Abstract

The design of high quality factor (Q) optical cavities in two dimensional photonic crystal (PC) slab waveguides based upon a momentum space picture is presented. The results of a symmetry analysis of defect modes in hexagonal and square host photonic lattices are used to determine cavity geometries that produce modes which by their very symmetry reduce the vertical radiation loss from the PC slab. Further improvements in the Q are achieved through tailoring of the defect geometry in Fourier space to limit coupling between the dominant momentum components of a given defect mode and those momentum components which are either not reflected by the PC mirror or which lie within the radiation cone of the cladding surrounding the PC slab. Numerical investigations using the finite-difference time-domain (FDTD) method predict that radiation losses can be significantly suppressed through these methods, culminating with a graded square lattice design whose total Q approaches 105 with a mode volume of approximately 0.25 cubic half-wavelengths in vacuum.

© 2002 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. Yokoyama, “Physics and Device Application of Optical Microcavities,” Science 256, 66–70 (1992).
    [CrossRef] [PubMed]
  2. J. L. Jewell, J. P. Harbison, A. Scherer, Y. H. Lee, and L. T. Florez, “Vertical-Cavity Surface-Emitting Lasers: Design, Growth, Fabrication, Characterization,” IEEE J. Quan. Elec. 27, 1332–1346 (1991).
    [CrossRef]
  3. S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode lasers,” Appl. Phys. Lett. 60, 289–291 (1992).
    [CrossRef]
  4. S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, “Ultralow-threshold Raman laser using spherical dielectric microcavity,” Nature 415, 621–623 (2002).
    [CrossRef] [PubMed]
  5. B. E. Little, S. T. Chu, W. Pan, D. Ripin, T. Kaneko, Y. Kokubun, and E. Ippen, “Vertically Coupled Glass Microring Resonator Channel Dropping Filters,” IEEE Photonics Tech. Lett. 11, 215–217 (1999).
    [CrossRef]
  6. S. Noda, A. Chutinan, and M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature 407, 608–610 (2000).
    [CrossRef] [PubMed]
  7. S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Channel drop filters in photonic crystals,” Opt. Express 3, 4–11 (1998), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-3-1-4.
    [CrossRef] [PubMed]
  8. G. Khitrova, H. M. Gibbs, F. Jahnke, M. Kira, and S. W. Koch, “Nonlinear optics of normal-mode-coupling semiconductor microcavities,” Rev. Mod. Phys. 71, 1591–1639 (1999).
    [CrossRef]
  9. D. M. Atkin, P. S. J. Russell, T. A. Birks, and P. J. Roberts, “Photonic bandstructure of guided Bloch modes in high index films fully etched through with periodic microstructure,” J. Mod. Opt. 43, 1035–1053 (1996).
    [CrossRef]
  10. S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejaki, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
    [CrossRef]
  11. A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, “Coupled-resonator optical waveguide: a proposal andanalysis,” Opt. Lett. 24, 711–713 (1999).
    [CrossRef]
  12. C. Smith, R. De la Rue, M. Rattier, S. Olivier, H. Benisty, C. Weisbuch, T. Krauss, U. Oesterlé, and R. Houdré, “Coupled guide and cavity in a two-dimensional photonic crystal,” Appl. Phys. Lett. 78, 1487–1489 (2001).
    [CrossRef]
  13. O. Painter, K. Srinivasan, J. D. O’Brien, A. Scherer, and P. D. Dapkus, “Tailoring of the resonant mode properties of optical nanocavities in two-dimensional photonic crystal slab waveguides,” J. Opt. A 3, S161–S170 (2001).
    [CrossRef]
  14. O. J. Painter, A. Husain, A. Scherer, J. D. O’Brien, I. Kim, and P. D. Dapkus, “Room Temperature Photonic Crystal Defect Lasers at Near-Infrared Wavelengths in InGaAsP,” J. Lightwave Tech. 17, 2082–2088 (1999).
    [CrossRef]
  15. O. Painter, J. Vučković, and A. Scherer, “Defect Modes of a Two-Dimensional Photonic Crystal in an Optically Thin Dielectric Slab,” J. Opt. Soc. Am. B 16, 275–285 (1999).
    [CrossRef]
  16. J. Vučković, M. Lončar, H. Mabuchi, and A. Scherer, “Design of photonic crystal microcavities for cavity QED,” Phys. Rev. E 65 (2002).
  17. T. Yoshie, J. Vučković, A. Scherer, H. Chen, and D. Deppe, “High quality two-dimensional photonic crystal slab cavities,” Appl. Phys. Lett. 79, 4289–4291 (2001).
    [CrossRef]
  18. O. Painter and K. Srinivasan, “Localized defect states in two-dimensional photonic crystal slab waveguides: a simple model based upon symmetry analysis,” submitted to Phys. Rev. B (2002).
  19. This can be viewed in the far-field as elimination of lower-order multi-pole radiation components[23].
  20. E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopou-los, “Donor and acceptor modes in photonic band-structure,” Phys. Rev. Lett. 67, 3380–3383 (1991).
    [CrossRef] [PubMed]
  21. M. Tinkham, Group Theory and Quantum Mechanics, International Series in Pure and Applied Physics (McGaw-Hill, Inc., New York, NY, 1964).
  22. K. Sakoda, Optical Properties of Photonic Crystals (Springer-Verlag, Berlin, Germany, 2001).
  23. S. G. Johnson, S. Fan, A. Mekis, and J. D. Joannopoulos, “Multipole-cancellation mechanism for high-Q cavities in the absence of a complete photonic bandgap,” Appl. Phys. Lett. 78, 3388–3390 (2001).
    [CrossRef]

2002 (3)

S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, “Ultralow-threshold Raman laser using spherical dielectric microcavity,” Nature 415, 621–623 (2002).
[CrossRef] [PubMed]

J. Vučković, M. Lončar, H. Mabuchi, and A. Scherer, “Design of photonic crystal microcavities for cavity QED,” Phys. Rev. E 65 (2002).

