Yang, Y.

Y. Yang, C. Peng, Y. Liang, Z. Li, and S. Noda, “Analytical perspective for bound states in the continuum in photonic crystal slabs,” Phys. Rev. Lett. 113, 037401 (2014).
[Crossref]

Yin, H.

L. Li and H. Yin, “Bound states in the continuum in double layer structures,” Sci. Rep. 6, 26988 (2016).
[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, J. F.

V. Pacradouni, W. J. Mandeville, A. R. Cowan, P. Paddon, J. F. Young, and S. R. Johnson, “Photonic band structure of dielectric membranes periodically textured in two dimensions,” Phys. Rev.B 62, 4204–4207 (2000).
[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]

Yuan, L.

L. Yuan and Y. Y. Lu, “Propagating Bloch modes above the lightline on a periodic array of cylinders,” J. Phys. B 50, 05LT01 (2017).
[Crossref]

L. Yuan and Y. Y. Lu, “Bound states in the continuum on periodic structures: perturbation theory and robustness,” Opt. Lett. 42, 4490–4493 (2017).
[Crossref]

Zhang, H.

Z. Wang, H. Zhang, L. Ni, W. Hu, and C. Peng, “Analytical perspective of interfering resonances in high-index-contrast periodic photonic structures,” IEEE J. Quantum Electron. 52, 1–9 (2016).
[Crossref]

Zhang, S.

Zhang, X.

Zhang, Z.-Q.

Y.-X. Xiao, G. Ma, Z.-Q. Zhang, and C. Chan, “Topological subspace-induced bound state in the continuum,” Phys. Rev. Lett. 118, 166803 (2017).
[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]

X. Gao, C. W. Hsu, B. Zhen, X. Lin, J. D. Joannopoulos, M. Soljačić, and H. Chen, “Formation mechanism of guided resonances and bound states in the continuum in photonic crystal slabs,” Sci. Rep. 6, 31908 (2016).
[Crossref]

B. Zhen, C. W. Hsu, L. Lu, A. D. Stone, and M. Soljačić, “Topological nature of optical bound states in the continuum,” Phys. Rev. Lett. 113, 257401 (2014).
[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]

Zhou, Y.

Zhou, Z.

X. Cui, H. Tian, Y. Du, G. Shi, and Z. Zhou, “Normal incidence filters using symmetry-protected modes in dielectric subwavelength gratings,” Sci. Rep. 6, 36066 (2016).
[Crossref]

ACS Photon. (1)

Z. F. Sadrieva, I. S. Sinev, K. L. Koshelev, A. Samusev, I. V. Iorsh, O. Takayama, R. Malureanu, A. A. Bogdanov, and A. V. Lavrinenko, “Transition from optical bound states in the continuum to leaky resonances: role of substrate and roughness,” ACS Photon. 4, 723–727 (2017).
[Crossref]

Adv. Opt. Photon. (1)

Appl. Phys. Lett. (1)

A. Taghizadeh and I.-S. Chung, “Quasi bound states in the continuum with few unit cells of photonic crystal slab,” Appl. Phys. Lett. 111, 031114 (2017).
[Crossref]

IEEE J. Quantum Electron. (1)

Z. Wang, H. Zhang, L. Ni, W. Hu, and C. Peng, “Analytical perspective of interfering resonances in high-index-contrast periodic photonic structures,” IEEE J. Quantum Electron. 52, 1–9 (2016).
[Crossref]

J. Math. Phys. (1)

R. F. Ndangali and S. V. Shabanov, “Electromagnetic bound states in the radiation continuum for periodic double arrays of subwavelength dielectric cylinders,” J. Math. Phys. 51, 102901 (2010).
[Crossref]

J. Opt. Soc. Am. A (2)

J. Opt. Soc. Am. B (3)

J. Phys. B (2)

L. Yuan and Y. Y. Lu, “Propagating Bloch modes above the lightline on a periodic array of cylinders,” J. Phys. B 50, 05LT01 (2017).
[Crossref]

Z. Hu and Y. Y. Lu, “Resonances and bound states in the continuum on periodic arrays of slightly noncircular cylinders,” J. Phys. B 51, 035402 (2018).
[Crossref]

J. Vac. Sci. Technol. B (1)

E. Penzo, S. Romano, Y. Wang, S. Dhuey, L. D. Negro, V. Mocella, and S. Cabrini, “Patterning of electrically tunable light-emitting photonic structures demonstrating bound states in the continuum,” J. Vac. Sci. Technol. B 35, 06G401 (2017).
[Crossref]

Nat. Photonics (1)

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, “Flat dielectric grating reflectors with focusing abilities,” Nat. Photonics 4, 466–470 (2010).
[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 (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]

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

New J. Phys. (1)

F. Monticone and A. Alù, “Bound states within the radiation continuum in diffraction gratings and the role of leaky modes,” New J. Phys. 19, 093011 (2017).
[Crossref]

Opt. Express (4)

Opt. Lett. (3)

Phys. Rev. A (4)

E. N. Bulgakov and D. N. Maksimov, “Bound states in the continuum and polarization singularities in periodic arrays of dielectric rods,” Phys. Rev. A 96, 063833 (2017).
[Crossref]

E. N. Bulgakov and A. F. Sadreev, “Light trapping above the light cone in a one-dimensional array of dielectric spheres,” Phys. Rev. A 92, 023816 (2015).
[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]

E. N. Bulgakov and A. F. Sadreev, “Bound states in the continuum with high orbital angular momentum in a dielectric rod with periodically modulated permittivity,” Phys. Rev. A 96, 013841 (2017).
[Crossref]

