Abstract

2D photonic crystal (2DPC) structures consisting in 2D silicon nanopillar arrays in silica are investigated. The main motivation of this work lies in that 2D rod arrays should be easily combined with refractive structures (e. g. micro-wire waveguides), unlike 2DPC consisting in hole lattices. Such an association is expected to lead to both new functionalities and larger scale integration. In this paper, we study the loss mechanism for non degenerated Bloch modes located at Γ-point in a 2DPC slab constituted by a square lattice of silicon rods in silica. For such modes, we show that the quality factor is mainly governed by the lateral losses. To further inhibit the lateral losses, a photonic heterostructure is used. 3D FDTD calculations show that quality factors of 4000 are achieved. To reduce the vertical losses, the 2DPC heterostructure is associated with a vertical Bragg mirror, thus resulting in very high quality factors (>40000).

© 2008 Optical Society of America

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  1. B. Ben Bakir, Ch. Seassal, X. Letartre, and P. Viktorovitch, "Surface-emitting microlaser combining two-dimensional photonic crystal membrane and vertical Bragg mirror," Appl. Phys. Lett. 88, 081113 (2006).
    [CrossRef]
  2. T. Ochiai and K. Sakoda, "Dispersion relation and optical transmittance of a hexagonal photonic crystal slab," Phys. Rev. B 63, 125107 (2001).
    [CrossRef]
  3. S. Boutami, B. Ben Bakir, H. Hattori, X. Letartre, J. L. Leclerq, P. Rojo-Romeo, M. Garrigues, C. Seassal, and P. Viktorovitch, "Broadband and compact 2D photonic crystal reflectors with controllable polarization dependence," IEEE Photon. Technol. Lett. 18, 835 (2006).
    [CrossRef]
  4. J. Mouette, C. Seassal, X. Letame, P. Rojo-Romeo, J.-L. Leclercq, P Regreny, P. Viktorovitch, E. Jalaguier, P. Perreau, and H. Moriceau, "Very low threshold vertical emitting laser operation in InP graphite photonic crystal slab on silicon" Electron. Lett. 39, 526 (2002).
    [CrossRef]
  5. http://ab-initio.mit.edu/wiki/index.php/Meep.
  6. 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]
  7. C. Sauvan, G. Lecamp. P. Lalanne, and J. P. Hugonin, "Modal-reflectivity enhancement by geometry tuning in Photonic Crystal microcavities," Opt. Express 13, 245 (2005).
    [CrossRef] [PubMed]
  8. X. Letartre, J. Mouette, J. L. Leclerq, P. Rojo-Romeo, C. Seassal, and P. Viktorovitxh, "Switching devices with spatial and spectral resolution combining photonic crystal and MOEMS structures," J. Lightwave Technol. 21, 1691-1699 (2003).
    [CrossRef]
  9. B. S. Song, S. Noda, T. Asano, and Y. Akahane, "Ultra-high-Q photonic double-heterostructure nanocavity," Nature 4, 207 (2005).
    [CrossRef]
  10. F. Bordas, M. J. Steel, C. Seassal, and A. Rahmani, "Confinement of band-edge modes in a photonic crystal slab," Opt. Express 15, 108090 (2007).
    [CrossRef]

2007 (1)

F. Bordas, M. J. Steel, C. Seassal, and A. Rahmani, "Confinement of band-edge modes in a photonic crystal slab," Opt. Express 15, 108090 (2007).
[CrossRef]

2006 (2)

B. Ben Bakir, Ch. Seassal, X. Letartre, and P. Viktorovitch, "Surface-emitting microlaser combining two-dimensional photonic crystal membrane and vertical Bragg mirror," Appl. Phys. Lett. 88, 081113 (2006).
[CrossRef]

S. Boutami, B. Ben Bakir, H. Hattori, X. Letartre, J. L. Leclerq, P. Rojo-Romeo, M. Garrigues, C. Seassal, and P. Viktorovitch, "Broadband and compact 2D photonic crystal reflectors with controllable polarization dependence," IEEE Photon. Technol. Lett. 18, 835 (2006).
[CrossRef]

2005 (3)

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]

B. S. Song, S. Noda, T. Asano, and Y. Akahane, "Ultra-high-Q photonic double-heterostructure nanocavity," Nature 4, 207 (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 (2005).
[CrossRef] [PubMed]

