Abstract

One-dimensional (1D) infinite periodic systems exhibit vanishing group velocity and diverging density of states (DOS) near band edges. However, in practice, systems have finite sizes, and inevitably, this prompts the question of whether helpful physical quantities related to infinite systems, such as the group velocity that is deduced from the band structure, remain relevant in finite systems. For instance, one may wonder how the DOS divergence can be approached with finite systems. Intuitively, one may expect that the implementation of larger and larger DOS, or equivalently smaller and smaller group velocities, would critically increase the system length. Based on general 1D-wave physics arguments, we demonstrate that the large slow-light DOS enhancement of periodic systems can be observed with very short systems, whose lengths scale with the logarithm of the inverse of the group velocities. The understanding obtained for 1D systems leads us to propose a novel sort of microstructure to enhance light-matter interactions, a sort of photonic speed bump that abruptly changes the speed of light by a few orders of magnitude without any reflection. We show that the DOS enhancements of speed bumps result from a classical electromagnetic resonance characterized by a single resonance mode and also that the nature and properties of the resonance are markedly different from those of classical defect-mode photonic-crystal cavities.

© 2017 Optical Society of America

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References

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2016 (3)

W. Xue, Y. Yu, L. Ottaviano, Y. Chen, E. Semenova, K. Yvind, and J. Mork, “Threshold characteristics of slow-light photonic crystal lasers,” Phys. Rev. Lett. 116, 063901 (2016).
[Crossref]

A. Krasnok, S. Glybovski, M. Petrov, S. Makarov, R. Savelev, P. Belov, C. Simovski, and Y. Kivshar, “Demonstration of the enhanced Purcell factor in all-dielectric structures,” Appl. Phys. Lett. 108, 211105 (2016).
[Crossref]

R. Faggiani, A. Baron, X. Zang, L. Lalouat, S. A. Schulz, B. O’Regan, K. Vynck, B. Cluzel, F. de Fornel, T. F. Krauss, and P. Lalanne, “Lower bound for the spatial extent of localized modes in photonic-crystal waveguides with small random imperfections,” Sci. Rep. 6, 27037 (2016).
[Crossref]

2015 (4)

K. Kondo, N. Ishikura, T. Tamura, and T. Baba, “Temporal pulse compression by dynamic slow-light tuning in photonic-crystal waveguides,” Phys. Rev. A 91, 023831 (2015).
[Crossref]

I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kiršanskė, T. Pregnolato, H. El-Ella, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Deterministic photon-emitter coupling in chiral photonic circuits,” Nat. Nanotechnol. 10, 775–778 (2015).
[Crossref]

A. Goban, C.-L. Hung, J. D. Hood, S.-P. Yu, J. A. Muniz, O. Painter, and H. J. Kimble, “Superradiance for atoms trapped along a photonic crystal waveguide,” Phys. Rev. Lett. 115, 063601 (2015).
[Crossref]

P. Lodahl, S. Mahmoodian, and S. Stobbe, “Interfacing single photons and single quantum dots with photonic nanostructures,” Rev. Mod. Phys. 87, 347–400 (2015).
[Crossref]

2014 (6)

J. Mork, Y. Chen, and M. Heuck, “Photonic crystal Fano laser: terahertz modulation and ultrashort pulse generation,” Phys. Rev. Lett. 113, 163901 (2014).
[Crossref]

A. Goban, C.-L. Hung, S.-P. Yu, J. D. Hood, J. A. Muniz, J. H. Lee, M. J. Martin, A. C. McClung, K. S. Choi, D. E. Chang, O. Painter, and H. J. Kimble, “Atom-light interactions in photonic crystals,” Nat. Commun. 5, 3808 (2014).
[Crossref]

E. Yeganegi, A. Lagendijk, A. P. Mosk, and W. L. Vos, “Local density of optical states in the band gap of a finite one-dimensional photonic crystal,” Phys. Rev. B 89, 045123 (2014).
[Crossref]

D. K. Gramotnev and S. I. Bozhevolnyi, “Nanofocusing of electromagnetic radiation,” Nat. Photonics 8, 13–22 (2014).
[Crossref]

M. G. Scullion, A. Di Falco, and T. F. Krauss, “Contra-directional coupling into slotted photonic crystals for spectrometric applications,” Opt. Lett. 39, 4345–4348 (2014).
[Crossref]

M. Arcari, I. Söllner, A. Javadi, S. Lindskov Hansen, S. Mahmoodian, J. Liu, H. Thyrrestrup, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Near-unity coupling efficiency of a quantum emitter to a photonic crystal waveguide,” Phys. Rev. Lett. 113, 093603 (2014).
[Crossref]

2013 (3)

A. Lovera, B. Gallinet, P. Nordlander, and O. J. F. Martin, “Mechanisms of Fano resonances in coupled plasmonic systems,” ACS Nano 7, 4527–4536 (2013).
[Crossref]

C. Sauvan, J. P. Hugonin, I. S. Maksymov, and P. Lalanne, “Theory of the spontaneous optical emission of nanosize photonic and plasmon resonators,” Phys. Rev. Lett. 110, 237401 (2013).
[Crossref]

Q. Bai, M. Perrin, C. Sauvan, J. P. Hugonin, and P. Lalanne, “Efficient and intuitive method for the analysis of light scattering by a resonant nanostructure,” Opt. Express 21, 27371–27382 (2013).
[Crossref]

2012 (3)

2011 (1)

M. G. Scullion, A. Di Falco, and T. F. Krauss, “Slotted photonic crystal cavities with integrated microfluidics for biosensing applications,” Biosens. Bioelectron. 27, 101–105 (2011).
[Crossref]

2010 (3)

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

A. I. Fernandez-Dominguez, S. A. Maier, and J. B. Pendry, “Collection and concentration of light by touching spheres: a transformation optics approach,” Phys. Rev. Lett. 105, 266807 (2010).
[Crossref]

K. A. Atlasov, M. Felici, K. F. Karlsson, P. Gallo, A. Rudra, B. Dwir, and E. Kapon, “1D photonic band formation and photon localization in finite-size photonic-crystal waveguides,” Opt. Express 18, 117–122 (2010).
[Crossref]

2009 (2)

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3, 206–210 (2009).
[Crossref]

A. Baron, A. Ryasnyanskiy, N. Dubreuil, P. Delaye, Q. V. Tran, S. Combrié, A. de Rossi, R. Frey, and G. Roosen, “Light localization induced enhancement of third order nonlinearities in a GaAs photonic crystal waveguide,” Opt. Express 17, 552–557 (2009).
[Crossref]

2008 (2)

P. Lalanne, C. Sauvan, and J. P. Hugonin, “Photon confinement in photonic crystal nanocavities,” Laser Photon. Rev. 2, 514–526 (2008).
[Crossref]

S. Mookherjea, J. S. Park, S.-H. Yang, and P. R. Bandaru, “Localization in silicon nanophotonic slow-light waveguides,” Nat. Photonics 2, 90–93 (2008).
[Crossref]

2007 (3)

2002 (2)

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, “Adiabatic theorem and continuous coupled-mode theory for efficient taper transitions in photonic crystals,” Phys. Rev. E 66, 066608 (2002).
[Crossref]

M. Soljačić, S. G. Johnson, S. Fan, M. Ibanescu, E. Ippen, and J. D. Joannopoulos, “Photonic-crystal slow-light enhancement of nonlinear phase sensitivity,” J. Opt. Soc. Am. B 19, 2052–2059 (2002).
[Crossref]

1996 (1)

J. M. Bendickson, J. P. Dowling, and M. Scalora, “Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structure,” Phys. Rev. E 53, 4107–4121 (1996).
[Crossref]

1994 (1)

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band-edge laser: a new approach to gain enhancement mode,” J. Appl. Phys. 75, 1896–1899 (1994).
[Crossref]

1972 (1)

A. A. Cottey, “Solutions of Schrödinger’s equation at a band edge in a one dimensional crystal,” J. Phys. C 5, 2583–2590 (1972).
[Crossref]

Arcari, M.

M. Arcari, I. Söllner, A. Javadi, S. Lindskov Hansen, S. Mahmoodian, J. Liu, H. Thyrrestrup, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Near-unity coupling efficiency of a quantum emitter to a photonic crystal waveguide,” Phys. Rev. Lett. 113, 093603 (2014).
[Crossref]

Ashcroft, N. W.

N. W. Ashcroft and N. D. Mermin, Solid State Physics (Holt, Rinehart and Winston, 1976).

Atlasov, K. A.

Baba, T.

K. Kondo, N. Ishikura, T. Tamura, and T. Baba, “Temporal pulse compression by dynamic slow-light tuning in photonic-crystal waveguides,” Phys. Rev. A 91, 023831 (2015).
[Crossref]

Bai, Q.

