Abstract

In the framework of the temporal coupled mode theory we consider bound states embedded in the continuum (BSC) of photonic crystal waveguide as a capacity for light storage. A symmetry protected BSC occurs in two off-channel microresonators positioned symmetrically relative to the waveguide. We demonstrate that the symmetry protected BSC captures a fraction of a light pulse due to the Kerr effect as the pulse passes by the microresonators. However the amount of captured light is found to be strongly sensitive to the parameters of the gaussian light pulse such as basic frequency, duration and intensity. In contrast to the above case the BSC resulted from a full destructive interference of two eigenmodes of a single microresonator accumulates a fixed amount of light dependent on the material parameters of the microresonator but independent of the light pulse. The BSCs in the Fabry-Perot resonator show similar effects. We also show that the accumulated light can be released by a secondary pulse. These phenomena pave a way for all-optical storage and release of light.

© 2015 Optical Society of America

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References

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  34. E. N. Bulgakov, K. N. Pichugin, and A. F. Sadreev, “Symmetry breaking for transmission in a photonic waveguide coupled with two off-channel nonlinear defects,” Phys. Rev. B 83, 045109 (2011).
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    [Crossref]
  39. W. Suh, Z. Wang, and S. Fan, “Temporal coupled-mode theory and the presence of non-orthogonal modes in lossless multimode cavities,” IEEE J. Quantum Electron. 40(10), 1511–1518 (2004).
    [Crossref]
  40. E. N. Bulgakov and A. F. Sadreev, “All-optical diode based on dipole modes of Kerr microcavity in asymmetric L-shaped photonic crystal waveguide,” Opt. Lett. 39(7), 1787–1790 (2014).
    [Crossref] [PubMed]
  41. K. Busch, S. F. Mingaleev, A. Garcia-Martin, M. Schillinger, and D. Hermann, “The Wannier function approach to photonic crystal circuits,” J. Phys.: Cond. Mat. 15, R1233–R1256 (2003).
  42. K. N. Pichugin and A. F. Sadreev, “Frequency comb generation for wave transmission through the nonlinear dimer,” J. Phys.: Conf. Ser. 574012037 (2015).
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    [Crossref] [PubMed]
  44. A. E. Miroshnichenko, S. F. Mingaleev, S. Flach, and Yu. S. Kivshar, “Nonlinear Fano resonance and bistable wave transmission,” Phys. Rev. E 71, 036626 (2005).
    [Crossref]
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    [Crossref]

2015 (4)

R. Yang, W. Zhu, and J. Li, “Realization of trapped rainbow in 1D slab waveguide with surface dispersion engineering,” Opt. Express 23(5), 6326–6335 (2015).
[Crossref] [PubMed]

M. Song, H. Yu, C. Wang, N. Yao, M. Pu, J. Luo, Z. Zhang, and X. Luo, “Sharp Fano resonance induced by a single layer of nanorods with perturbed periodicity,” Opt. Express 23(3), 2895–2903 (2015).
[Crossref] [PubMed]

M. Zhang and X. Zhang, “Ultrasensitive optical absorption in graphene based on bound states in the continuum,” Sci. Rep. 5, 8266 (2015).
[Crossref] [PubMed]

K. N. Pichugin and A. F. Sadreev, “Frequency comb generation for wave transmission through the nonlinear dimer,” J. Phys.: Conf. Ser. 574012037 (2015).

2014 (5)

E. N. Bulgakov and A. F. Sadreev, “All-optical diode based on dipole modes of Kerr microcavity in asymmetric L-shaped photonic crystal waveguide,” Opt. Lett. 39(7), 1787–1790 (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]

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] [PubMed]

B. Zhen, C. W. Hsu, L. Lu, A. D. Stone, and M. Soljačić, “Topological nature of bound states in the radiation continuum,” Phys. Rev. Lett. 113, 257401 (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 (4)

G. Corrielli, G. DellaValle, A. Crespi, R. Osellame, and S. Longhi, “Observation of surface states with algebraic localization,” Phys. Rev. Lett. 111, 220403 (2013).
[Crossref] [PubMed]

S. Weimann, Y. Xu, R. Keil, A. E. Miroshnichenko, A. Tunnermann, S. Nolte, A. A. Sukhorukov, A. Szameit, and Yu. 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, S.-L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, “Bloch surface eigenstates within the radiation continuum,” Light: Sci. Appl. 2, 1–5 (2013).

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] [PubMed]

2012 (3)

M. I. Molina, A. E. Miroshnichenko, and Yu. S. Kivshar, “Surface bound states in the continuum,” Phys. Rev. Lett. 108, 070401 (2012).
[Crossref] [PubMed]

F. Morichetti, C. Ferrari, A. Canciamilla, and A. Melloni, “The first decade of coupled resonator optical waveguides: bringing slow light to applications,” Laser Photonics Rev. 6, 74–96 (2012).
[Crossref]

S. He, Y. He, and Y. Jin, “Revealing the truth about trapped rainbow storage of light in metamaterials,” Sci. Rep. 583, 1–9 (2012).

2011 (2)

E. N. Bulgakov, K. N. Pichugin, and A. F. Sadreev, “Symmetry breaking for transmission in a photonic waveguide coupled with two off-channel nonlinear defects,” Phys. Rev. B 83, 045109 (2011).
[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, 183901 (2011).
[Crossref] [PubMed]

2010 (3)

M. Notomi, “Manipulating light with strongly modulated photonic crystals,” Rep. Progr. Phys. 73, 096501 (2010).
[Crossref]

V. N. Smolyaninova, I. I. Smolyaninov, A. V. Kildishev, and V. M. Shalaev, “Experimental observation of the trapped rainbow,” Appl. Phys. Lett. 96, 211121 (2010).
[Crossref]

E. N. Bulgakov and A. F. Sadreev, “Bound states in photonic Fabry-Perot resonator with nonlinear off-channel defects,” Phys. Rev. B 81, 115128 (2010).
[Crossref]

2009 (4)

S. Longhi, “Optical analogue of coherent population trapping via a continuum in optical waveguide arrays,” J. Mod. Opt. 56, 729–737 (2009).
[Crossref]

F. Dreisow, A. Szameit, M. Heinrich, R. Keil, S. Nolte, A. Tünnermann, and S. Longhi, “Adiabatic transfer of light via a continuum in optical waveguides,” Opt. Lett. 34, 2405–2407 (2009).
[Crossref] [PubMed]

E. N. Bulgakov and A. F. Sadreev, “Resonance induced by a bound state in the continuum in a two-level nonlinear Fano-Anderson model,” Phys. Rev. B 80, 115308 (2009);
[Crossref]

M. Notomi, E. Kuramochi, and H. Taniyama, “Ultrahigh-Q nanocavity with 1D photonic gap,” Opt. Express 16, 11096–11102 (2009).

2008 (5)

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

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]

S. Longhi, “Transfer of light waves in optical waveguides via a continuum,” Phys. Rev. A 78, 013815 (2008).
[Crossref]

J. He, Y. Jin, Z. Hong, and S. He, “Slow light in a dielectric waveguide with negative-refractive-index photonic crystal cladding,” Opt. Express,  16, 11077–11082 (2008).
[Crossref] [PubMed]

T. Baba, “Slow light in photonics crystals,” Nat. Photonics,  2, 465–473 (2008).
[Crossref]

2007 (2)

T. F. Krauss, “Slow light in photonic crystal waveguides,” J. Phys. D 40, 2666–2670 (2007).
[Crossref]

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “Trapped rainbow storage of light in metamaterials,” Nature 450, 397–401 (2007).
[Crossref] [PubMed]

2005 (4)

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Real-space observation of ultraslow light in Photonic Crystal Waveguides,” Phys. Rev. Lett. 94, 073903 (2005).
[Crossref] [PubMed]

D. Englund, I. Fushman, and J. Vuckovic, “General recipe for designing photonic crystal cavities,” Opt. Express 13, 5961–5975 (2005).
[Crossref] [PubMed]

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

A. E. Miroshnichenko, S. F. Mingaleev, S. Flach, and Yu. S. Kivshar, “Nonlinear Fano resonance and bistable wave transmission,” Phys. Rev. E 71, 036626 (2005).
[Crossref]

2004 (1)

W. Suh, Z. Wang, and S. Fan, “Temporal coupled-mode theory and the presence of non-orthogonal modes in lossless multimode cavities,” IEEE J. Quantum Electron. 40(10), 1511–1518 (2004).
[Crossref]

2003 (5)

K. Busch, S. F. Mingaleev, A. Garcia-Martin, M. Schillinger, and D. Hermann, “The Wannier function approach to photonic crystal circuits,” J. Phys.: Cond. Mat. 15, R1233–R1256 (2003).

Z. Wang and S. Fan, “Compact all-pass filters in photonic crystals as the building block for high-capacity optical delay lines,” Phys. Rev. E 68, 066616 (2003).
[Crossref]

Sh. Fan, W. Suh, and J. D. Joannopoulos, “Temporal coupled-mode theory for the Fano resonance in optical resonators,” J. Opt. Soc. Am. A 20, 569–572 (2003).
[Crossref]

I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, “Guided modes in negative-refractive-index waveguides,” Phys. Rev. E 67, 057602 (2003).
[Crossref]

A. Melloni, F. Morichetti, and M. Martinelli, “Optical slow wave structures,” Opt. Photon. News 14, 44–48 (2003).
[Crossref]

1999 (1)

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. J. Khan, C. Manolatou, and H. A. Haus, “Theoretical analysis of channel drop tunneling processes,” Phys. Rev. B 59(24), 15882–15892 (1999).
[Crossref]

1985 (1)

H. Friedrich and D. Wintgen, “Interfering resonances and bound states in the continuum,” Phys. Rev. A 32, 3231–3242 (1985).
[Crossref] [PubMed]

Baba, T.

T. Baba, “Slow light in photonics crystals,” Nat. Photonics,  2, 465–473 (2008).
[Crossref]

Boardman, A. D.

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “Trapped rainbow storage of light in metamaterials,” Nature 450, 397–401 (2007).
[Crossref] [PubMed]

Bogaerts, W.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Real-space observation of ultraslow light in Photonic Crystal Waveguides,” Phys. Rev. Lett. 94, 073903 (2005).
[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, 183902 (2008).
[Crossref] [PubMed]

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, “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, “All-optical diode based on dipole modes of Kerr microcavity in asymmetric L-shaped photonic crystal waveguide,” Opt. Lett. 39(7), 1787–1790 (2014).
[Crossref] [PubMed]

E. N. Bulgakov, K. N. Pichugin, and A. F. Sadreev, “Symmetry breaking for transmission in a photonic waveguide coupled with two off-channel nonlinear defects,” Phys. Rev. B 83, 045109 (2011).
[Crossref]

E. N. Bulgakov and A. F. Sadreev, “Bound states in photonic Fabry-Perot resonator with nonlinear off-channel defects,” Phys. Rev. B 81, 115128 (2010).
[Crossref]

E. N. Bulgakov and A. F. Sadreev, “Resonance induced by a bound state in the continuum in a two-level nonlinear Fano-Anderson model,” Phys. Rev. B 80, 115308 (2009);
[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]

Busch, K.