O. Painter and K. Srinivasan, “Localized defect states in two-dimensional photonic crystal slab waveguides: a simple model based upon symmetry analysis,” submitted to Phys. Rev. B (2002).

2001 (4)

S. G. Johnson, S. Fan, A. Mekis, and J. D. Joannopoulos, “Multipole-cancellation mechanism for high-Q cavities in the absence of a complete photonic bandgap,” Appl. Phys. Lett. 78, 3388–3390 (2001).
[CrossRef]

T. Yoshie, J. Vučković, A. Scherer, H. Chen, and D. Deppe, “High quality two-dimensional photonic crystal slab cavities,” Appl. Phys. Lett. 79, 4289–4291 (2001).
[CrossRef]

C. Smith, R. De la Rue, M. Rattier, S. Olivier, H. Benisty, C. Weisbuch, T. Krauss, U. Oesterlé, and R. Houdré, “Coupled guide and cavity in a two-dimensional photonic crystal,” Appl. Phys. Lett. 78, 1487–1489 (2001).
[CrossRef]

O. Painter, K. Srinivasan, J. D. O’Brien, A. Scherer, and P. D. Dapkus, “Tailoring of the resonant mode properties of optical nanocavities in two-dimensional photonic crystal slab waveguides,” J. Opt. A 3, S161–S170 (2001).
[CrossRef]

2000 (1)

S. Noda, A. Chutinan, and M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature 407, 608–610 (2000).
[CrossRef] [PubMed]

1999 (6)

G. Khitrova, H. M. Gibbs, F. Jahnke, M. Kira, and S. W. Koch, “Nonlinear optics of normal-mode-coupling semiconductor microcavities,” Rev. Mod. Phys. 71, 1591–1639 (1999).
[CrossRef]

B. E. Little, S. T. Chu, W. Pan, D. Ripin, T. Kaneko, Y. Kokubun, and E. Ippen, “Vertically Coupled Glass Microring Resonator Channel Dropping Filters,” IEEE Photonics Tech. Lett. 11, 215–217 (1999).
[CrossRef]

O. J. Painter, A. Husain, A. Scherer, J. D. O’Brien, I. Kim, and P. D. Dapkus, “Room Temperature Photonic Crystal Defect Lasers at Near-Infrared Wavelengths in InGaAsP,” J. Lightwave Tech. 17, 2082–2088 (1999).
[CrossRef]

O. Painter, J. Vučković, and A. Scherer, “Defect Modes of a Two-Dimensional Photonic Crystal in an Optically Thin Dielectric Slab,” J. Opt. Soc. Am. B 16, 275–285 (1999).
[CrossRef]

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejaki, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
[CrossRef]

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, “Coupled-resonator optical waveguide: a proposal andanalysis,” Opt. Lett. 24, 711–713 (1999).
[CrossRef]

1998 (1)

1996 (1)

D. M. Atkin, P. S. J. Russell, T. A. Birks, and P. J. Roberts, “Photonic bandstructure of guided Bloch modes in high index films fully etched through with periodic microstructure,” J. Mod. Opt. 43, 1035–1053 (1996).
[CrossRef]

1992 (2)

H. Yokoyama, “Physics and Device Application of Optical Microcavities,” Science 256, 66–70 (1992).
[CrossRef] [PubMed]

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode lasers,” Appl. Phys. Lett. 60, 289–291 (1992).
[CrossRef]

1991 (2)

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopou-los, “Donor and acceptor modes in photonic band-structure,” Phys. Rev. Lett. 67, 3380–3383 (1991).
[CrossRef] [PubMed]

J. L. Jewell, J. P. Harbison, A. Scherer, Y. H. Lee, and L. T. Florez, “Vertical-Cavity Surface-Emitting Lasers: Design, Growth, Fabrication, Characterization,” IEEE J. Quan. Elec. 27, 1332–1346 (1991).
[CrossRef]

Atkin, D. M.

D. M. Atkin, P. S. J. Russell, T. A. Birks, and P. J. Roberts, “Photonic bandstructure of guided Bloch modes in high index films fully etched through with periodic microstructure,” J. Mod. Opt. 43, 1035–1053 (1996).
[CrossRef]

Benisty, H.

C. Smith, R. De la Rue, M. Rattier, S. Olivier, H. Benisty, C. Weisbuch, T. Krauss, U. Oesterlé, and R. Houdré, “Coupled guide and cavity in a two-dimensional photonic crystal,” Appl. Phys. Lett. 78, 1487–1489 (2001).
[CrossRef]

Birks, T. A.

D. M. Atkin, P. S. J. Russell, T. A. Birks, and P. J. Roberts, “Photonic bandstructure of guided Bloch modes in high index films fully etched through with periodic microstructure,” J. Mod. Opt. 43, 1035–1053 (1996).
[CrossRef]

Brommer, K. D.

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopou-los, “Donor and acceptor modes in photonic band-structure,” Phys. Rev. Lett. 67, 3380–3383 (1991).
[CrossRef] [PubMed]

Chen, H.

T. Yoshie, J. