Abstract

External waves incident on a periodic metamaterial lattice couple to it at frequencies corresponding to the leaky, or second, stop band. The resulting leaky-mode or guided-mode resonance effects are useful in device design and spectral manipulation. Indeed, some of the most important properties of metamaterials are associated with the leaky stopband. Thus motivated, we treat the band dynamics of leaky-mode resonant photonic lattices. In particular, properties of the band gap and conditions for band closure and band flips under multimode conditions are quantified. For a symmetric lattice, the nonleaky band edge hosts a bound state in the continuum whose band transition reverses the modal symmetry of the band edge modes. The leaky edge supports a guided-mode resonant radiative peak that also undergoes band flip upon band closure. We analyze a canonical one-dimensional lattice with exact numerical methods and a semianalytical formulation modified to handle the multimodal case. We show that the band dynamics of the various leaky modes present differ appreciably with, for example, the band associated with the fundamental TE0 and the first higher order TE1 modes closing at differing values of dielectric-constant modulation. We compare the thin-film lattice with an infinite lattice and find an approximate analytical condition for band closure that we verify with rigorous computations.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2019 (2)

K. Fan, I. V. Shadrivov, and W. J. Padilla, “Dynamic bound states in the continuum,” Optica 6(2), 169–173 (2019).
[Crossref]

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

2018 (8)

Y. H. Ko and R. Magnusson, “Wideband dielectric metamaterial reflectors: Mie scattering or leaky bloch mode resonance?” Optica 5(3), 289–294 (2018).
[Crossref]

E. N. Bulgakov and D. N. Maksimov, “Avoided crossings and bound states in the continuum in low-contrast dielectric gratings,” Phys. Rev. A (Coll. Park) 98(5), 053840 (2018).
[Crossref]

M. Minkov, I. A. D. Williamson, M. Xiao, and S. Fan, “Zero-index bound states in the continuum,” Phys. Rev. Lett. 121(26), 263901 (2018).
[Crossref] [PubMed]

L. Carletti, K. Koshelev, C. De Angelis, and Y. Kivshar, “Giant nonlinear response at the nanoscale driven by bound states in the continuum,” Phys. Rev. Lett. 121(3), 033903 (2018).
[Crossref] [PubMed]

H. M. Doeleman, F. Monticone, W. Hollander, A. Alù, and A. F. Koenderink, “Experimental observation of a polarization vortex at an optical bound state in the continuum,” Nat. Photonics 12(7), 397–401 (2018).
[Crossref]

E. N. Bulgakov, D. N. Maksimov, P. N. Semina, and S. A. Skorobogatov, “Propagating bound states in the continuum in dielectric gratings,” J. Opt. Soc. Am. B 35(6), 1218–1222 (2018).
[Crossref]

K. Koshelev, S. Lepeshov, M. Liu, A. Bogdanov, and Y. Kivshar, “Asymmetric metasurfaces with high-Q resonances governed by bound states in the continuum,” Phys. Rev. Lett. 121(19), 193903 (2018).
[Crossref] [PubMed]

S. I. Azzam, V. M. Shalaev, A. Boltasseva, and A. V. Kildishev, “Formation of bound states in the continuum in hybrid plasmonic-photonic systems,” Phys. Rev. Lett. 121(25), 253901 (2018).
[Crossref] [PubMed]

2017 (3)

S.-G. Lee, S. H. Kim, K. J. Kim, and C. S. Kee, “Polarization-independent electromagnetically induced transparency-like transmission in coupled guided-mode resonance structures,” Appl. Phys. Lett. 110(11), 111106 (2017).
[Crossref]

K. Yamada, K. J. Lee, Y. H. Ko, J. Inoue, K. Kintaka, S. Ura, and R. Magnusson, “Flat-top narrowband filters enabled by guided-mode resonance in two-level waveguides,” Opt. Lett. 42(20), 4127–4130 (2017).
[Crossref] [PubMed]

Y.-X. Xiao, G. Ma, Z.-Q. Zhang, and C. T. Chan, “Topological subspace-induced bound state in the continuum,” Phys. Rev. Lett. 118(16), 166803 (2017).
[Crossref] [PubMed]

2016 (1)

C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, and M. Soljačić, “Bound states in the continuum,” Nat. Rev. Mater. 1(9), 16048 (2016).
[Crossref]

2015 (1)

2014 (6)

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(25), 257401 (2014).
[Crossref] [PubMed]

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(3), 037401 (2014).
[Crossref] [PubMed]

E. N. Bulgakov and A. F. Sadreev, “Robust bound state in the continuum in a nonlinear microcavity embedded in a photonic crystal waveguide,” Opt. Lett. 39(17), 5212–5215 (2014).
[Crossref] [PubMed]

F. Monticone and A. Alù, “Embedded photonic eigenvalues in 3D nanostructures,” Phys. Rev. Lett. 112(21), 213903 (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(5), 053801 (2014).
[Crossref]

T. Lepetit and B. Kanté, “Controlling multipolar radiation with symmetries for electromagnetic bound states in the continuum,” Phys. Rev. B Condens. Matter Mater. Phys. 90(24), 241103 (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(7457), 188–191 (2013).
[Crossref] [PubMed]

C. W. Hsu, B. Zhen, S.-L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Bloch surface eigenstates within the radiation continuum,” Light Sci. Appl. 2(7), 1–5 (2013).
[Crossref]

2011 (1)

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(18), 183901 (2011).
[Crossref] [PubMed]

2010 (1)

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[Crossref]

2008 (2)

R. Magnusson and M. Shokooh-Saremi, “Physical basis for wideband resonant reflectors,” Opt. Express 16(5), 3456–3462 (2008).
[Crossref] [PubMed]

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

2007 (1)

1997 (1)

D. Rosenblatt, A. Sharon, and A. A. Friesem, “Resonant grating waveguide structure,” IEEE J. Quantum Electron. 33(11), 2038–2059 (1997).
[Crossref]

1993 (1)

1985 (1)

R. F. Kazarinov and C. H. Henry, “Second-order distributed feedback lasers with mode selection provided by first-order radiation loss,” IEEE J. Quantum Electron. 21(2), 144–150 (1985).
[Crossref]

Alù, A.

H. M. Doeleman, F. Monticone, W. Hollander, A. Alù, and A. F. Koenderink, “Experimental observation of a polarization vortex at an optical bound state in the continuum,” Nat. Photonics 12(7), 397–401 (2018).
[Crossref]

F. Monticone and A. Alù, “Embedded photonic eigenvalues in 3D nanostructures,” Phys. Rev. Lett. 112(21), 213903 (2014).
[Crossref]

Azzam, S. I.

S. I. Azzam, V. M. Shalaev, A. Boltasseva, and A. V. Kildishev, “Formation of bound states in the continuum in hybrid plasmonic-photonic systems,” Phys. Rev. Lett. 121(25), 253901 (2018).
[Crossref] [PubMed]

Bermel, P.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[Crossref]

Bogdanov, A.

K. Koshelev, S. Lepeshov, M. Liu, A. Bogdanov, and Y. Kivshar, “Asymmetric metasurfaces with high-Q resonances governed by bound states in the continuum,” Phys. Rev. Lett. 121(19), 193903 (2018).
[Crossref] [PubMed]

Boltasseva, A.

S. I. Azzam, V. M. Shalaev, A. Boltasseva, and A. V. Kildishev, “Formation of bound states in the continuum in hybrid plasmonic-photonic systems,” Phys. Rev. Lett. 121(25), 253901 (2018).
[Crossref] [PubMed]

Borisov, A. G.

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

Bulgakov, E. N.

E. N. Bulgakov and D. N. Maksimov, “Avoided crossings and bound states in the continuum in low-contrast dielectric gratings,” Phys. Rev. A (Coll. Park) 98(5), 053840 (2018).
[Crossref]

E. N. Bulgakov, D. N. Maksimov, P. N. Semina, and S. A. Skorobogatov, “Propagating bound states in the continuum in dielectric gratings,” J. Opt. Soc. Am. B 35(6), 1218–1222 (2018).
[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(5), 053801 (2014).
[Crossref]

E. N. Bulgakov and A. F. Sadreev, “Robust bound state in the continuum in a nonlinear microcavity embedded in a photonic crystal waveguide,” Opt. Lett. 39(17), 5212–5215 (2014).
[Crossref] [PubMed]

Carletti, L.