K. Busch, S. F. Mingaleev, A. Garcia-Martin, M. Schillinger, and D. Hermann, “The Wannier function approach to photonic crystal circuits,” J. Phys.: Cond. Mat. 15, R1233–R1256 (2003).

Canciamilla, A.

F. Morichetti, C. Ferrari, A. Canciamilla, and A. Melloni, “The first decade of coupled resonator optical waveguides: bringing slow light to applications,” Laser Photonics Rev. 6, 74–96 (2012).
[Crossref]

Chua, S.-L.

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, 1–5 (2013).

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] [PubMed]

Corrielli, G.

G. Corrielli, G. DellaValle, A. Crespi, R. Osellame, and S. Longhi, “Observation of surface states with algebraic localization,” Phys. Rev. Lett. 111, 220403 (2013).
[Crossref] [PubMed]

Crespi, A.

G. Corrielli, G. DellaValle, A. Crespi, R. Osellame, and S. Longhi, “Observation of surface states with algebraic localization,” Phys. Rev. Lett. 111, 220403 (2013).
[Crossref] [PubMed]

DellaValle, G.

G. Corrielli, G. DellaValle, A. Crespi, R. Osellame, and S. Longhi, “Observation of surface states with algebraic localization,” Phys. Rev. Lett. 111, 220403 (2013).
[Crossref] [PubMed]

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

F. Dreisow, A. Szameit, M. Heinrich, R. Keil, S. Nolte, A. Tünnermann, and S. Longhi, “Adiabatic transfer of light via a continuum in optical waveguides,” Opt. Lett. 34, 2405–2407 (2009).
[Crossref] [PubMed]

Engelen, R. J. P.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Real-space observation of ultraslow light in Photonic Crystal Waveguides,” Phys. Rev. Lett. 94, 073903 (2005).
[Crossref] [PubMed]

Englund, D.

Fan, S.

W. Suh, Z. Wang, and S. Fan, “Temporal coupled-mode theory and the presence of non-orthogonal modes in lossless multimode cavities,” IEEE J. Quantum Electron. 40(10), 1511–1518 (2004).
[Crossref]

Z. Wang and S. Fan, “Compact all-pass filters in photonic crystals as the building block for high-capacity optical delay lines,” Phys. Rev. E 68, 066616 (2003).
[Crossref]

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. J. Khan, C. Manolatou, and H. A. Haus, “Theoretical analysis of channel drop tunneling processes,” Phys. Rev. B 59(24), 15882–15892 (1999).
[Crossref]

Fan, Sh.

Ferrari, C.

F. Morichetti, C. Ferrari, A. Canciamilla, and A. Melloni, “The first decade of coupled resonator optical waveguides: bringing slow light to applications,” Laser Photonics Rev. 6, 74–96 (2012).
[Crossref]

Flach, S.

A. E. Miroshnichenko, S. F. Mingaleev, S. Flach, and Yu. S. Kivshar, “Nonlinear Fano resonance and bistable wave transmission,” Phys. Rev. E 71, 036626 (2005).
[Crossref]

Friedrich, H.

H. Friedrich and D. Wintgen, “Interfering resonances and bound states in the continuum,” Phys. Rev. A 32, 3231–3242 (1985).
[Crossref] [PubMed]

Fushman, I.

Garcia-Martin, A.

K. Busch, S. F. Mingaleev, A. Garcia-Martin, M. Schillinger, and D. Hermann, “The Wannier function approach to photonic crystal circuits,” J. Phys.: Cond. Mat. 15, R1233–R1256 (2003).

Gersen, H.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Real-space observation of ultraslow light in Photonic Crystal Waveguides,” Phys. Rev. Lett. 94, 073903 (2005).
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He, J.

He, S.

S. He, Y. He, and Y. Jin, “Revealing the truth about trapped rainbow storage of light in metamaterials,” Sci. Rep. 583, 1–9 (2012).

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S. He, Y. He, and Y. Jin, “Revealing the truth about trapped rainbow storage of light in metamaterials,” Sci. Rep. 583, 1–9 (2012).

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F. Dreisow, A. Szameit, M. Heinrich, R. Keil, S. Nolte, A. Tünnermann, and S. Longhi, “Adiabatic transfer of light via a continuum in optical waveguides,” Opt. Lett. 34, 2405–2407 (2009).
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Hermann, D.

K. Busch, S. F. Mingaleev, A. Garcia-Martin, M. Schillinger, and D. Hermann, “The Wannier function approach to photonic crystal circuits,” J. Phys.: Cond. Mat. 15, R1233–R1256 (2003).

Hess, O.

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “Trapped rainbow storage of light in metamaterials,” Nature 450, 397–401 (2007).
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Hong, Z.

Hsu, C. W.

B. Zhen, C. W. Hsu, L. Lu, A. D. Stone, and M. Soljačić, “Topological nature of bound states in the radiation continuum,” Phys. Rev. Lett. 113, 257401 (2014).
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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).
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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, 1–5 (2013).

Jin, Y.

S. He, Y. He, and Y. Jin, “Revealing the truth about trapped rainbow storage of light in metamaterials,” Sci. Rep. 583, 1–9 (2012).