2003 (1)

2002 (1)

J. Mouette, C. Seassal, X. Letame, P. Rojo-Romeo, J.-L. Leclercq, P Regreny, P. Viktorovitch, E. Jalaguier, P. Perreau, and H. Moriceau, "Very low threshold vertical emitting laser operation in InP graphite photonic crystal slab on silicon" Electron. Lett. 39, 526 (2002).
[CrossRef]

2001 (1)

T. Ochiai and K. Sakoda, "Dispersion relation and optical transmittance of a hexagonal photonic crystal slab," Phys. Rev. B 63, 125107 (2001).
[CrossRef]

Akahane, Y.

B. S. Song, S. Noda, T. Asano, and Y. Akahane, "Ultra-high-Q photonic double-heterostructure nanocavity," Nature 4, 207 (2005).
[CrossRef]

Asano, T.

B. S. Song, S. Noda, T. Asano, and Y. Akahane, "Ultra-high-Q photonic double-heterostructure nanocavity," Nature 4, 207 (2005).
[CrossRef]

Ben Bakir, B.

S. Boutami, B. Ben Bakir, H. Hattori, X. Letartre, J. L. Leclerq, P. Rojo-Romeo, M. Garrigues, C. Seassal, and P. Viktorovitch, "Broadband and compact 2D photonic crystal reflectors with controllable polarization dependence," IEEE Photon. Technol. Lett. 18, 835 (2006).
[CrossRef]

B. Ben Bakir, Ch. Seassal, X. Letartre, and P. Viktorovitch, "Surface-emitting microlaser combining two-dimensional photonic crystal membrane and vertical Bragg mirror," Appl. Phys. Lett. 88, 081113 (2006).
[CrossRef]

Bordas, F.

F. Bordas, M. J. Steel, C. Seassal, and A. Rahmani, "Confinement of band-edge modes in a photonic crystal slab," Opt. Express 15, 108090 (2007).
[CrossRef]

Boutami, S.

S. Boutami, B. Ben Bakir, H. Hattori, X. Letartre, J. L. Leclerq, P. Rojo-Romeo, M. Garrigues, C. Seassal, and P. Viktorovitch, "Broadband and compact 2D photonic crystal reflectors with controllable polarization dependence," IEEE Photon. Technol. Lett. 18, 835 (2006).
[CrossRef]

Garrigues, M.

S. Boutami, B. Ben Bakir, H. Hattori, X. Letartre, J. L. Leclerq, P. Rojo-Romeo, M. Garrigues, C. Seassal, and P. Viktorovitch, "Broadband and compact 2D photonic crystal reflectors with controllable polarization dependence," IEEE Photon. Technol. Lett. 18, 835 (2006).
[CrossRef]

Hattori, H.

S. Boutami, B. Ben Bakir, H. Hattori, X. Letartre, J. L. Leclerq, P. Rojo-Romeo, M. Garrigues, C. Seassal, and P. Viktorovitch, "Broadband and compact 2D photonic crystal reflectors with controllable polarization dependence," IEEE Photon. Technol. Lett. 18, 835 (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]

Jalaguier, E.

J. Mouette, C. Seassal, X. Letame, P. Rojo-Romeo, J.-L. Leclercq, P Regreny, P. Viktorovitch, E. Jalaguier, P. Perreau, and H. Moriceau, "Very low threshold vertical emitting laser operation in InP graphite photonic crystal slab on silicon" Electron. Lett. 39, 526 (2002).
[CrossRef]

Lalanne, 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]

Lecamp, G.

Leclercq, J.-L.

J. Mouette, C. Seassal, X. Letame, P. Rojo-Romeo, J.-L. Leclercq, P Regreny, P. Viktorovitch, E. Jalaguier, P. Perreau, and H. Moriceau, "Very low threshold vertical emitting laser operation in InP graphite photonic crystal slab on silicon" Electron. Lett. 39, 526 (2002).
[CrossRef]

Leclerq, J. L.