L. Carletti, K. Koshelev, C. De Angelis, and Y. Kivshar, “Giant nonlinear response at the nanoscale driven by bound states in the continuum,” Phys. Rev. Lett. 121(3), 033903 (2018).
[Crossref] [PubMed]

Chan, C. T.

Y.-X. Xiao, G. Ma, Z.-Q. Zhang, and C. T. Chan, “Topological subspace-induced bound state in the continuum,” Phys. Rev. Lett. 118(16), 166803 (2017).
[Crossref] [PubMed]

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(7457), 188–191 (2013).
[Crossref] [PubMed]

C. W. Hsu, B. Zhen, S.-L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Bloch surface eigenstates within the radiation continuum,” Light Sci. Appl. 2(7), 1–5 (2013).
[Crossref]

De Angelis, C.

L. Carletti, K. Koshelev, C. De Angelis, and Y. Kivshar, “Giant nonlinear response at the nanoscale driven by bound states in the continuum,” Phys. Rev. Lett. 121(3), 033903 (2018).
[Crossref] [PubMed]

Ding, Y.

Doeleman, H. M.

H. M. Doeleman, F. Monticone, W. Hollander, A. Alù, and A. F. Koenderink, “Experimental observation of a polarization vortex at an optical bound state in the continuum,” Nat. Photonics 12(7), 397–401 (2018).
[Crossref]

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(18), 183901 (2011).
[Crossref] [PubMed]

Fan, K.

Fan, S.

M. Minkov, I. A. D. Williamson, M. Xiao, and S. Fan, “Zero-index bound states in the continuum,” Phys. Rev. Lett. 121(26), 263901 (2018).
[Crossref] [PubMed]

Friesem, A. A.

D. Rosenblatt, A. Sharon, and A. A. Friesem, “Resonant grating waveguide structure,” IEEE J. Quantum Electron. 33(11), 2038–2059 (1997).
[Crossref]

Heinrich, M.

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(18), 183901 (2011).
[Crossref] [PubMed]

Henry, C. H.

R. F. Kazarinov and C. H. Henry, “Second-order distributed feedback lasers with mode selection provided by first-order radiation loss,” IEEE J. Quantum Electron. 21(2), 144–150 (1985).
[Crossref]

Hollander, W.

H. M. Doeleman, F. Monticone, W. Hollander, A. Alù, and A. F. Koenderink, “Experimental observation of a polarization vortex at an optical bound state in the continuum,” Nat. Photonics 12(7), 397–401 (2018).
[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(9), 16048 (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(25), 257401 (2014).
[Crossref] [PubMed]

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(7457), 188–191 (2013).
[Crossref] [PubMed]

C. W. Hsu, B. Zhen, S.-L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Bloch surface eigenstates within the radiation continuum,” Light Sci. Appl. 2(7), 1–5 (2013).
[Crossref]

Ibanescu, M.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[Crossref]

Inoue, J.

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(9), 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(7457), 188–191 (2013).
[Crossref] [PubMed]

C. W. Hsu, B. Zhen, S.-L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Bloch surface eigenstates within the radiation continuum,” Light Sci. Appl. 2(7), 1–5 (2013).
[Crossref]

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[Crossref]

Johnson, S. G.

C. W. Hsu, B. Zhen, S.-L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Bloch surface eigenstates within the radiation continuum,” Light Sci. Appl. 2(7), 1–5 (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(7457), 188–191 (2013).
[Crossref] [PubMed]

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[Crossref]

Kanté, B.

T. Lepetit and B. Kanté, “Controlling multipolar radiation with symmetries for electromagnetic bound states in the continuum,” Phys. Rev. B Condens. Matter Mater. Phys. 90(24), 241103 (2014).
[Crossref]

Kazarinov, R. F.

R. F. Kazarinov and C. H. Henry, “Second-order distributed feedback lasers with mode selection provided by first-order radiation loss,” IEEE J. Quantum Electron. 21(2), 144–150 (1985).
[Crossref]

Kee, C. S.

S.-G. Lee, S. H. Kim, K. J. Kim, and C. S. Kee, “Polarization-independent electromagnetically induced transparency-like transmission in coupled guided-mode resonance structures,” Appl. Phys. Lett. 110(11), 111106 (2017).
[Crossref]

Kildishev, A. V.