J. He, Y. Jin, Z. Hong, and S. He, “Slow light in a dielectric waveguide with negative-refractive-index photonic crystal cladding,” Opt. Express,  16, 11077–11082 (2008).
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J. Joannopoulos, R. D. Meade, and J. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University Press, 1995).

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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, 1–5 (2013).

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).
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Sh. Fan, W. Suh, and J. D. Joannopoulos, “Temporal coupled-mode theory for the Fano resonance in optical resonators,” J. Opt. Soc. Am. A 20, 569–572 (2003).
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S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. J. Khan, C. Manolatou, and H. A. Haus, “Theoretical analysis of channel drop tunneling processes,” Phys. Rev. B 59(24), 15882–15892 (1999).
[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).
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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, 1–5 (2013).

Karle, T. J.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Real-space observation of ultraslow light in Photonic Crystal Waveguides,” Phys. Rev. Lett. 94, 073903 (2005).
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S. Weimann, Y. Xu, R. Keil, A. E. Miroshnichenko, A. Tunnermann, S. Nolte, A. A. Sukhorukov, A. Szameit, and Yu. S. Kivshar, “Compact surface Fano states embedded in the continuum of waveguide arrays,” Phys. Rev. Lett. 111, 240403 (2013).
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F. Dreisow, A. Szameit, M. Heinrich, R. Keil, S. Nolte, A. Tünnermann, and S. Longhi, “Adiabatic transfer of light via a continuum in optical waveguides,” Opt. Lett. 34, 2405–2407 (2009).
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S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. J. Khan, C. Manolatou, and H. A. Haus, “Theoretical analysis of channel drop tunneling processes,” Phys. Rev. B 59(24), 15882–15892 (1999).
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Kildishev, A. V.

V. N. Smolyaninova, I. I. Smolyaninov, A. V. Kildishev, and V. M. Shalaev, “Experimental observation of the trapped rainbow,” Appl. Phys. Lett. 96, 211121 (2010).
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I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, “Guided modes in negative-refractive-index waveguides,” Phys. Rev. E 67, 057602 (2003).
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Kivshar, Yu. S.

S. Weimann, Y. Xu, R. Keil, A. E. Miroshnichenko, A. Tunnermann, S. Nolte, A. A. Sukhorukov, A. Szameit, and Yu. S. Kivshar, “Compact surface Fano states embedded in the continuum of waveguide arrays,” Phys. Rev. Lett. 111, 240403 (2013).
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M. I. Molina, A. E. Miroshnichenko, and Yu. S. Kivshar, “Surface bound states in the continuum,” Phys. Rev. Lett. 108, 070401 (2012).
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A. E. Miroshnichenko, S. F. Mingaleev, S. Flach, and Yu. S. Kivshar, “Nonlinear Fano resonance and bistable wave transmission,” Phys. Rev. E 71, 036626 (2005).
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Korterik, J. P.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Real-space observation of ultraslow light in Photonic Crystal Waveguides,” Phys. Rev. Lett. 94, 073903 (2005).
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H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Real-space observation of ultraslow light in Photonic Crystal Waveguides,” Phys. Rev. Lett. 94, 073903 (2005).
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Kuipers, L.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Real-space observation of ultraslow light in Photonic Crystal Waveguides,” Phys. Rev. Lett. 94, 073903 (2005).
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M. Notomi, E. Kuramochi, and H. Taniyama, “Ultrahigh-Q nanocavity with 1D photonic gap,” Opt. Express 16, 11096–11102 (2009).

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).
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Li, J.

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, 037401 (2014).
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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).
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G. Corrielli, G. DellaValle, A. Crespi, R. Osellame, and S. Longhi, “Observation of surface states with algebraic localization,” Phys. Rev. Lett. 111, 220403 (2013).
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F. Dreisow, A. Szameit, M. Heinrich, R. Keil, S. Nolte, A. Tünnermann, and S. Longhi, “Adiabatic transfer of light via a continuum in optical waveguides,” Opt. Lett. 34, 2405–2407 (2009).
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S. Longhi, “Transfer of light waves in optical waveguides via a continuum,” Phys. Rev. A 78, 013815 (2008).
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B. Zhen, C. W. Hsu, L. Lu, A. D. Stone, and M. Soljačić, “Topological nature of bound states in the radiation continuum,” Phys. Rev. Lett. 113, 257401 (2014).
[Crossref]

Luo, J.

Luo, X.

Manolatou, C.

S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. J. Khan, C. Manolatou, and H. A. Haus, “Theoretical analysis of channel drop tunneling processes,” Phys. Rev. B 59(24), 15882–15892 (1999).
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A. Melloni, F. Morichetti, and M. Martinelli, “Optical slow wave structures,” Opt. Photon. News 14, 44–48 (2003).
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J. Joannopoulos, R. D. Meade, and J. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University Press, 1995).

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A. Melloni, F. Morichetti, and M. Martinelli, “Optical slow wave structures,” Opt. Photon. News 14, 44–48 (2003).
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A. E. Miroshnichenko, S. F. Mingaleev, S. Flach, and Yu. S. Kivshar, “Nonlinear Fano resonance and bistable wave transmission,” Phys. Rev. E 71, 036626 (2005).
[Crossref]

K. Busch, S. F. Mingaleev, A. Garcia-Martin, M. Schillinger, and D. Hermann, “The Wannier function approach to photonic crystal circuits,” J. Phys.: Cond. Mat. 15, R1233–R1256 (2003).

Miroshnichenko, A. E.