S. Boutami, B. Ben Bakir, H. Hattori, X. Letartre, J. L. Leclerq, P. Rojo-Romeo, M. Garrigues, C. Seassal, and P. Viktorovitch, "Broadband and compact 2D photonic crystal reflectors with controllable polarization dependence," IEEE Photon. Technol. Lett. 18, 835 (2006).
[CrossRef]

X. Letartre, J. Mouette, J. L. Leclerq, P. Rojo-Romeo, C. Seassal, and P. Viktorovitxh, "Switching devices with spatial and spectral resolution combining photonic crystal and MOEMS structures," J. Lightwave Technol. 21, 1691-1699 (2003).
[CrossRef]

Letame, X.

J. Mouette, C. Seassal, X. Letame, P. Rojo-Romeo, J.-L. Leclercq, P Regreny, P. Viktorovitch, E. Jalaguier, P. Perreau, and H. Moriceau, "Very low threshold vertical emitting laser operation in InP graphite photonic crystal slab on silicon" Electron. Lett. 39, 526 (2002).
[CrossRef]

Letartre, X.

B. Ben Bakir, Ch. Seassal, X. Letartre, and P. Viktorovitch, "Surface-emitting microlaser combining two-dimensional photonic crystal membrane and vertical Bragg mirror," Appl. Phys. Lett. 88, 081113 (2006).
[CrossRef]

S. Boutami, B. Ben Bakir, H. Hattori, X. Letartre, J. L. Leclerq, P. Rojo-Romeo, M. Garrigues, C. Seassal, and P. Viktorovitch, "Broadband and compact 2D photonic crystal reflectors with controllable polarization dependence," IEEE Photon. Technol. Lett. 18, 835 (2006).
[CrossRef]

X. Letartre, J. Mouette, J. L. Leclerq, P. Rojo-Romeo, C. Seassal, and P. Viktorovitxh, "Switching devices with spatial and spectral resolution combining photonic crystal and MOEMS structures," J. Lightwave Technol. 21, 1691-1699 (2003).
[CrossRef]

Moriceau, H.

J. Mouette, C. Seassal, X. Letame, P. Rojo-Romeo, J.-L. Leclercq, P Regreny, P. Viktorovitch, E. Jalaguier, P. Perreau, and H. Moriceau, "Very low threshold vertical emitting laser operation in InP graphite photonic crystal slab on silicon" Electron. Lett. 39, 526 (2002).
[CrossRef]

Mouette, J.

X. Letartre, J. Mouette, J. L. Leclerq, P. Rojo-Romeo, C. Seassal, and P. Viktorovitxh, "Switching devices with spatial and spectral resolution combining photonic crystal and MOEMS structures," J. Lightwave Technol. 21, 1691-1699 (2003).
[CrossRef]

J. Mouette, C. Seassal, X. Letame, P. Rojo-Romeo, J.-L. Leclercq, P Regreny, P. Viktorovitch, E. Jalaguier, P. Perreau, and H. Moriceau, "Very low threshold vertical emitting laser operation in InP graphite photonic crystal slab on silicon" Electron. Lett. 39, 526 (2002).
[CrossRef]

Noda, S.

B. S. Song, S. Noda, T. Asano, and Y. Akahane, "Ultra-high-Q photonic double-heterostructure nanocavity," Nature 4, 207 (2005).
[CrossRef]

Ochiai, T.

T. Ochiai and K. Sakoda, "Dispersion relation and optical transmittance of a hexagonal photonic crystal slab," Phys. Rev. B 63, 125107 (2001).
[CrossRef]

Perreau, P.

J. Mouette, C. Seassal, X. Letame, P. Rojo-Romeo, J.-L. Leclercq, P Regreny, P. Viktorovitch, E. Jalaguier, P. Perreau, and H. Moriceau, "Very low threshold vertical emitting laser operation in InP graphite photonic crystal slab on silicon" Electron. Lett. 39, 526 (2002).
[CrossRef]

Rahmani, A.

F. Bordas, M. J. Steel, C. Seassal, and A. Rahmani, "Confinement of band-edge modes in a photonic crystal slab," Opt. Express 15, 108090 (2007).
[CrossRef]

Regreny, P

J. Mouette, C. Seassal, X. Letame, P. Rojo-Romeo, J.-L. Leclercq, P Regreny, P. Viktorovitch, E. Jalaguier, P. Perreau, and H. Moriceau, "Very low threshold vertical emitting laser operation in InP graphite photonic crystal slab on silicon" Electron. Lett. 39, 526 (2002).
[CrossRef]

Rojo-Romeo, P.

