Abstract

Abstract

We study the confinement of low group velocity band-edge modes in a photonic crystal slab. We use a rigorous, three dimensional, finite-difference time-domain method to compute the electromagnetic properties of the modes of the photonic structures. We show that by combining a defect mode approach with the high-density of states associated with band-edge modes, one can design compact, fabrication-tolerant, high-Q photonic microcavities. The electromagnetic confinement properties of these cavities can foster enhanced radiation dynamics and should be well suited for ultralow-threshold microlasers and cavity quantum electrodynamics.

© 2007 Optical Society of America

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  1. E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
    [CrossRef] [PubMed]
  2. S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486- 2489 (1987).
    [CrossRef] [PubMed]
  3. J. D. Joannopoulos, R. D. Meade, J. N. Winn, "Photonic Crystals: Molding the Flow of Light" (Princeton, 1995).
  4. K. Sakoda, "Optical Properties of Photonic Crystals," 2nd edition (Springer, 2004).
  5. Y. Akahane, T. Asano, B. -S. Song, and S. Noda, "Fine-tuned high-Q photonic-crystal nanocavity," Opt. Express 13, 1202-1214 (2005).
    [CrossRef] [PubMed]
  6. A. M. Yacomotti, P. Monnier, F. Raineri, B. Ben Bakir, C. Seassal, R. Raj, and J. A. Levenson, "Fast Thermo- Optical Excitability in a Two-Dimensional Photonic Crystal," Phys. Rev. Lett. 97, 143904 (2006).
    [CrossRef] [PubMed]
  7. C. Monat, C. Seassal, X. Letartre, P. Regreny, P. Rojo-Romeo, P. Viktorovitch, M. Le Vassor d’Yerville, D. Cassagne, J. P. Albert, E. Jalaguier, S. Pocas, and B. Aspar, "InP-based two-dimensional photonic crystal on silicon: In-plane Bloch mode laser," Appl. Phys. Lett. 81, 5102-5104 (2002).
    [CrossRef]
  8. B. Ben Bakir, C. Seassal, X. Letartre, P. Viktorovitch, M. Zussy, L. Di Cioccio, and J. M. Fedeli, "Surfaceemitting microlaser combining two-dimensional photonic crystal membrane and vertical Bragg mirror," Appl. Phys. Lett. 88, 081113 (2006).
    [CrossRef]
  9. K. Srinivasan and O. Painter, "Fourier space design of high-Q cavities in standard and compressed hexagonal lattice photonic crystals," Opt. Express 11, 579-593 (2003).
    [CrossRef] [PubMed]
  10. Kartik Srinivasan, Paul E. Barclay and Oskar Painter, "Fabrication-tolerant high quality factor photonic crystal microcavities," Opt. Express 12, 1458-1463 (2004).
    [CrossRef] [PubMed]
  11. http://www.rsoftdesign.com
  12. O. Painter, K. Srinivasan, and P.E. Barclay, "A Wannier-like Equation for Localized Resonant Cavity Modes of Locally Perturbed Photonic Crystals," Phys. Rev. B,  68, 035214 (2003).
    [CrossRef]
  13. O. Painter, K. Srinivasan, "Localized defect states in two-dimensional photonic crystal slab waveguides: a simple model based upon symmetry analysis," Phys. Rev. B,  68, 035110 (2003).
    [CrossRef]
  14. C. Sauvan, G. Lecamp, P. Lalanne, and J. P. Hugonin, "Modal-reflectivity enhancement by geometry tuning in Photonic Crystal microcavities," Opt. Express 13, 245-255 (2005)
    [CrossRef] [PubMed]
  15. C. Sauvan, P. Lalanne, and J. P. Hugonin, "Slow-wave effect and mode-profile matching in photonic crystal microcavities," Phys. Rev. B 71, 165118 (2005)
    [CrossRef]
  16. V. A. Mandelshtam and H. S. Taylor, "Harmonic inversion of time signals," J. Chem. Phys. 107, 6756-6769 (1997). Erratum, ibid. 109 (10), 4128 (1998).
    [CrossRef]
  17. Y. Akahane, T. Asano, B.-S. Song, and S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944-947 (2003)
    [PubMed]
  18. Soon-Hong Kwon, Se-Heon Kim, Sun-Kyung Kim and Yong-Hee Lee, "Small, low-loss heterogeneous photonic bandedge laser," Opt. Express 12, 5356-5361 (2004).
    [CrossRef] [PubMed]
  19. K. Srinivasan and O. Painter, "Momentum space design of high-Q photonic crystal optical cavities," Opt. Express 10, 670-684 (2002).
    [PubMed]
  20. A. Rahmani and P. C. Chaumet, "Optical trapping near a photonic crystal," Opt. Express 14, 6353-6358 (2006)
    [CrossRef] [PubMed]
  21. M. Barth and O. Benson, "Manipulation of dielectric particles using photonic crystal cavities," Appl. Phys. Lett. 89, 253114 (2006)
    [CrossRef]