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

M. I. Molina, A. E. Miroshnichenko, and Yu. S. Kivshar, “Surface bound states in the continuum,” Phys. Rev. Lett. 108, 070401 (2012).
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A. E. Miroshnichenko, S. F. Mingaleev, S. Flach, and Yu. S. Kivshar, “Nonlinear Fano resonance and bistable wave transmission,” Phys. Rev. E 71, 036626 (2005).
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M. I. Molina, A. E. Miroshnichenko, and Yu. S. Kivshar, “Surface bound states in the continuum,” Phys. Rev. Lett. 108, 070401 (2012).
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F. Morichetti, C. Ferrari, A. Canciamilla, and A. Melloni, “The first decade of coupled resonator optical waveguides: bringing slow light to applications,” Laser Photonics Rev. 6, 74–96 (2012).
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A. Melloni, F. Morichetti, and M. Martinelli, “Optical slow wave structures,” Opt. Photon. News 14, 44–48 (2003).
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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, 037401 (2014).
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Nolte, S.

S. Weimann, Y. Xu, R. Keil, A. E. Miroshnichenko, A. Tunnermann, S. Nolte, A. A. Sukhorukov, A. Szameit, and Yu. S. Kivshar, “Compact surface Fano states embedded in the continuum of waveguide arrays,” Phys. Rev. Lett. 111, 240403 (2013).
[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, 183901 (2011).
[Crossref] [PubMed]

F. Dreisow, A. Szameit, M. Heinrich, R. Keil, S. Nolte, A. Tünnermann, and S. Longhi, “Adiabatic transfer of light via a continuum in optical waveguides,” Opt. Lett. 34, 2405–2407 (2009).
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M. Notomi, E. Kuramochi, and H. Taniyama, “Ultrahigh-Q nanocavity with 1D photonic gap,” Opt. Express 16, 11096–11102 (2009).

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G. Corrielli, G. DellaValle, A. Crespi, R. Osellame, and S. Longhi, “Observation of surface states with algebraic localization,” Phys. Rev. Lett. 111, 220403 (2013).
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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, 183901 (2011).
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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, 037401 (2014).
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K. N. Pichugin and A. F. Sadreev, “Frequency comb generation for wave transmission through the nonlinear dimer,” J. Phys.: Conf. Ser. 574012037 (2015).

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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, 183901 (2011).
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Sadreev, A. F.

K. N. Pichugin and A. F. Sadreev, “Frequency comb generation for wave transmission through the nonlinear dimer,” J. Phys.: Conf. Ser. 574012037 (2015).

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).
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E. N. Bulgakov and A. F. Sadreev, “All-optical diode based on dipole modes of Kerr microcavity in asymmetric L-shaped photonic crystal waveguide,” Opt. Lett. 39(7), 1787–1790 (2014).
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E. N. Bulgakov and A. F. Sadreev, “Bound states in photonic Fabry-Perot resonator with nonlinear off-channel defects,” Phys. Rev. B 81, 115128 (2010).
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E. N. Bulgakov and A. F. Sadreev, “Resonance induced by a bound state in the continuum in a two-level nonlinear Fano-Anderson model,” Phys. Rev. B 80, 115308 (2009);
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E. N. Bulgakov and A. F. Sadreev, “Bound states in the continuum in photonic waveguides inspired by defects,” Phys. Rev. B 78, 075105 (2008).
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K. Busch, S. F. Mingaleev, A. Garcia-Martin, M. Schillinger, and D. Hermann, “The Wannier function approach to photonic crystal circuits,” J. Phys.: Cond. Mat. 15, R1233–R1256 (2003).

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, 183901 (2011).
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D. C. Marinica, A. G. Borisov, and S. V. Shabanov, “Bound States in the Continuum in Photonics,” Phys. Rev. Lett. 100, 183902 (2008).
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I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, “Guided modes in negative-refractive-index waveguides,” Phys. Rev. E 67, 057602 (2003).
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Shalaev, V. M.

V. N. Smolyaninova, I. I. Smolyaninov, A. V. Kildishev, and V. M. Shalaev, “Experimental observation of the trapped rainbow,” Appl. Phys. Lett. 96, 211121 (2010).
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S. P. Shipman and S. Venakides, “Resonant transmission near nonrobust periodic slab modes,” Phys. Rev. E 71, 026611 (2005).
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V. N. Smolyaninova, I. I. Smolyaninov, A. V. Kildishev, and V. M. Shalaev, “Experimental observation of the trapped rainbow,” Appl. Phys. Lett. 96, 211121 (2010).
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V. N. Smolyaninova, I. I. Smolyaninov, A. V. Kildishev, and V. M. Shalaev, “Experimental observation of the trapped rainbow,” Appl. Phys. Lett. 96, 211121 (2010).
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B. Zhen, C. W. Hsu, L. Lu, A. D. Stone, and M. Soljačić, “Topological nature of bound states in the radiation continuum,” Phys. Rev. Lett. 113, 257401 (2014).
[Crossref]

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, 1–5 (2013).

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).
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Song, M.

Stone, A. D.

B. Zhen, C. W. Hsu, L. Lu, A. D. Stone, and M. Soljačić, “Topological nature of bound states in the radiation continuum,” Phys. Rev. Lett. 113, 257401 (2014).
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W. Suh, Z. Wang, and S. Fan, “Temporal coupled-mode theory and the presence of non-orthogonal modes in lossless multimode cavities,” IEEE J. Quantum Electron. 40(10), 1511–1518 (2004).
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Sh. Fan, W. Suh, and J. D. Joannopoulos, “Temporal coupled-mode theory for the Fano resonance in optical resonators,” J. Opt. Soc. Am. A 20, 569–572 (2003).
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Sukhorukov, A. A.