S. Boutami, B. Ben Bakir, H. Hattori, X. Letartre, J. L. Leclerq, P. Rojo-Romeo, M. Garrigues, C. Seassal, and P. Viktorovitch, "Broadband and compact 2D photonic crystal reflectors with controllable polarization dependence," IEEE Photon. Technol. Lett. 18, 835 (2006).
[CrossRef]

X. Letartre, J. Mouette, J. L. Leclerq, P. Rojo-Romeo, C. Seassal, and P. Viktorovitxh, "Switching devices with spatial and spectral resolution combining photonic crystal and MOEMS structures," J. Lightwave Technol. 21, 1691-1699 (2003).
[CrossRef]

J. Mouette, C. Seassal, X. Letame, P. Rojo-Romeo, J.-L. Leclercq, P Regreny, P. Viktorovitch, E. Jalaguier, P. Perreau, and H. Moriceau, "Very low threshold vertical emitting laser operation in InP graphite photonic crystal slab on silicon" Electron. Lett. 39, 526 (2002).
[CrossRef]

Sakoda, K.

T. Ochiai and K. Sakoda, "Dispersion relation and optical transmittance of a hexagonal photonic crystal slab," Phys. Rev. B 63, 125107 (2001).
[CrossRef]

Sauvan, C.

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

Seassal, C.

F. Bordas, M. J. Steel, C. Seassal, and A. Rahmani, "Confinement of band-edge modes in a photonic crystal slab," Opt. Express 15, 108090 (2007).
[CrossRef]

S. Boutami, B. Ben Bakir, H. Hattori, X. Letartre, J. L. Leclerq, P. Rojo-Romeo, M. Garrigues, C. Seassal, and P. Viktorovitch, "Broadband and compact 2D photonic crystal reflectors with controllable polarization dependence," IEEE Photon. Technol. Lett. 18, 835 (2006).
[CrossRef]

X. Letartre, J. Mouette, J. L. Leclerq, P. Rojo-Romeo, C. Seassal, and P. Viktorovitxh, "Switching devices with spatial and spectral resolution combining photonic crystal and MOEMS structures," J. Lightwave Technol. 21, 1691-1699 (2003).
[CrossRef]

J. Mouette, C. Seassal, X. Letame, P. Rojo-Romeo, J.-L. Leclercq, P Regreny, P. Viktorovitch, E. Jalaguier, P. Perreau, and H. Moriceau, "Very low threshold vertical emitting laser operation in InP graphite photonic crystal slab on silicon" Electron. Lett. 39, 526 (2002).
[CrossRef]

Seassal, Ch.

B. Ben Bakir, Ch. Seassal, X. Letartre, and P. Viktorovitch, "Surface-emitting microlaser combining two-dimensional photonic crystal membrane and vertical Bragg mirror," Appl. Phys. Lett. 88, 081113 (2006).
[CrossRef]

Song, B. S.

B. S. Song, S. Noda, T. Asano, and Y. Akahane, "Ultra-high-Q photonic double-heterostructure nanocavity," Nature 4, 207 (2005).
[CrossRef]

Steel, M. J.

F. Bordas, M. J. Steel, C. Seassal, and A. Rahmani, "Confinement of band-edge modes in a photonic crystal slab," Opt. Express 15, 108090 (2007).
[CrossRef]

Viktorovitch, P.

S. Boutami, B. Ben Bakir, H. Hattori, X. Letartre, J. L. Leclerq, P. Rojo-Romeo, M. Garrigues, C. Seassal, and P. Viktorovitch, "Broadband and compact 2D photonic crystal reflectors with controllable polarization dependence," IEEE Photon. Technol. Lett. 18, 835 (2006).
[CrossRef]

B. Ben Bakir, Ch. Seassal, X. Letartre, and P. Viktorovitch, "Surface-emitting microlaser combining two-dimensional photonic crystal membrane and vertical Bragg mirror," Appl. Phys. Lett. 88, 081113 (2006).
[CrossRef]

J. Mouette, C. Seassal, X. Letame, P. Rojo-Romeo, J.-L. Leclercq, P Regreny, P. Viktorovitch, E. Jalaguier, P. Perreau, and H. Moriceau, "Very low threshold vertical emitting laser operation in InP graphite photonic crystal slab on silicon" Electron. Lett. 39, 526 (2002).
[CrossRef]

Viktorovitxh, P.