Bandaru, P. R.

S. Mookherjea, J. S. Park, S.-H. Yang, and P. R. Bandaru, “Localization in silicon nanophotonic slow-light waveguides,” Nat. Photonics 2, 90–93 (2008).
[Crossref]

Baron, A.

R. Faggiani, A. Baron, X. Zang, L. Lalouat, S. A. Schulz, B. O’Regan, K. Vynck, B. Cluzel, F. de Fornel, T. F. Krauss, and P. Lalanne, “Lower bound for the spatial extent of localized modes in photonic-crystal waveguides with small random imperfections,” Sci. Rep. 6, 27037 (2016).
[Crossref]

A. Baron, A. Ryasnyanskiy, N. Dubreuil, P. Delaye, Q. V. Tran, S. Combrié, A. de Rossi, R. Frey, and G. Roosen, “Light localization induced enhancement of third order nonlinearities in a GaAs photonic crystal waveguide,” Opt. Express 17, 552–557 (2009).
[Crossref]

Belov, P.

A. Krasnok, S. Glybovski, M. Petrov, S. Makarov, R. Savelev, P. Belov, C. Simovski, and Y. Kivshar, “Demonstration of the enhanced Purcell factor in all-dielectric structures,” Appl. Phys. Lett. 108, 211105 (2016).
[Crossref]

Bendickson, J. M.

J. M. Bendickson, J. P. Dowling, and M. Scalora, “Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structure,” Phys. Rev. E 53, 4107–4121 (1996).
[Crossref]

Bendsøe, M. P.

M. P. Bendsøe and O. Sigmund, Topology Optimization—Theory, Methods and Applications (Springer-Verlag, 2003).

Bienstman, P.

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, “Adiabatic theorem and continuous coupled-mode theory for efficient taper transitions in photonic crystals,” Phys. Rev. E 66, 066608 (2002).
[Crossref]

Bloemer, M. J.

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band-edge laser: a new approach to gain enhancement mode,” J. Appl. Phys. 75, 1896–1899 (1994).
[Crossref]

Bourderionnet, J.

J. Sancho, J. Bourderionnet, J. Lloret, S. Combrié, I. Gasulla, S. Xavier, S. Sales, P. Colman, G. Lehoucq, D. Dolfi, J. Capmany, and A. De Rossi, “Integrable microwave filter based on a photonic crystal delay line,” Nat. Commun. 3, 1075 (2012).
[Crossref]

Bowden, C. M.

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band-edge laser: a new approach to gain enhancement mode,” J. Appl. Phys. 75, 1896–1899 (1994).
[Crossref]

Boyd, S. P.

Bozhevolnyi, S. I.

D. K. Gramotnev and S. I. Bozhevolnyi, “Nanofocusing of electromagnetic radiation,” Nat. Photonics 8, 13–22 (2014).
[Crossref]

Capmany, J.

J. Sancho, J. Bourderionnet, J. Lloret, S. Combrié, I. Gasulla, S. Xavier, S. Sales, P. Colman, G. Lehoucq, D. Dolfi, J. Capmany, and A. De Rossi, “Integrable microwave filter based on a photonic crystal delay line,” Nat. Commun. 3, 1075 (2012).
[Crossref]

Chang, D. E.

A. Goban, C.-L. Hung, S.-P. Yu, J. D. Hood, J. A. Muniz, J. H. Lee, M. J. Martin, A. C. McClung, K. S. Choi, D. E. Chang, O. Painter, and H. J. Kimble, “Atom-light interactions in photonic crystals,” Nat. Commun. 5, 3808 (2014).
[Crossref]

Chen, Y.

W. Xue, Y. Yu, L. Ottaviano, Y. Chen, E. Semenova, K. Yvind, and J. Mork, “Threshold characteristics of slow-light photonic crystal lasers,” Phys. Rev. Lett. 116, 063901 (2016).
[Crossref]

J. Mork, Y. Chen, and M. Heuck, “Photonic crystal Fano laser: terahertz modulation and ultrashort pulse generation,” Phys. Rev. Lett. 113, 163901 (2014).
[Crossref]

Choi, K. S.

A. Goban, C.-L. Hung, S.-P. Yu, J. D. Hood, J. A. Muniz, J. H. Lee, M. J. Martin, A. C. McClung, K. S. Choi, D. E. Chang, O. Painter, and H. J. Kimble, “Atom-light interactions in photonic crystals,” Nat. Commun. 5, 3808 (2014).
[Crossref]

Cluzel, B.