S. Weimann, Y. Xu, R. Keil, A. E. Miroshnichenko, A. Tunnermann, S. Nolte, A. A. Sukhorukov, A. Szameit, and Yu. S. Kivshar, “Compact surface Fano states embedded in the continuum of waveguide arrays,” Phys. Rev. Lett. 111, 240403 (2013).
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I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, “Guided modes in negative-refractive-index waveguides,” Phys. Rev. E 67, 057602 (2003).
[Crossref]

Szameit, A.

S. Weimann, Y. Xu, R. Keil, A. E. Miroshnichenko, A. Tunnermann, S. Nolte, A. A. Sukhorukov, A. Szameit, and Yu. S. Kivshar, “Compact surface Fano states embedded in the continuum of waveguide arrays,” Phys. Rev. Lett. 111, 240403 (2013).
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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, 183901 (2011).
[Crossref] [PubMed]

F. Dreisow, A. Szameit, M. Heinrich, R. Keil, S. Nolte, A. Tünnermann, and S. Longhi, “Adiabatic transfer of light via a continuum in optical waveguides,” Opt. Lett. 34, 2405–2407 (2009).
[Crossref] [PubMed]

Taniyama, H.

M. Notomi, E. Kuramochi, and H. Taniyama, “Ultrahigh-Q nanocavity with 1D photonic gap,” Opt. Express 16, 11096–11102 (2009).

Tsakmakidis, K. L.

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “Trapped rainbow storage of light in metamaterials,” Nature 450, 397–401 (2007).
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Tunnermann, A.

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

van Hulst, N. F.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Real-space observation of ultraslow light in Photonic Crystal Waveguides,” Phys. Rev. Lett. 94, 073903 (2005).
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Venakides, S.

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

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S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. J. Khan, C. Manolatou, and H. A. Haus, “Theoretical analysis of channel drop tunneling processes,” Phys. Rev. B 59(24), 15882–15892 (1999).
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Wang, C.

Wang, Z.

W. Suh, Z. Wang, and S. Fan, “Temporal coupled-mode theory and the presence of non-orthogonal modes in lossless multimode cavities,” IEEE J. Quantum Electron. 40(10), 1511–1518 (2004).
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Z. Wang and S. Fan, “Compact all-pass filters in photonic crystals as the building block for high-capacity optical delay lines,” Phys. Rev. E 68, 066616 (2003).
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S. Weimann, Y. Xu, R. Keil, A. E. Miroshnichenko, A. Tunnermann, S. Nolte, A. A. Sukhorukov, A. Szameit, and Yu. S. Kivshar, “Compact surface Fano states embedded in the continuum of waveguide arrays,” Phys. Rev. Lett. 111, 240403 (2013).
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J. Joannopoulos, R. D. Meade, and J. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University Press, 1995).

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Yang, R.

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] [PubMed]

Yao, N.

Yu, H.

Zhang, M.

M. Zhang and X. Zhang, “Ultrasensitive optical absorption in graphene based on bound states in the continuum,” Sci. Rep. 5, 8266 (2015).
[Crossref] [PubMed]

Zhang, X.

M. Zhang and X. Zhang, “Ultrasensitive optical absorption in graphene based on bound states in the continuum,” Sci. Rep. 5, 8266 (2015).
[Crossref] [PubMed]

Zhang, Z.

Zhen, B.

B. Zhen, C. W. Hsu, L. Lu, A. D. Stone, and M. Soljačić, “Topological nature of bound states in the radiation 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).
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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, 1–5 (2013).

Zhu, W.

Appl. Phys. Lett. (1)

V. N. Smolyaninova, I. I. Smolyaninov, A. V. Kildishev, and V. M. Shalaev, “Experimental observation of the trapped rainbow,” Appl. Phys. Lett. 96, 211121 (2010).
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IEEE J. Quantum Electron. (1)

W. Suh, Z. Wang, and S. Fan, “Temporal coupled-mode theory and the presence of non-orthogonal modes in lossless multimode cavities,” IEEE J. Quantum Electron. 40(10), 1511–1518 (2004).
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J. Mod. Opt. (1)

S. Longhi, “Optical analogue of coherent population trapping via a continuum in optical waveguide arrays,” J. Mod. Opt. 56, 729–737 (2009).
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J. Opt. Soc. Am. A (1)

J. Phys. D (1)

T. F. Krauss, “Slow light in photonic crystal waveguides,” J. Phys. D 40, 2666–2670 (2007).
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J. Phys.: Cond. Mat. (1)

K. Busch, S. F. Mingaleev, A. Garcia-Martin, M. Schillinger, and D. Hermann, “The Wannier function approach to photonic crystal circuits,” J. Phys.: Cond. Mat. 15, R1233–R1256 (2003).

J. Phys.: Conf. Ser. (1)

K. N. Pichugin and A. F. Sadreev, “Frequency comb generation for wave transmission through the nonlinear dimer,” J. Phys.: Conf. Ser. 574012037 (2015).

Laser Photonics Rev. (1)

F. Morichetti, C. Ferrari, A. Canciamilla, and A. Melloni, “The first decade of coupled resonator optical waveguides: bringing slow light to applications,” Laser Photonics Rev. 6, 74–96 (2012).
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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, 1–5 (2013).