S. I. Azzam, V. M. Shalaev, A. Boltasseva, and A. V. Kildishev, “Formation of bound states in the continuum in hybrid plasmonic-photonic systems,” Phys. Rev. Lett. 121(25), 253901 (2018).
[Crossref] [PubMed]

Kim, K. J.

S.-G. Lee, S. H. Kim, K. J. Kim, and C. S. Kee, “Polarization-independent electromagnetically induced transparency-like transmission in coupled guided-mode resonance structures,” Appl. Phys. Lett. 110(11), 111106 (2017).
[Crossref]

Kim, S. H.

S.-G. Lee, S. H. Kim, K. J. Kim, and C. S. Kee, “Polarization-independent electromagnetically induced transparency-like transmission in coupled guided-mode resonance structures,” Appl. Phys. Lett. 110(11), 111106 (2017).
[Crossref]

Kintaka, K.

Kivshar, Y.

K. Koshelev, S. Lepeshov, M. Liu, A. Bogdanov, and Y. Kivshar, “Asymmetric metasurfaces with high-Q resonances governed by bound states in the continuum,” Phys. Rev. Lett. 121(19), 193903 (2018).
[Crossref] [PubMed]

L. Carletti, K. Koshelev, C. De Angelis, and Y. Kivshar, “Giant nonlinear response at the nanoscale driven by bound states in the continuum,” Phys. Rev. Lett. 121(3), 033903 (2018).
[Crossref] [PubMed]

Ko, Y. H.

Koenderink, A. F.

H. M. Doeleman, F. Monticone, W. Hollander, A. Alù, and A. F. Koenderink, “Experimental observation of a polarization vortex at an optical bound state in the continuum,” Nat. Photonics 12(7), 397–401 (2018).
[Crossref]

Koshelev, K.

K. Koshelev, S. Lepeshov, M. Liu, A. Bogdanov, and Y. Kivshar, “Asymmetric metasurfaces with high-Q resonances governed by bound states in the continuum,” Phys. Rev. Lett. 121(19), 193903 (2018).
[Crossref] [PubMed]

L. Carletti, K. Koshelev, C. De Angelis, and Y. Kivshar, “Giant nonlinear response at the nanoscale driven by bound states in the continuum,” Phys. Rev. Lett. 121(3), 033903 (2018).
[Crossref] [PubMed]

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(7457), 188–191 (2013).
[Crossref] [PubMed]

Lee, K. J.

Lee, S.-G.

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

S.-G. Lee, S. H. Kim, K. J. Kim, and C. S. Kee, “Polarization-independent electromagnetically induced transparency-like transmission in coupled guided-mode resonance structures,” Appl. Phys. Lett. 110(11), 111106 (2017).
[Crossref]

Lepeshov, S.

K. Koshelev, S. Lepeshov, M. Liu, A. Bogdanov, and Y. Kivshar, “Asymmetric metasurfaces with high-Q resonances governed by bound states in the continuum,” Phys. Rev. Lett. 121(19), 193903 (2018).
[Crossref] [PubMed]

Lepetit, T.

T. Lepetit and B. Kanté, “Controlling multipolar radiation with symmetries for electromagnetic bound states in the continuum,” Phys. Rev. B Condens. Matter Mater. Phys. 90(24), 241103 (2014).
[Crossref]

Li, Z.

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(3), 037401 (2014).
[Crossref] [PubMed]

Liang, 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(3), 037401 (2014).
[Crossref] [PubMed]

Liu, M.

K. Koshelev, S. Lepeshov, M. Liu, A. Bogdanov, and Y. Kivshar, “Asymmetric metasurfaces with high-Q resonances governed by bound states in the continuum,” Phys. Rev. Lett. 121(19), 193903 (2018).
[Crossref] [PubMed]

Lu, L.

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(25), 257401 (2014).
[Crossref] [PubMed]

Ma, G.

Y.-X. Xiao, G. Ma, Z.-Q. Zhang, and C. T. Chan, “Topological subspace-induced bound state in the continuum,” Phys. Rev. Lett. 118(16), 166803 (2017).
[Crossref] [PubMed]

Magnusson, R.

Maksimov, D. N.

E. N. Bulgakov and D. N. Maksimov, “Avoided crossings and bound states in the continuum in low-contrast dielectric gratings,” Phys. Rev. A (Coll. Park) 98(5), 053840 (2018).
[Crossref]

E. N. Bulgakov, D. N. Maksimov, P. N. Semina, and S. A. Skorobogatov, “Propagating bound states in the continuum in dielectric gratings,” J. Opt. Soc. Am. B 35(6), 1218–1222 (2018).
[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(18), 183902 (2008).
[Crossref] [PubMed]

Minkov, M.

M. Minkov, I. A. D. Williamson, M. Xiao, and S. Fan, “Zero-index bound states in the continuum,” Phys. Rev. Lett. 121(26), 263901 (2018).
[Crossref] [PubMed]

Monticone, F.

H. M. Doeleman, F. Monticone, W. Hollander, A. Alù, and A. F. Koenderink, “Experimental observation of a polarization vortex at an optical bound state in the continuum,” Nat. Photonics 12(7), 397–401 (2018).
[Crossref]

F. Monticone and A. Alù, “Embedded photonic eigenvalues in 3D nanostructures,” Phys. Rev. Lett. 112(21), 213903 (2014).
[Crossref]

Niraula, M.

Noda, S.

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(3), 037401 (2014).
[Crossref] [PubMed]

Nolte, S.

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(18), 183901 (2011).
[Crossref] [PubMed]

Oskooi, A. F.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[Crossref]

Padilla, W. J.

Peleg, O.

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(18), 183901 (2011).
[Crossref] [PubMed]

Peng, C.

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(3), 037401 (2014).
[Crossref] [PubMed]

Plotnik, Y.

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(18), 183901 (2011).
[Crossref] [PubMed]

Rosenblatt, D.

D. Rosenblatt, A. Sharon, and A. A. Friesem, “Resonant grating waveguide structure,” IEEE J. Quantum Electron. 33(11), 2038–2059 (1997).
[Crossref]

Roundy, D.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[Crossref]

Sadreev, A. F.

E. N. Bulgakov and A. F. Sadreev, “Robust bound state in the continuum in a nonlinear microcavity embedded in a photonic crystal waveguide,” Opt. Lett. 39(17), 5212–5215 (2014).
[Crossref] [PubMed]

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(5), 053801 (2014).
[Crossref]

Segev, M.

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(18), 183901 (2011).
[Crossref] [PubMed]

Semina, P. N.

Shabanov, S. V.

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

Shadrivov, I. V.

Shalaev, V. M.

S. I. Azzam, V. M. Shalaev, A. Boltasseva, and A. V. Kildishev, “Formation of bound states in the continuum in hybrid plasmonic-photonic systems,” Phys. Rev. Lett. 121(25), 253901 (2018).
[Crossref] [PubMed]

Sharon, A.

D. Rosenblatt, A. Sharon, and A. A. Friesem, “Resonant grating waveguide structure,” IEEE J. Quantum Electron. 33(11), 2038–2059 (1997).
[Crossref]

Shokooh-Saremi, M.

Skorobogatov, S. A.

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(9), 16048 (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(25), 257401 (2014).
[Crossref] [PubMed]

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(7457), 188–191 (2013).
[Crossref] [PubMed]

C. W. Hsu, B. Zhen, S.-L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Bloch surface eigenstates within the radiation continuum,” Light Sci. Appl. 2(7), 1–5 (2013).
[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(9), 16048 (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(25), 257401 (2014).
[Crossref] [PubMed]

Szameit, A.

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(18), 183901 (2011).
[Crossref] [PubMed]

Ura, S.

Wang, S. S.

Williamson, I. A. D.

M. Minkov, I. A. D. Williamson, M. Xiao, and S. Fan, “Zero-index bound states in the continuum,” Phys. Rev. Lett. 121(26), 263901 (2018).
[Crossref] [PubMed]

Xiao, M.

M. Minkov, I. A. D. Williamson, M. Xiao, and S. Fan, “Zero-index bound states in the continuum,” Phys. Rev. Lett. 121(26), 263901 (2018).
[Crossref] [PubMed]

Xiao, Y.-X.