R. Faggiani, A. Baron, X. Zang, L. Lalouat, S. A. Schulz, B. O’Regan, K. Vynck, B. Cluzel, F. de Fornel, T. F. Krauss, and P. Lalanne, “Lower bound for the spatial extent of localized modes in photonic-crystal waveguides with small random imperfections,” Sci. Rep. 6, 27037 (2016).
[Crossref]

Colman, P.

J. Sancho, J. Bourderionnet, J. Lloret, S. Combrié, I. Gasulla, S. Xavier, S. Sales, P. Colman, G. Lehoucq, D. Dolfi, J. Capmany, and A. De Rossi, “Integrable microwave filter based on a photonic crystal delay line,” Nat. Commun. 3, 1075 (2012).
[Crossref]

Combrié, S.

Corcoran, B.

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3, 206–210 (2009).
[Crossref]

Cottey, A. A.

A. A. Cottey, “Solutions of Schrödinger’s equation at a band edge in a one dimensional crystal,” J. Phys. C 5, 2583–2590 (1972).
[Crossref]

de Fornel, F.

R. Faggiani, A. Baron, X. Zang, L. Lalouat, S. A. Schulz, B. O’Regan, K. Vynck, B. Cluzel, F. de Fornel, T. F. Krauss, and P. Lalanne, “Lower bound for the spatial extent of localized modes in photonic-crystal waveguides with small random imperfections,” Sci. Rep. 6, 27037 (2016).
[Crossref]

De Rossi, A.

Delaye, P.

Di Falco, A.

M. G. Scullion, A. Di Falco, and T. F. Krauss, “Contra-directional coupling into slotted photonic crystals for spectrometric applications,” Opt. Lett. 39, 4345–4348 (2014).
[Crossref]

M. G. Scullion, A. Di Falco, and T. F. Krauss, “Slotted photonic crystal cavities with integrated microfluidics for biosensing applications,” Biosens. Bioelectron. 27, 101–105 (2011).
[Crossref]

Dicaire, I.

Dolfi, D.

J. Sancho, J. Bourderionnet, J. Lloret, S. Combrié, I. Gasulla, S. Xavier, S. Sales, P. Colman, G. Lehoucq, D. Dolfi, J. Capmany, and A. De Rossi, “Integrable microwave filter based on a photonic crystal delay line,” Nat. Commun. 3, 1075 (2012).
[Crossref]

Dowling, J. P.

J. M. Bendickson, J. P. Dowling, and M. Scalora, “Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structure,” Phys. Rev. E 53, 4107–4121 (1996).
[Crossref]

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band-edge laser: a new approach to gain enhancement mode,” J. Appl. Phys. 75, 1896–1899 (1994).
[Crossref]

Dubreuil, N.

Dwir, B.

Eggleton, B. J.

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Q. Bai, M. Perrin, C. Sauvan, J. P. Hugonin, and P. Lalanne, “Efficient and intuitive method for the analysis of light scattering by a resonant nanostructure,” Opt. Express 21, 27371–27382 (2013).
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C. Sauvan, J. P. Hugonin, I. S. Maksymov, and P. Lalanne, “Theory of the spontaneous optical emission of nanosize photonic and plasmon resonators,” Phys. Rev. Lett. 110, 237401 (2013).
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P. Lalanne, C. Sauvan, and J. P. Hugonin, “Photon confinement in photonic crystal nanocavities,” Laser Photon. Rev. 2, 514–526 (2008).
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Savelev, R.

A. Krasnok, S. Glybovski, M. Petrov, S. Makarov, R. Savelev, P. Belov, C. Simovski, and Y. Kivshar, “Demonstration of the enhanced Purcell factor in all-dielectric structures,” Appl. Phys. Lett. 108, 211105 (2016).
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Scalora, M.

J. M. Bendickson, J. P. Dowling, and M. Scalora, “Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structure,” Phys. Rev. E 53, 4107–4121 (1996).
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J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band-edge laser: a new approach to gain enhancement mode,” J. Appl. Phys. 75, 1896–1899 (1994).
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R. Faggiani, A. Baron, X. Zang, L. Lalouat, S. A. Schulz, B. O’Regan, K. Vynck, B. Cluzel, F. de Fornel, T. F. Krauss, and P. Lalanne, “Lower bound for the spatial extent of localized modes in photonic-crystal waveguides with small random imperfections,” Sci. Rep. 6, 27037 (2016).
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M. G. Scullion, A. Di Falco, and T. F. Krauss, “Slotted photonic crystal cavities with integrated microfluidics for biosensing applications,” Biosens. Bioelectron. 27, 101–105 (2011).
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Semenova, E.