2006

A. M. Yacomotti, P. Monnier, F. Raineri, B. Ben Bakir, C. Seassal, R. Raj, and J. A. Levenson, "Fast Thermo- Optical Excitability in a Two-Dimensional Photonic Crystal," Phys. Rev. Lett. 97, 143904 (2006).
[CrossRef] [PubMed]

B. Ben Bakir, C. Seassal, X. Letartre, P. Viktorovitch, M. Zussy, L. Di Cioccio, and J. M. Fedeli, "Surfaceemitting microlaser combining two-dimensional photonic crystal membrane and vertical Bragg mirror," Appl. Phys. Lett. 88, 081113 (2006).
[CrossRef]

M. Barth and O. Benson, "Manipulation of dielectric particles using photonic crystal cavities," Appl. Phys. Lett. 89, 253114 (2006)
[CrossRef]

A. Rahmani and P. C. Chaumet, "Optical trapping near a photonic crystal," Opt. Express 14, 6353-6358 (2006)
[CrossRef] [PubMed]

2005

2004

2003

K. Srinivasan and O. Painter, "Fourier space design of high-Q cavities in standard and compressed hexagonal lattice photonic crystals," Opt. Express 11, 579-593 (2003).
[CrossRef] [PubMed]

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944-947 (2003)
[PubMed]

O. Painter, K. Srinivasan, and P.E. Barclay, "A Wannier-like Equation for Localized Resonant Cavity Modes of Locally Perturbed Photonic Crystals," Phys. Rev. B,  68, 035214 (2003).
[CrossRef]

O. Painter, K. Srinivasan, "Localized defect states in two-dimensional photonic crystal slab waveguides: a simple model based upon symmetry analysis," Phys. Rev. B,  68, 035110 (2003).
[CrossRef]

2002

C. Monat, C. Seassal, X. Letartre, P. Regreny, P. Rojo-Romeo, P. Viktorovitch, M. Le Vassor d’Yerville, D. Cassagne, J. P. Albert, E. Jalaguier, S. Pocas, and B. Aspar, "InP-based two-dimensional photonic crystal on silicon: In-plane Bloch mode laser," Appl. Phys. Lett. 81, 5102-5104 (2002).
[CrossRef]

K. Srinivasan and O. Painter, "Momentum space design of high-Q photonic crystal optical cavities," Opt. Express 10, 670-684 (2002).
[PubMed]

1987

E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486- 2489 (1987).
[CrossRef] [PubMed]

Akahane, Y.

Y. Akahane, T. Asano, B. -S. Song, and S. Noda, "Fine-tuned high-Q photonic-crystal nanocavity," Opt. Express 13, 1202-1214 (2005).
[CrossRef] [PubMed]

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944-947 (2003)
[PubMed]

Asano, T.

Y. Akahane, T. Asano, B. -S. Song, and S. Noda, "Fine-tuned high-Q photonic-crystal nanocavity," Opt. Express 13, 1202-1214 (2005).
[CrossRef] [PubMed]

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944-947 (2003)
[PubMed]

Barclay, P.E.

O. Painter, K. Srinivasan, and P.E. Barclay, "A Wannier-like Equation for Localized Resonant Cavity Modes of Locally Perturbed Photonic Crystals," Phys. Rev. B,  68, 035214 (2003).
[CrossRef]

Barth, M.

M. Barth and O. Benson, "Manipulation of dielectric particles using photonic crystal cavities," Appl. Phys. Lett. 89, 253114 (2006)
[CrossRef]

Ben Bakir, B.