Y.-X. Xiao, G. Ma, Z.-Q. Zhang, and C. T. Chan, “Topological subspace-induced bound state in the continuum,” Phys. Rev. Lett. 118(16), 166803 (2017).
[Crossref] [PubMed]

Yamada, K.

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(3), 037401 (2014).
[Crossref] [PubMed]

Yoon, J. W.

Zhang, Z.-Q.

Y.-X. Xiao, G. Ma, Z.-Q. Zhang, and C. T. Chan, “Topological subspace-induced bound state in the continuum,” Phys. Rev. Lett. 118(16), 166803 (2017).
[Crossref] [PubMed]

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(9), 16048 (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(25), 257401 (2014).
[Crossref] [PubMed]

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(7457), 188–191 (2013).
[Crossref] [PubMed]

C. W. Hsu, B. Zhen, S.-L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Bloch surface eigenstates within the radiation continuum,” Light Sci. Appl. 2(7), 1–5 (2013).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

S.-G. Lee, S. H. Kim, K. J. Kim, and C. S. Kee, “Polarization-independent electromagnetically induced transparency-like transmission in coupled guided-mode resonance structures,” Appl. Phys. Lett. 110(11), 111106 (2017).
[Crossref]

Comput. Phys. Commun. (1)

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comput. Phys. Commun. 181(3), 687–702 (2010).
[Crossref]

IEEE J. Quantum Electron. (2)

R. F. Kazarinov and C. H. Henry, “Second-order distributed feedback lasers with mode selection provided by first-order radiation loss,” IEEE J. Quantum Electron. 21(2), 144–150 (1985).
[Crossref]

D. Rosenblatt, A. Sharon, and A. A. Friesem, “Resonant grating waveguide structure,” IEEE J. Quantum Electron. 33(11), 2038–2059 (1997).
[Crossref]

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

Light Sci. Appl. (1)

C. W. Hsu, B. Zhen, S.-L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Bloch surface eigenstates within the radiation continuum,” Light Sci. Appl. 2(7), 1–5 (2013).
[Crossref]

Nat. Photonics (1)

H. M. Doeleman, F. Monticone, W. Hollander, A. Alù, and A. F. Koenderink, “Experimental observation of a polarization vortex at an optical bound state in the continuum,” Nat. Photonics 12(7), 397–401 (2018).
[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(9), 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(7457), 188–191 (2013).
[Crossref] [PubMed]

Opt. Express (2)

Opt. Lett. (3)

Optica (2)

Phys. Rev. A (1)

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(5), 053801 (2014).
[Crossref]

Phys. Rev. A (Coll. Park) (1)

E. N. Bulgakov and D. N. Maksimov, “Avoided crossings and bound states in the continuum in low-contrast dielectric gratings,” Phys. Rev. A (Coll. Park) 98(5), 053840 (2018).
[Crossref]

Phys. Rev. B (1)

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

Phys. Rev. B Condens. Matter Mater. Phys. (1)

T. Lepetit and B. Kanté, “Controlling multipolar radiation with symmetries for electromagnetic bound states in the continuum,” Phys. Rev. B Condens. Matter Mater. Phys. 90(24), 241103 (2014).
[Crossref]

Phys. Rev. Lett. (10)

K. Koshelev, S. Lepeshov, M. Liu, A. Bogdanov, and Y. Kivshar, “Asymmetric metasurfaces with high-Q resonances governed by bound states in the continuum,” Phys. Rev. Lett. 121(19), 193903 (2018).
[Crossref] [PubMed]

F. Monticone and A. Alù, “Embedded photonic eigenvalues in 3D nanostructures,” Phys. Rev. Lett. 112(21), 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(3), 037401 (2014).
[Crossref] [PubMed]

M. Minkov, I. A. D. Williamson, M. Xiao, and S. Fan, “Zero-index bound states in the continuum,” Phys. Rev. Lett. 121(26), 263901 (2018).
[Crossref] [PubMed]

L. Carletti, K. Koshelev, C. De Angelis, and Y. Kivshar, “Giant nonlinear response at the nanoscale driven by bound states in the continuum,” Phys. Rev. Lett. 121(3), 033903 (2018).
[Crossref] [PubMed]

Y.-X. Xiao, G. Ma, Z.-Q. Zhang, and C. T. Chan, “Topological subspace-induced bound state in the continuum,” Phys. Rev. Lett. 118(16), 166803 (2017).
[Crossref] [PubMed]

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(18), 183901 (2011).
[Crossref] [PubMed]

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

S. I. Azzam, V. M. Shalaev, A. Boltasseva, and A. V. Kildishev, “Formation of bound states in the continuum in hybrid plasmonic-photonic systems,” Phys. Rev. Lett. 121(25), 253901 (2018).
[Crossref] [PubMed]

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(25), 257401 (2014).
[Crossref] [PubMed]

Other (6)

A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 1995).