W. Xue, Y. Yu, L. Ottaviano, Y. Chen, E. Semenova, K. Yvind, and J. Mork, “Threshold characteristics of slow-light photonic crystal lasers,” Phys. Rev. Lett. 116, 063901 (2016).
[Crossref]

Sigmund, O.

M. P. Bendsøe and O. Sigmund, Topology Optimization—Theory, Methods and Applications (Springer-Verlag, 2003).

Simovski, C.

A. Krasnok, S. Glybovski, M. Petrov, S. Makarov, R. Savelev, P. Belov, C. Simovski, and Y. Kivshar, “Demonstration of the enhanced Purcell factor in all-dielectric structures,” Appl. Phys. Lett. 108, 211105 (2016).
[Crossref]

Skorobogatiy, M. A.

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, “Adiabatic theorem and continuous coupled-mode theory for efficient taper transitions in photonic crystals,” Phys. Rev. E 66, 066608 (2002).
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Soljacic, M.

Söllner, I.

I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kiršanskė, T. Pregnolato, H. El-Ella, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Deterministic photon-emitter coupling in chiral photonic circuits,” Nat. Nanotechnol. 10, 775–778 (2015).
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M. Arcari, I. Söllner, A. Javadi, S. Lindskov Hansen, S. Mahmoodian, J. Liu, H. Thyrrestrup, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Near-unity coupling efficiency of a quantum emitter to a photonic crystal waveguide,” Phys. Rev. Lett. 113, 093603 (2014).
[Crossref]

Song, J. D.

I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kiršanskė, T. Pregnolato, H. El-Ella, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Deterministic photon-emitter coupling in chiral photonic circuits,” Nat. Nanotechnol. 10, 775–778 (2015).
[Crossref]

M. Arcari, I. Söllner, A. Javadi, S. Lindskov Hansen, S. Mahmoodian, J. Liu, H. Thyrrestrup, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Near-unity coupling efficiency of a quantum emitter to a photonic crystal waveguide,” Phys. Rev. Lett. 113, 093603 (2014).
[Crossref]

Stobbe, S.

I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kiršanskė, T. Pregnolato, H. El-Ella, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Deterministic photon-emitter coupling in chiral photonic circuits,” Nat. Nanotechnol. 10, 775–778 (2015).
[Crossref]

P. Lodahl, S. Mahmoodian, and S. Stobbe, “Interfacing single photons and single quantum dots with photonic nanostructures,” Rev. Mod. Phys. 87, 347–400 (2015).
[Crossref]

M. Arcari, I. Söllner, A. Javadi, S. Lindskov Hansen, S. Mahmoodian, J. Liu, H. Thyrrestrup, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Near-unity coupling efficiency of a quantum emitter to a photonic crystal waveguide,” Phys. Rev. Lett. 113, 093603 (2014).
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Thyrrestrup, H.

M. Arcari, I. Söllner, A. Javadi, S. Lindskov Hansen, S. Mahmoodian, J. Liu, H. Thyrrestrup, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Near-unity coupling efficiency of a quantum emitter to a photonic crystal waveguide,” Phys. Rev. Lett. 113, 093603 (2014).
[Crossref]

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[Crossref]

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R. Faggiani, A. Baron, X. Zang, L. Lalouat, S. A. Schulz, B. O’Regan, K. Vynck, B. Cluzel, F. de Fornel, T. F. Krauss, and P. Lalanne, “Lower bound for the spatial extent of localized modes in photonic-crystal waveguides with small random imperfections,” Sci. Rep. 6, 27037 (2016).
[Crossref]

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White, T. P.

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3, 206–210 (2009).
[Crossref]

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J. Sancho, J. Bourderionnet, J. Lloret, S. Combrié, I. Gasulla, S. Xavier, S. Sales, P. Colman, G. Lehoucq, D. Dolfi, J. Capmany, and A. De Rossi, “Integrable microwave filter based on a photonic crystal delay line,” Nat. Commun. 3, 1075 (2012).
[Crossref]

Xue, W.