A. M. Yacomotti, P. Monnier, F. Raineri, B. Ben Bakir, C. Seassal, R. Raj, and J. A. Levenson, "Fast Thermo- Optical Excitability in a Two-Dimensional Photonic Crystal," Phys. Rev. Lett. 97, 143904 (2006).
[CrossRef] [PubMed]

B. Ben Bakir, C. Seassal, X. Letartre, P. Viktorovitch, M. Zussy, L. Di Cioccio, and J. M. Fedeli, "Surfaceemitting microlaser combining two-dimensional photonic crystal membrane and vertical Bragg mirror," Appl. Phys. Lett. 88, 081113 (2006).
[CrossRef]

Benson, O.

M. Barth and O. Benson, "Manipulation of dielectric particles using photonic crystal cavities," Appl. Phys. Lett. 89, 253114 (2006)
[CrossRef]

Chaumet, P. C.

Di Cioccio, L.

B. Ben Bakir, C. Seassal, X. Letartre, P. Viktorovitch, M. Zussy, L. Di Cioccio, and J. M. Fedeli, "Surfaceemitting microlaser combining two-dimensional photonic crystal membrane and vertical Bragg mirror," Appl. Phys. Lett. 88, 081113 (2006).
[CrossRef]

Fedeli, J. M.

B. Ben Bakir, C. Seassal, X. Letartre, P. Viktorovitch, M. Zussy, L. Di Cioccio, and J. M. Fedeli, "Surfaceemitting microlaser combining two-dimensional photonic crystal membrane and vertical Bragg mirror," Appl. Phys. Lett. 88, 081113 (2006).
[CrossRef]

Hugonin, J. P.

C. Sauvan, P. Lalanne, and J. P. Hugonin, "Slow-wave effect and mode-profile matching in photonic crystal microcavities," Phys. Rev. B 71, 165118 (2005)
[CrossRef]

C. Sauvan, G. Lecamp, P. Lalanne, and J. P. Hugonin, "Modal-reflectivity enhancement by geometry tuning in Photonic Crystal microcavities," Opt. Express 13, 245-255 (2005)
[CrossRef] [PubMed]

John, S.

S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486- 2489 (1987).
[CrossRef] [PubMed]

Lalanne, P.

C. Sauvan, G. Lecamp, P. Lalanne, and J. P. Hugonin, "Modal-reflectivity enhancement by geometry tuning in Photonic Crystal microcavities," Opt. Express 13, 245-255 (2005)
[CrossRef] [PubMed]

C. Sauvan, P. Lalanne, and J. P. Hugonin, "Slow-wave effect and mode-profile matching in photonic crystal microcavities," Phys. Rev. B 71, 165118 (2005)
[CrossRef]

Lecamp, G.

Letartre, X.

B. Ben Bakir, C. Seassal, X. Letartre, P. Viktorovitch, M. Zussy, L. Di Cioccio, and J. M. Fedeli, "Surfaceemitting microlaser combining two-dimensional photonic crystal membrane and vertical Bragg mirror," Appl. Phys. Lett. 88, 081113 (2006).
[CrossRef]

C. Monat, C. Seassal, X. Letartre, P. Regreny, P. Rojo-Romeo, P. Viktorovitch, M. Le Vassor d’Yerville, D. Cassagne, J. P. Albert, E. Jalaguier, S. Pocas, and B. Aspar, "InP-based two-dimensional photonic crystal on silicon: In-plane Bloch mode laser," Appl. Phys. Lett. 81, 5102-5104 (2002).
[CrossRef]

Levenson, J. A.

A. M. Yacomotti, P. Monnier, F. Raineri, B. Ben Bakir, C. Seassal, R. Raj, and J. A. Levenson, "Fast Thermo- Optical Excitability in a Two-Dimensional Photonic Crystal," Phys. Rev. Lett. 97, 143904 (2006).
[CrossRef] [PubMed]

Monat, C.

C. Monat, C. Seassal, X. Letartre, P. Regreny, P. Rojo-Romeo, P. Viktorovitch, M. Le Vassor d’Yerville, D. Cassagne, J. P. Albert, E. Jalaguier, S. Pocas, and B. Aspar, "InP-based two-dimensional photonic crystal on silicon: In-plane Bloch mode laser," Appl. Phys. Lett. 81, 5102-5104 (2002).
[CrossRef]

Monnier, P.

A. M. Yacomotti, P. Monnier, F. Raineri, B. Ben Bakir, C. Seassal, R. Raj, and J. A. Levenson, "Fast Thermo- Optical Excitability in a Two-Dimensional Photonic Crystal," Phys. Rev. Lett. 97, 143904 (2006).
[CrossRef] [PubMed]

Noda, S.

Y. Akahane, T. Asano, B. -S. Song, and S. Noda, "Fine-tuned high-Q photonic-crystal nanocavity," Opt. Express 13, 1202-1214 (2005).
[CrossRef] [PubMed]

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944-947 (2003)
[PubMed]

Painter, O.

O. Painter, K. Srinivasan, "Localized defect states in two-dimensional photonic crystal slab waveguides: a simple model based upon symmetry analysis," Phys. Rev. B,  68, 035110 (2003).
[CrossRef]

K. Srinivasan and O. Painter, "Fourier space design of high-Q cavities in standard and compressed hexagonal lattice photonic crystals," Opt. Express 11, 579-593 (2003).
[CrossRef] [PubMed]

O. Painter, K. Srinivasan, and P.E. Barclay, "A Wannier-like Equation for Localized Resonant Cavity Modes of Locally Perturbed Photonic Crystals," Phys. Rev. B,  68, 035214 (2003).
[CrossRef]

K. Srinivasan and O. Painter, "Momentum space design of high-Q photonic crystal optical cavities," Opt. Express 10, 670-684 (2002).
[PubMed]

Rahmani, A.

Raineri, F.

A. M. Yacomotti, P. Monnier, F. Raineri, B. Ben Bakir, C. Seassal, R. Raj, and J. A. Levenson, "Fast Thermo- Optical Excitability in a Two-Dimensional Photonic Crystal," Phys. Rev. Lett. 97, 143904 (2006).
[CrossRef] [PubMed]

Raj, R.

A. M. Yacomotti, P. Monnier, F. Raineri, B. Ben Bakir, C. Seassal, R. Raj, and J. A. Levenson, "Fast Thermo- Optical Excitability in a Two-Dimensional Photonic Crystal," Phys. Rev. Lett. 97, 143904 (2006).
[CrossRef] [PubMed]

Regreny, P.

C. Monat, C. Seassal, X. Letartre, P. Regreny, P. Rojo-Romeo, P. Viktorovitch, M. Le Vassor d’Yerville, D. Cassagne, J. P. Albert, E. Jalaguier, S. Pocas, and B. Aspar, "InP-based two-dimensional photonic crystal on silicon: In-plane Bloch mode laser," Appl. Phys. Lett. 81, 5102-5104 (2002).
[CrossRef]

Rojo-Romeo, P.

C. Monat, C. Seassal, X. Letartre, P. Regreny, P. Rojo-Romeo, P. Viktorovitch, M. Le Vassor d’Yerville, D. Cassagne, J. P. Albert, E. Jalaguier, S. Pocas, and B. Aspar, "InP-based two-dimensional photonic crystal on silicon: In-plane Bloch mode laser," Appl. Phys. Lett. 81, 5102-5104 (2002).
[CrossRef]

Sauvan, C.

C. Sauvan, P. Lalanne, and J. P. Hugonin, "Slow-wave effect and mode-profile matching in photonic crystal microcavities," Phys. Rev. B 71, 165118 (2005)
[CrossRef]

C. Sauvan, G. Lecamp, P. Lalanne, and J. P. Hugonin, "Modal-reflectivity enhancement by geometry tuning in Photonic Crystal microcavities," Opt. Express 13, 245-255 (2005)
[CrossRef] [PubMed]

Seassal, C.

A. M. Yacomotti, P. Monnier, F. Raineri, B. Ben Bakir, C. Seassal, R. Raj, and J. A. Levenson, "Fast Thermo- Optical Excitability in a Two-Dimensional Photonic Crystal," Phys. Rev. Lett. 97, 143904 (2006).
[CrossRef] [PubMed]

B. Ben Bakir, C. Seassal, X. Letartre, P. Viktorovitch, M. Zussy, L. Di Cioccio, and J. M. Fedeli, "Surfaceemitting microlaser combining two-dimensional photonic crystal membrane and vertical Bragg mirror," Appl. Phys. Lett. 88, 081113 (2006).
[CrossRef]

C. Monat, C. Seassal, X. Letartre, P. Regreny, P. Rojo-Romeo, P. Viktorovitch, M. Le Vassor d’Yerville, D. Cassagne, J. P. Albert, E. Jalaguier, S. Pocas, and B. Aspar, "InP-based two-dimensional photonic crystal on silicon: In-plane Bloch mode laser," Appl. Phys. Lett. 81, 5102-5104 (2002).
[CrossRef]

Song, B. -S.

Song, B.-S.

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944-947 (2003)
[PubMed]

Srinivasan, K.

O. Painter, K. Srinivasan, "Localized defect states in two-dimensional photonic crystal slab waveguides: a simple model based upon symmetry analysis," Phys. Rev. B,  68, 035110 (2003).
[CrossRef]

K. Srinivasan and O. Painter, "Fourier space design of high-Q cavities in standard and compressed hexagonal lattice photonic crystals," Opt. Express 11, 579-593 (2003).
[CrossRef] [PubMed]

O. Painter, K. Srinivasan, and P.E. Barclay, "A Wannier-like Equation for Localized Resonant Cavity Modes of Locally Perturbed Photonic Crystals," Phys. Rev. B,  68, 035214 (2003).
[CrossRef]

K. Srinivasan and O. Painter, "Momentum space design of high-Q photonic crystal optical cavities," Opt. Express 10, 670-684 (2002).
[PubMed]

Viktorovitch, P.

B. Ben Bakir, C. Seassal, X. Letartre, P. Viktorovitch, M. Zussy, L. Di Cioccio, and J. M. Fedeli, "Surfaceemitting microlaser combining two-dimensional photonic crystal membrane and vertical Bragg mirror," Appl. Phys. Lett. 88, 081113 (2006).
[CrossRef]

C. Monat, C. Seassal, X. Letartre, P. Regreny, P. Rojo-Romeo, P. Viktorovitch, M. Le Vassor d’Yerville, D. Cassagne, J. P. Albert, E. Jalaguier, S. Pocas, and B. Aspar, "InP-based two-dimensional photonic crystal on silicon: In-plane Bloch mode laser," Appl. Phys. Lett. 81, 5102-5104 (2002).
[CrossRef]

Yablonovitch, E.

E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

Yacomotti, A. M.

A. M. Yacomotti, P. Monnier, F. Raineri, B. Ben Bakir, C. Seassal, R. Raj, and J. A. Levenson, "Fast Thermo- Optical Excitability in a Two-Dimensional Photonic Crystal," Phys. Rev. Lett. 97, 143904 (2006).
[CrossRef] [PubMed]

Zussy, M.

B. Ben Bakir, C. Seassal, X. Letartre, P. Viktorovitch, M. Zussy, L. Di Cioccio, and J. M. Fedeli, "Surfaceemitting microlaser combining two-dimensional photonic crystal membrane and vertical Bragg mirror," Appl. Phys. Lett. 88, 081113 (2006).
[CrossRef]

Appl. Phys. Lett.

M. Barth and O. Benson, "Manipulation of dielectric particles using photonic crystal cavities," Appl. Phys. Lett. 89, 253114 (2006)
[CrossRef]

C. Monat, C. Seassal, X. Letartre, P. Regreny, P. Rojo-Romeo, P. Viktorovitch, M. Le Vassor d’Yerville, D. Cassagne, J. P. Albert, E. Jalaguier, S. Pocas, and B. Aspar, "InP-based two-dimensional photonic crystal on silicon: In-plane Bloch mode laser," Appl. Phys. Lett. 81, 5102-5104 (2002).
[CrossRef]

B. Ben Bakir, C. Seassal, X. Letartre, P. Viktorovitch, M. Zussy, L. Di Cioccio, and J. M. Fedeli, "Surfaceemitting microlaser combining two-dimensional photonic crystal membrane and vertical Bragg mirror," Appl. Phys. Lett. 88, 081113 (2006).
[CrossRef]

Nature

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944-947 (2003)
[PubMed]

Opt. Express

Phys. Rev. B

O. Painter, K. Srinivasan, and P.E. Barclay, "A Wannier-like Equation for Localized Resonant Cavity Modes of Locally Perturbed Photonic Crystals," Phys. Rev. B,  68, 035214 (2003).
[CrossRef]

O. Painter, K. Srinivasan, "Localized defect states in two-dimensional photonic crystal slab waveguides: a simple model based upon symmetry analysis," Phys. Rev. B,  68, 035110 (2003).
[CrossRef]

C. Sauvan, P. Lalanne, and J. P. Hugonin, "Slow-wave effect and mode-profile matching in photonic crystal microcavities," Phys. Rev. B 71, 165118 (2005)
[CrossRef]

Phys. Rev. Lett.

E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486- 2489 (1987).
[CrossRef] [PubMed]

A. M. Yacomotti, P. Monnier, F. Raineri, B. Ben Bakir, C. Seassal, R. Raj, and J. A. Levenson, "Fast Thermo- Optical Excitability in a Two-Dimensional Photonic Crystal," Phys. Rev. Lett. 97, 143904 (2006).
[CrossRef] [PubMed]

Other

http://www.rsoftdesign.com

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

K. Sakoda, "Optical Properties of Photonic Crystals," 2nd edition (Springer, 2004).

V. A. Mandelshtam and H. S. Taylor, "Harmonic inversion of time signals," J. Chem. Phys. 107, 6756-6769 (1997). Erratum, ibid. 109 (10), 4128 (1998).
[CrossRef]

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Figures (9)

Fig. 1.
Fig. 1.

Frequency of the band-edges versus the filling factor for a PC slab. a is the period of the crystal and λ is the wavelength of the mode. The vertical dashed line corresponds to a crystal with a filling factor f=0.37. The horizontal dash-dotted lines mark the band edges of a crystal with f=0.37. Insets: Lattice geometry of the photonic crystal slab and location of main symmetry points in the first Brillouin zone.

Fig. 2.
Fig. 2.

Examples of structures: V 2 2 cavity (left) and V 0 4 cavity (right). Only the top-right quadrant (2D projection of one octant of the computational window) is shown. The core has a hexagonal shape, with a higher air filling factor than the mirror (fmirror=0.37). Hexagonal rings of intermediary hole radii can be used to soften the transition from the core to the mirror region.

Fig. 3.
Fig. 3.

Quality factor Q (solid lines) and frequency (dashed lines) of the confined band-edge mode versus the filling factor of the core for Vj 2 cavities with j=0, 1, 2.

Fig. 4.
Fig. 4.

Quality factor (solid line) and mode volume (dashed line) versus core filling factor for a V 2 2 cavity. The circles and squares represent the in-plane, and out-of-plane quality factors, respectively. The arrows at the top of the graph indicate the filling factors for which the field maps in Fig. 5 were computed.

Fig. 5.
Fig. 5.

Near-field map of Hz (top row) and |��(Hz)| (bottom row) for the V 2 2 cavity. From left to right, the columns correspond to the values of the filling factor marked on Fig. 3 (f=0.40, 0.48, and 0.58, respectively). On the real-space plots, the black hexagon delineates the core region. On the FFT plots, the white hexagon outlines the boundary of the first Brillouin zone and the yellow circle materializes the boundary of the light cone

Fig. 6.
Fig. 6.

Quality factor Q of the confined slow-light mode vs. filling factor of the core for V 2 i cavities with i=1,2,3,4,5.

Fig. 7.
Fig. 7.

Frequency of the confined slow-light mode vs. filling factor of the core for V 2 i cavities with i=1,2,3,4,5. The solid line without symbols represents the valence band-edge for a perfect (infinite) crystal.

Fig. 8.
Fig. 8.

Normalized mode volume of the confined slow-light mode vs. filling factor of the core for V 2 i cavities with i=1,2,3,4,5.

Fig. 9.
Fig. 9.

Quality factor vs. the number j of adaptation layers for Vj 2 cavities for a filling factor of the core f core=0.48.

Tables (3)

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Table 1. Evolution of frequency n and quality factor Q with grid resolution for a V 2 2 cavity at f=0.48.

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Table 2. Evolution of frequency ν and quality factor Q with grid resolution for a V 2 1 cavity at f=0.52.

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Table 3. Evolution of frequency ν and quality factor Q with grid resolution for a V 2 5 cavity at f=0.44.

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