Nat. Photonics (1)

T. Baba, “Slow light in photonics crystals,” Nat. Photonics,  2, 465–473 (2008).
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Nature (2)

K. L. Tsakmakidis, A. D. Boardman, and O. Hess, “Trapped rainbow storage of light in metamaterials,” Nature 450, 397–401 (2007).
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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).
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Opt. Express (5)

Opt. Lett. (3)

Opt. Photon. News (1)

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Phys. Rev. A (3)

S. Longhi, “Transfer of light waves in optical waveguides via a continuum,” Phys. Rev. A 78, 013815 (2008).
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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).
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H. Friedrich and D. Wintgen, “Interfering resonances and bound states in the continuum,” Phys. Rev. A 32, 3231–3242 (1985).
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Phys. Rev. B (5)

E. N. Bulgakov and A. F. Sadreev, “Resonance induced by a bound state in the continuum in a two-level nonlinear Fano-Anderson model,” Phys. Rev. B 80, 115308 (2009);
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E. N. Bulgakov and A. F. Sadreev, “Bound states in photonic Fabry-Perot resonator with nonlinear off-channel defects,” Phys. Rev. B 81, 115128 (2010).
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E. N. Bulgakov, K. N. Pichugin, and A. F. Sadreev, “Symmetry breaking for transmission in a photonic waveguide coupled with two off-channel nonlinear defects,” Phys. Rev. B 83, 045109 (2011).
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E. N. Bulgakov and A. F. Sadreev, “Bound states in the continuum in photonic waveguides inspired by defects,” Phys. Rev. B 78, 075105 (2008).
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S. Fan, P. R. Villeneuve, J. D. Joannopoulos, M. J. Khan, C. Manolatou, and H. A. Haus, “Theoretical analysis of channel drop tunneling processes,” Phys. Rev. B 59(24), 15882–15892 (1999).
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Phys. Rev. E (4)

S. P. Shipman and S. Venakides, “Resonant transmission near nonrobust periodic slab modes,” Phys. Rev. E 71, 026611 (2005).
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I. V. Shadrivov, A. A. Sukhorukov, and Y. S. Kivshar, “Guided modes in negative-refractive-index waveguides,” Phys. Rev. E 67, 057602 (2003).
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A. E. Miroshnichenko, S. F. Mingaleev, S. Flach, and Yu. S. Kivshar, “Nonlinear Fano resonance and bistable wave transmission,” Phys. Rev. E 71, 036626 (2005).
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Z. Wang and S. Fan, “Compact all-pass filters in photonic crystals as the building block for high-capacity optical delay lines,” Phys. Rev. E 68, 066616 (2003).
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Phys. Rev. Lett. (8)

M. I. Molina, A. E. Miroshnichenko, and Yu. S. Kivshar, “Surface bound states in the continuum,” Phys. Rev. Lett. 108, 070401 (2012).
[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, 037401 (2014).
[Crossref] [PubMed]

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

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, “Real-space observation of ultraslow light in Photonic Crystal Waveguides,” Phys. Rev. Lett. 94, 073903 (2005).
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D. C. Marinica, A. G. Borisov, and S. V. Shabanov, “Bound States in the Continuum in Photonics,” Phys. Rev. Lett. 100, 183902 (2008).
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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, 183901 (2011).
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G. Corrielli, G. DellaValle, A. Crespi, R. Osellame, and S. Longhi, “Observation of surface states with algebraic localization,” Phys. Rev. Lett. 111, 220403 (2013).
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S. Weimann, Y. Xu, R. Keil, A. E. Miroshnichenko, A. Tunnermann, S. Nolte, A. A. Sukhorukov, A. Szameit, and Yu. S. Kivshar, “Compact surface Fano states embedded in the continuum of waveguide arrays,” Phys. Rev. Lett. 111, 240403 (2013).
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Rep. Progr. Phys. (1)

M. Notomi, “Manipulating light with strongly modulated photonic crystals,” Rep. Progr. Phys. 73, 096501 (2010).
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Sci. Rep. (2)

S. He, Y. He, and Y. Jin, “Revealing the truth about trapped rainbow storage of light in metamaterials,” Sci. Rep. 583, 1–9 (2012).

M. Zhang and X. Zhang, “Ultrasensitive optical absorption in graphene based on bound states in the continuum,” Sci. Rep. 5, 8266 (2015).
[Crossref] [PubMed]

Other (1)

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

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Figures (5)

Fig. 1
Fig. 1 (a). The single row of the rods is removed from the PhC to form a directional photonic waveguide which supports a band of guided even TM mode. Two defect rods shown in gray with the Kerr effect are inserted symmetrically relative to the waveguide to form identical off-channel optical microresonators coupled with the waveguide. (b). Equivalent CMT presentation for PhC layout. (c). Electric field profile in the symmetry protected BSC.
Fig. 2
Fig. 2 (a). Amplitudes of eigenmodes of resonators under application of a gaussian pulse in the PhC waveguide shown in Fig. 1(a). Green dash line shows the profile of the injected pulse with parameters: E 0 = 0.575, ν = 10−4, σ = 10000, dash-dot line shows the symmetric mode amplitude |as | and red solid line shows the amplitude of the antisymmetric |aa | BSC mode. The amplitude of trapped light aa (∞) in the symmetry protected BSC vs: (b). Amplitude E 0, (c) The detuning parameter ν, and (d) The duration of impulse σ for E 0 = 0.575 of the gaussian pulse Eq. (6). (e). The release of light from BSC after application of a secondary gaussian pulse with σ = 10797, ν = 0.0001, E 0 = 0.7741. The parameters of the resonators are the following: with the parameters ω 0 = 0.352, γ = 0.01, u = 0.001, λ = 0.0001.
Fig. 3
Fig. 3 (a). The same PhC structure as shown in Fig 1(a) however with single in-channel microresonator. Four linear defect rods of the same radius with dielectric constant ε are shown by green circles. (b). The eigenfrequencies of two eigenmodes (monopole and quadrupole-diag) shown as dependent on the dielectric constant of the central defect rod. (c). Light trapping by the BSC for the first pulse with amplitude E 0 = 0.2 and duration 2 × 104. The release of light by the secondary pulse with amplitude E 0 = 0.006 and duration 2 × 104. Inset shows details of excitation dynamics of eigenmode amplitudes after application of the first pulse. The parameters substituted into the CMT equations (9) are taken from Ref. [25]: ω 1 = 0.36, ω 2 = 0.365, γ 1 = 3 · 10−5, γ 2 = 1.3 · 10−4, u = 1.77 · 10−4, λ 11 = 10−4.
Fig. 4
Fig. 4 (a). Layout of 2D PhC which forms the Fabry-Perot resonator. Two defect rods shown by gray with the Kerr effect are inserted near by PhC waveguide. (b). Equivalent CMT presentation for PhC layout with equivalent parameters: γ = 0.01, λ = 0.0001, ω 0 = 0.352, u = 0.
Fig. 5
Fig. 5 Time evolution of mode amplitudes |A 1| (blue solid line) and |A 2| (red dash line) after the injection of a first gaussian pulse shown by green dash-dot line with σ = 10000, E 0 = 0.3522, ν = 10−5 (a) and a secondary pulse with σ = 4705, E 0 = 0.545, ν = 10−5. Black dash lines show the BSC amplitude given by Eq. (15).

Equations (16)

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A s , a = ( A 1 ± A 2 ) / 2 , ω s , a = ω 0 ± u ,
i A ˙ s = ( ω s + 2 i γ ) A s i γ E i n e i ω t , i A ˙ a = ω a A a ,
i A ˙ 1 = ( ω 0 + λ | A 1 | 2 ) A 1 + i γ ( A 1 + A 2 ) + u A 2 i γ E i n ( t ) e i ω t , i A ˙ 2 = ( ω 0 + λ | A 2 | 2 ) A 2 + i γ ( A 1 + A 2 ) + u A 1 i γ E i n ( t ) e i ω t ,
λ = ω 0 n 0 c 2 n 2 2 8 π a 2 E m 4 ( x , y ) d x d y , N m = ε ( x , y ) E m 2 ( x , y ) d x d y = a 2 c n 2
i a ˙ s = ( ν + λ [ | a s | 2 + 2 | a a | 2 ] ) a s + λ a a 2 a s * + 2 i γ a s i γ E i n ( t ) , i a ˙ a = ( ν + λ [ | a a | 2 + 2 | a s | 2 ] ) a a + λ a s 2 a a * .
E i n ( t ) = E 0 exp ( t 2 / 2 σ 2 ) .
i A ˙ 1 = ( ω 1 + λ 11 | A 1 | 2 + i γ 1 ) A 1 + ( u + λ 12 ( A 1 A 2 * + A 1 * A 2 ) + i γ 1 γ 2 ) A 2 i γ 1 E i n ( t ) , i A ˙ 2 = ( ω 2 + λ 22 | A 1 | 2 + i γ 2 ) A 2 + ( u + λ 12 ( A 1 A 2 * + A 1 * A 2 ) + i γ 1 γ 2 ) A 1 i γ 2 E i n ( t ) ,
λ m n = ω 0 n 0 c 2 n 2 2 8 π a 2 E m 2 ( x , y ) E n 2 ( x , y ) d x d y
( ω 1 + λ 11 | A 1 | 2 ω + i γ 1 u + λ 12 ( A 1 A 2 * + A 1 * A 2 ) + i γ 1 γ 2 u + λ 12 ( A 1 A 2 * + A 1 * A 2 ) + i γ 1 γ 2 ω 2 + λ 22 | A 2 | 2 ω + i γ 2 ) ( A 1 A 2 ) = i ( γ 1 γ 2 ) E 0 .
ω 2 ω 1 = u ( γ 2 γ 1 ) γ 1 γ 2 , ω B S C = ω 1 + u γ 2 γ 1 ,
λ 11 | A 1 c | 2 = ω 2 ω 1 + u ( γ 2 γ 1 ) γ 1 γ 2 , | A 2 c | 2 = γ 1 γ 2 | A 1 c | 2
I 2 c = | A 2 c | 2 = γ 1 γ 2 I 1 c , I 1 , c I 2 c , ω B S C ω 2 u γ 1 γ 2 .
i A ˙ 1 = ( ω 0 + λ | A 1 | 2 + i γ ) A 1 + i γ A 2 e i θ i γ E i n ( t ) e i ω t , i A ˙ 2 = ( ω 0 + λ | A 2 | 2 + i γ ) A 2 + i γ A 1 e i θ i γ E i n ( t ) e i ω t + i θ ,
i A ˙ 1 = ( ω 0 + λ | A 1 | 2 + i γ ) A 1 + i γ A 2 ( t τ ) i γ E i n ( t ) e i ω t , i A ˙ 2 = ( ω 0 + λ | A 2 | 2 + i γ ) A 2 + i γ A 1 ( t τ ) i γ E i n ( t τ ) e i ω ( t θ ) .
( ω 0 + λ | A 1 | 2 ω + i γ i γ e i τ ω i γ e i τ ω ω 0 + λ | A 2 | 2 ω + i γ )
τ ω = π n , | A 1 c | 2 = | A 2 c | 2 = 1 λ ( π n τ ω 0 ) ,

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