W. Xue, Y. Yu, L. Ottaviano, Y. Chen, E. Semenova, K. Yvind, and J. Mork, “Threshold characteristics of slow-light photonic crystal lasers,” Phys. Rev. Lett. 116, 063901 (2016).
[Crossref]

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S. Mookherjea, J. S. Park, S.-H. Yang, and P. R. Bandaru, “Localization in silicon nanophotonic slow-light waveguides,” Nat. Photonics 2, 90–93 (2008).
[Crossref]

Yeganegi, E.

E. Yeganegi, A. Lagendijk, A. P. Mosk, and W. L. Vos, “Local density of optical states in the band gap of a finite one-dimensional photonic crystal,” Phys. Rev. B 89, 045123 (2014).
[Crossref]

Yu, S.-P.

A. Goban, C.-L. Hung, J. D. Hood, S.-P. Yu, J. A. Muniz, O. Painter, and H. J. Kimble, “Superradiance for atoms trapped along a photonic crystal waveguide,” Phys. Rev. Lett. 115, 063601 (2015).
[Crossref]

A. Goban, C.-L. Hung, S.-P. Yu, J. D. Hood, J. A. Muniz, J. H. Lee, M. J. Martin, A. C. McClung, K. S. Choi, D. E. Chang, O. Painter, and H. J. Kimble, “Atom-light interactions in photonic crystals,” Nat. Commun. 5, 3808 (2014).
[Crossref]

Yu, Y.

W. Xue, Y. Yu, L. Ottaviano, Y. Chen, E. Semenova, K. Yvind, and J. Mork, “Threshold characteristics of slow-light photonic crystal lasers,” Phys. Rev. Lett. 116, 063901 (2016).
[Crossref]

Yvind, K.

W. Xue, Y. Yu, L. Ottaviano, Y. Chen, E. Semenova, K. Yvind, and J. Mork, “Threshold characteristics of slow-light photonic crystal lasers,” Phys. Rev. Lett. 116, 063901 (2016).
[Crossref]

Zang, X.

R. Faggiani, A. Baron, X. Zang, L. Lalouat, S. A. Schulz, B. O’Regan, K. Vynck, B. Cluzel, F. de Fornel, T. F. Krauss, and P. Lalanne, “Lower bound for the spatial extent of localized modes in photonic-crystal waveguides with small random imperfections,” Sci. Rep. 6, 27037 (2016).
[Crossref]

ACS Nano (1)

A. Lovera, B. Gallinet, P. Nordlander, and O. J. F. Martin, “Mechanisms of Fano resonances in coupled plasmonic systems,” ACS Nano 7, 4527–4536 (2013).
[Crossref]

Appl. Phys. Lett. (1)

A. Krasnok, S. Glybovski, M. Petrov, S. Makarov, R. Savelev, P. Belov, C. Simovski, and Y. Kivshar, “Demonstration of the enhanced Purcell factor in all-dielectric structures,” Appl. Phys. Lett. 108, 211105 (2016).
[Crossref]

Biosens. Bioelectron. (1)

M. G. Scullion, A. Di Falco, and T. F. Krauss, “Slotted photonic crystal cavities with integrated microfluidics for biosensing applications,” Biosens. Bioelectron. 27, 101–105 (2011).
[Crossref]

J. Appl. Phys. (1)

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, “The photonic band-edge laser: a new approach to gain enhancement mode,” J. Appl. Phys. 75, 1896–1899 (1994).
[Crossref]

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

J. Phys. C (1)

A. A. Cottey, “Solutions of Schrödinger’s equation at a band edge in a one dimensional crystal,” J. Phys. C 5, 2583–2590 (1972).
[Crossref]

Laser Photon. Rev. (1)

P. Lalanne, C. Sauvan, and J. P. Hugonin, “Photon confinement in photonic crystal nanocavities,” Laser Photon. Rev. 2, 514–526 (2008).
[Crossref]

Nat. Commun. (2)

A. Goban, C.-L. Hung, S.-P. Yu, J. D. Hood, J. A. Muniz, J. H. Lee, M. J. Martin, A. C. McClung, K. S. Choi, D. E. Chang, O. Painter, and H. J. Kimble, “Atom-light interactions in photonic crystals,” Nat. Commun. 5, 3808 (2014).
[Crossref]

J. Sancho, J. Bourderionnet, J. Lloret, S. Combrié, I. Gasulla, S. Xavier, S. Sales, P. Colman, G. Lehoucq, D. Dolfi, J. Capmany, and A. De Rossi, “Integrable microwave filter based on a photonic crystal delay line,” Nat. Commun. 3, 1075 (2012).
[Crossref]

Nat. Nanotechnol. (1)

I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kiršanskė, T. Pregnolato, H. El-Ella, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Deterministic photon-emitter coupling in chiral photonic circuits,” Nat. Nanotechnol. 10, 775–778 (2015).
[Crossref]

Nat. Photonics (3)

D. K. Gramotnev and S. I. Bozhevolnyi, “Nanofocusing of electromagnetic radiation,” Nat. Photonics 8, 13–22 (2014).
[Crossref]

S. Mookherjea, J. S. Park, S.-H. Yang, and P. R. Bandaru, “Localization in silicon nanophotonic slow-light waveguides,” Nat. Photonics 2, 90–93 (2008).
[Crossref]

B. Corcoran, C. Monat, C. Grillet, D. J. Moss, B. J. Eggleton, T. P. White, L. O’Faolain, and T. F. Krauss, “Green light emission in silicon through slow-light enhanced third-harmonic generation in photonic-crystal waveguides,” Nat. Photonics 3, 206–210 (2009).
[Crossref]

Opt. Express (6)

Opt. Lett. (3)

Phys. Rev. A (1)

K. Kondo, N. Ishikura, T. Tamura, and T. Baba, “Temporal pulse compression by dynamic slow-light tuning in photonic-crystal waveguides,” Phys. Rev. A 91, 023831 (2015).
[Crossref]

Phys. Rev. B (1)

E. Yeganegi, A. Lagendijk, A. P. Mosk, and W. L. Vos, “Local density of optical states in the band gap of a finite one-dimensional photonic crystal,” Phys. Rev. B 89, 045123 (2014).
[Crossref]

Phys. Rev. E (2)

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, “Adiabatic theorem and continuous coupled-mode theory for efficient taper transitions in photonic crystals,” Phys. Rev. E 66, 066608 (2002).
[Crossref]

J. M. Bendickson, J. P. Dowling, and M. Scalora, “Analytic expressions for the electromagnetic mode density in finite, one-dimensional, photonic band-gap structure,” Phys. Rev. E 53, 4107–4121 (1996).
[Crossref]

Phys. Rev. Lett. (6)

A. Goban, C.-L. Hung, J. D. Hood, S.-P. Yu, J. A. Muniz, O. Painter, and H. J. Kimble, “Superradiance for atoms trapped along a photonic crystal waveguide,” Phys. Rev. Lett. 115, 063601 (2015).
[Crossref]

W. Xue, Y. Yu, L. Ottaviano, Y. Chen, E. Semenova, K. Yvind, and J. Mork, “Threshold characteristics of slow-light photonic crystal lasers,” Phys. Rev. Lett. 116, 063901 (2016).
[Crossref]

J. Mork, Y. Chen, and M. Heuck, “Photonic crystal Fano laser: terahertz modulation and ultrashort pulse generation,” Phys. Rev. Lett. 113, 163901 (2014).
[Crossref]

M. Arcari, I. Söllner, A. Javadi, S. Lindskov Hansen, S. Mahmoodian, J. Liu, H. Thyrrestrup, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Near-unity coupling efficiency of a quantum emitter to a photonic crystal waveguide,” Phys. Rev. Lett. 113, 093603 (2014).
[Crossref]

A. I. Fernandez-Dominguez, S. A. Maier, and J. B. Pendry, “Collection and concentration of light by touching spheres: a transformation optics approach,” Phys. Rev. Lett. 105, 266807 (2010).
[Crossref]

C. Sauvan, J. P. Hugonin, I. S. Maksymov, and P. Lalanne, “Theory of the spontaneous optical emission of nanosize photonic and plasmon resonators,” Phys. Rev. Lett. 110, 237401 (2013).
[Crossref]

Rep. Prog. Phys. (1)

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

Rev. Mod. Phys. (1)

P. Lodahl, S. Mahmoodian, and S. Stobbe, “Interfacing single photons and single quantum dots with photonic nanostructures,” Rev. Mod. Phys. 87, 347–400 (2015).
[Crossref]

Sci. Rep. (1)

R. Faggiani, A. Baron, X. Zang, L. Lalouat, S. A. Schulz, B. O’Regan, K. Vynck, B. Cluzel, F. de Fornel, T. F. Krauss, and P. Lalanne, “Lower bound for the spatial extent of localized modes in photonic-crystal waveguides with small random imperfections,” Sci. Rep. 6, 27037 (2016).
[Crossref]

Other (3)

H. R. Haakh, S. Faez, and V. Sandoghdar, “Polaritonic states in a dielectric nanoguide: localization and strong coupling,” arXiv: 1510.07979 (2015).