Electron. Lett. (1)

J. Mouette, C. Seassal, X. Letame, P. Rojo-Romeo, J.-L. Leclercq, P Regreny, P. Viktorovitch, E. Jalaguier, P. Perreau, and H. Moriceau, "Very low threshold vertical emitting laser operation in InP graphite photonic crystal slab on silicon" Electron. Lett. 39, 526 (2002).
[CrossRef]

Appl. Phys. Lett. (1)

B. Ben Bakir, Ch. Seassal, X. Letartre, and P. Viktorovitch, "Surface-emitting microlaser combining two-dimensional photonic crystal membrane and vertical Bragg mirror," Appl. Phys. Lett. 88, 081113 (2006).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

S. Boutami, B. Ben Bakir, H. Hattori, X. Letartre, J. L. Leclerq, P. Rojo-Romeo, M. Garrigues, C. Seassal, and P. Viktorovitch, "Broadband and compact 2D photonic crystal reflectors with controllable polarization dependence," IEEE Photon. Technol. Lett. 18, 835 (2006).
[CrossRef]

J. Lightwave Technol. (1)

Nature (1)

B. S. Song, S. Noda, T. Asano, and Y. Akahane, "Ultra-high-Q photonic double-heterostructure nanocavity," Nature 4, 207 (2005).
[CrossRef]

Opt. Express (2)

F. Bordas, M. J. Steel, C. Seassal, and A. Rahmani, "Confinement of band-edge modes in a photonic crystal slab," Opt. Express 15, 108090 (2007).
[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 (2005).
[CrossRef] [PubMed]

Phys. Rev. B (2)

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]

T. Ochiai and K. Sakoda, "Dispersion relation and optical transmittance of a hexagonal photonic crystal slab," Phys. Rev. B 63, 125107 (2001).
[CrossRef]

Other (1)

http://ab-initio.mit.edu/wiki/index.php/Meep.

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Figures (12)

Fig. 1.
Fig. 1.

(a). View of the studied square lattice of silicon rods (top): the number of rows N is 5 in the figure. Reciprocal space associated to the square lattice (bottom). (b). Band diagram for TE polarization and for two silicon filling factors (28% and 50%): the studied A1 SBM is circled.

Fig. 2.
Fig. 2.

A1 quality factor as a function of the 2DPC slab surface and for filling factors ranging between 19 and 62%.

Fig. 3.
Fig. 3.

(a). Hz component of the magnetic field in the x-y plane and the y-z plane (b). (c) and (d) are the same for Ex component of the electric field in a 11*11 silicon pillar array in silica at 1.53µm for the fundamental A1 SBM.

Fig. 4.
Fig. 4.

Band diagram in complex frequency for the A1 SBM in the X direction of the reciprocal space. Results are given for filling factors ranging between 19 and 62%

Fig. 5.
Fig. 5.

A1 vertical quality factor as a function of the 2DPC slab size and for filling factors in the range 19 to 62%.

Fig. 6.
Fig. 6.

A1 band curvature around the Γ-point as a function of the 2DPC filling factor (19%> ff>62%).

Fig. 7.
Fig. 7.

Studied heterostructure and schematic band diagram showing the heterostructure effect.

Fig. 8.
Fig. 8.

Quality factor of the A1 SBM in the investigated heterostructure constituted by a 11*11 pillar well of filling factor 38% (a) and 50% (b) as a function of the barrier parameters: row number (1,2,3, 5) and filling factor, keeping the same lattice constant.

Fig. 9.
Fig. 9.

(a). Hz component of the magnetic field in the x-y plane and the y-z plane (b). (c) and (d) are the same for Ex component of the electric field.

Fig. 10.
Fig. 10.

Association between a photonic heterostructure and a vertical Bragg mirror.

Fig. 11.
Fig. 11.

Quality factor of the A1 SBM in the photonic heterostructure of Fig. 8(b) with 5 surrounding rows, as a function of the gap size between the heterostructure and the vertical Bragg mirror.

Fig. 12.
Fig. 12.

Hz component of the magnetic field (a) and Ex component of the electric field (b) in the heterostructure.

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