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

K. Inoue and K. Ohtaka, Photonic Crystals: Physics, Fabrication and Applications (Springer-Verlag, 2004).

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University, 1995).

K. Koshelev, A. Bogdanov, and Y. Kivshar, “Meta-optics and bound states in the continuum,” arXiv:1810.08698.

X. Gao, B. Zhen, M. Soljačić, H. Chen, and C. W. Hsu, “Bound states in the continuum in low-contrast fiber Bragg gratings,” arXiv:1707.01247.

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Figures (5)

Fig. 1
Fig. 1 (a) Schematic of a 1D leaky-mode photonic lattice for studying bound-state transitions. TE-polarized leaky guided modes are described by complex frequency Ω = ΩRe + i ΩIm. (b) Conceptual illustration of the bound-state transitions. Here, kz is the wavevector along the z-direction and X = π / Λ. Before and after closing the gaps ΔTE0 and ΔTE1, symmetry-protected BIC0 and BIC1 in red circles appear at the upper and lower band edges, respectively. The BIC band edges are nonradiative and thus not leaky whereas the opposite edges are leaky and represent the spectral placement of guided-mode resonance peaks.
Fig. 2
Fig. 2 FDTD simulated dispersion relations near the second stop band originating from (a) TE0 and (b) TE1 mode. K = 2π / Λ is the magnitude of the grating vector. Insets with blue and red colors illustrate spatial electric field distributions (Ey) of the band edge modes at the y = 0 plane. Vertical dotted lines represent the mirror planes (z = 0), at the center of the high dielectric constant part, in the computational cells. As the index modulation increases, symmetry-protected BICs with asymmetric electric field distributions transit from the upper to lower band edges. In the FDTD simulations, we use the computational cell of size Λ × 8Λ and spatial resolution is set to Δx = Δz = Λ/64.
Fig. 3
Fig. 3 Calculated coupling coefficients when (a) Δε = 0.40 and (b) Δε = 1.20 as a function of ρ. Size of the band gaps when (c) ρ = 0.49 and (d) ρ = 0.46. As the index modulation increases, the size of the gaps increases, decreases, becomes zero, and grows again. Band gaps ΔTE0 and ΔTE1 close at different index modulations.
Fig. 4
Fig. 4 Dispersion relations of the 1D photonic lattice with infinite lateral extent when (a) ρ = 0.25, (b) ρ = 0.35, and (c) ρ = 0.45. Spatial electric field distributions shown in the insets indicate that symmetry properties of band edge modes are reversed before and after the band gap closure. Refractive indices are set as nh = 2.60 and nl = 1.40.
Fig. 5
Fig. 5 (a) Relation between fill factor ρ and index modulation Δϵ when the modal gaps ΔTE0 and ΔTE1 close. (b) Effective-index ratio as a function of dielectric-constant modulation.

Tables (1)

Tables Icon

Table 1 Calculated Q factors of leaky band edge modes

Equations (7)

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

( 2 x 2 + 2 z 2 ) E y (x,z)+ε k 0 2 E y (x,z)=0.
Ω( k z )= Ω 0 ( i h 1 ± k z 2 + ( h 2 +i h 1 ) 2 )/(K h 0 ),
h 0,m = Ω - ε 0 ( x ) φ m (x) φ m * ( x )dx,
h 1,m = i K 3 Ω 4 ε 1 2 8 d 0 d 0 G( x, x ' ) φ m ( x ' ) φ m * ( x )d x ' dx ,
h 2,m =  K Ω 2 ε 2 4 d 0 φ m (x) φ m * ( x )dx,
U f = | ×E(r) | 2 d 3 r ε(r) | E(r) | 2 d 3 r .
λ 2 = L h = L l or ρ= N l N l + N h

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