M. P. Bendsøe and O. Sigmund, Topology Optimization—Theory, Methods and Applications (Springer-Verlag, 2003).

N. W. Ashcroft and N. D. Mermin, Solid State Physics (Holt, Rinehart and Winston, 1976).

Supplementary Material (1)

NameDescription
» Supplement 1: PDF (2696 KB)      (1) Impact of the evanescent Bloch modes on the speed bump LDOS (2) Impact of disorder on the photonic speed bumps (3) Transmission properties of the speed bumps

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Figures (5)

Fig. 1.
Fig. 1.

Mimicking periodic infinite media with finite periodic media. (a) 1D infinite periodic medium: the source couples to outgoing Bloch modes (black) that propagate away without any reflection. (b) 1D finite system: the Bloch modes are back-reflected onto the terminations and modify the field distribution inside the periodic structure. (c) 1D finite periodic medium with perfectly-matched boundaries (tapers): the Bloch modes are not reflected on the boundaries, and the source sees an infinite periodic medium. (a)–(c) The right insets sketch the corresponding DOS.

Fig. 2.
Fig. 2.

Photonic-crystal speed bump. (a) Schematic of an N-period-long speed bump that is composed of an N-period-long slow-W1 waveguide surrounded by bilayer-heterostructure tapers and fast-W1 waveguides. The waveguides are assumed to be etched in a membrane of thickness 220 nm and refractive index 3.45. The 2D photonic-crystal mirrors of the slow-W1 waveguide are made of a triangular lattice of air holes of periodicity a=232  nm. The fast-W1 waveguide is obtained by stretching the longitudinal period of the slow-W1 waveguide from a=232  nm to aL=245  nm, without changing the transverse period. (b) Dispersion curves of slow-W1 (red) and fast-W1 (black) waveguides. The operating frequency is marked with a horizontal dashed black line. (c) Amplitude of the y-component of the magnetic field of the slow-W1 (ng=1000) and fast-W1 (ng=6) Bloch modes at the operating frequency. The modes are normalized to carry a power flow of 1.

Fig. 3.
Fig. 3.

Taper optimization. (a) Taper layout. A slow-W1 waveguide is connected to an elongated fast-W1 waveguide through a bilayer-heterostructure taper, which is optimized by tuning the longitudinal periods a1 and a2 of the two layers. (b) Spectral dependence of the reflectance of the tapered interface for three tapers optimized to achieved an ultra-small reflectance (see the Table inset) for ng=100 (dotted blue), 500 (dotted-dashed green), and 1000 (dashed red) as a function of the group index of the slow W1 waveguide (bottom horizontal axis) or wavelength (top horizontal axis). The solid black curve shows the reflectance without taper. Inset: minimum taper reflectance and taper geometrical parameters.

Fig. 4.
Fig. 4.

Mimicking the Van Hove singularity with PhC speed bumps. Normalized LDOS (or Purcell factor) seen by an x-polarized source placed in the center of a 8-period-long speed bump optimized for operation at ng=100 (blue), 500 (green), 1000 (red), and without taper (black). The dashed black curve corresponds to the LDOS achieved for a fully periodic, infinite slow-W1 waveguide (Van Hove singularity). The blue, green, and red circles highlight the Purcell values achieved by the speed bump at nominal operation wavelengths for which the taper reflectance is almost null. Importantly, the dots are almost superimposed with the dashed black curve, demonstrating that the source emitting in the speed bump emits as if it were in a fully periodic waveguide. Inset: evolution of the Purcell factor with speed bump length Na for the same three optimized tapers at ng=100, 500, and 1000.

Fig. 5.
Fig. 5.

Optical properties of the speed bump resonance mode. (a) |Hy| for the resonance mode of a 4-period long speed bump. (b) Normalized LDOS seen by the x-polarized electric dipole source placed in the center of the speed bump, see (a). The black and dashed red curves are obtained with fully-vectorial Green-tensor calculations [27] and with the single-mode expansion formula, respectively. (c) Step-like transmission (red curve) under illumination by the guided Bloch mode of the fast-W1 waveguide. The dashed black line represents the band edge of the slow-W1 mode. All of the results in (a)–(c) are obtained for a speed bump with a taper optimized for ng=100.

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