Phys. Rev. B (4)

V. Mocella and S. Romano, “Giant field enhancement in photonic resonant lattices,” Phys. Rev. B 92, 155117 (2015).
[Crossref]

L. Ni, Z. Wang, C. Peng, and Z. Li, “Tunable optical bound states in the continuum beyond in-plane symmetry protection,” Phys. Rev. B 94, 245148 (2016).
[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]

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]

Phys. Rev. E (1)

S. P. Shipman and S. Venakides, “Resonant transmission near nonrobust periodic slab modes,” Phys. Rev. E 71, 026611 (2005).
[Crossref]

Phys. Rev. Lett. (9)

B. Zhen, C. W. Hsu, L. Lu, A. D. Stone, and M. Soljačić, “Topological nature of optical bound states in the continuum,” Phys. Rev. Lett. 113, 257401 (2014).
[Crossref]

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

R. A. Vicencio, C. Cantillano, L. Morales-Inostroza, B. Real, C. Meja-Cortés, S. Weimann, A. Szameit, and M. I. Molina, “Observation of localized states in Lieb photonic lattices,” Phys. Rev. Lett. 114, 245503 (2015).
[Crossref]

Y. Plotnik, O. Peleg, F. Dreisow, M. Heinrich, S. Nolte, A. Szameit, and M. Segev, “Experimental observation of optical bound states in the continuum,” Phys. Rev. Lett. 107, 28–31 (2011).
[Crossref]

S. Weimann, Y. Xu, R. Keil, A. E. Miroshnichenko, A. Tünnermann, S. Nolte, A. A. Sukhorukov, A. Szameit, and Y. S. Kivshar, “Compact surface fano states embedded in the continuum of waveguide arrays,” Phys. Rev. Lett. 111, 240403 (2013).
[Crossref]

E. N. Bulgakov and D. N. Maksimov, “Topological bound states in the continuum in arrays of dielectric spheres,” Phys. Rev. Lett. 118, 267401 (2017).
[Crossref]

Y.-X. Xiao, G. Ma, Z.-Q. Zhang, and C. Chan, “Topological subspace-induced bound state in the continuum,” Phys. Rev. Lett. 118, 166803 (2017).
[Crossref]

Y. Yang, C. Peng, Y. Liang, Z. Li, and S. Noda, “Analytical perspective for bound states in the continuum in photonic crystal slabs,” Phys. Rev. Lett. 113, 037401 (2014).
[Crossref]

F. Monticone and A. Alù, “Embedded photonic eigenvalues in 3D nanostructures,” Phys. Rev. Lett. 112, 213903 (2014).
[Crossref]

Phys. Rev.B (1)

V. Pacradouni, W. J. Mandeville, A. R. Cowan, P. Paddon, J. F. Young, and S. R. Johnson, “Photonic band structure of dielectric membranes periodically textured in two dimensions,” Phys. Rev.B 62, 4204–4207 (2000).
[Crossref]

Proc. IEEE (1)

F. Monticone and A. Alu, “Leaky-wave theory, techniques, and applications: from microwaves to visible frequencies,” Proc. IEEE 103, 793–821 (2015).
[Crossref]

Sci. Rep. (4)

X. Gao, C. W. Hsu, B. Zhen, X. Lin, J. D. Joannopoulos, M. Soljačić, and H. Chen, “Formation mechanism of guided resonances and bound states in the continuum in photonic crystal slabs,” Sci. Rep. 6, 31908 (2016).
[Crossref]

X. Cui, H. Tian, Y. Du, G. Shi, and Z. Zhou, “Normal incidence filters using symmetry-protected modes in dielectric subwavelength gratings,” Sci. Rep. 6, 36066 (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]

L. Li and H. Yin, “Bound states in the continuum in double layer structures,” Sci. Rep. 6, 26988 (2016).
[Crossref]

SIAM J. Appl. Math. (1)

S. Venakides and S. P. Shipman, “Resonance and bound states in photonic crystal slabs,” SIAM J. Appl. Math. 64, 322–342 (2003).
[Crossref]

Other (1)

E. Popov, Gratings: Theory and Numeric Applications (Institut Fresnel, 2012).

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Figures (3)

Fig. 1.
Fig. 1. Dielectric gratings: (a) one-sided grating and (b) two-sided grating.
Fig. 2.
Fig. 2. BICs in asymmetric DGs. (a)–(c) Mode profiles in the form of the real part of the electric vector component Ey (p.d.u.) for BICs 2,4,6 from Table 1, respectively. (d) Dispersion of the real part of the leaky-mode frequency: BIC 2, solid blue; BIC 4, dashed green; BIC 6, dashed-dotted brown. The white domain is given by Eq. (3). Red circles show the positions of the BICs. (e) Q-factor dispersion for the same leaky zones as in (d).
Fig. 3.
Fig. 3. BICs in symmetric DGs. (a),(b) Mode profiles in the form of the real part of the electric vector component Ey (p.d.u.) for BICs 7,8 from Table 1, respectively. (c) Position of BIC 7, solid blue, and BIC 8, dotted brown, under variation of the substrate thickness. The white domain is given by Eq. (3).

Tables (1)

Tables Icon

Table 1. BICs in DG for w=0.5a

Equations (3)

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

k02=kx,n2+kz2+ky2,kx,n=β2πn/a,
Ey(x,z)=n=Sn(z)eikx,nx.
βa<k0a<2πβa,

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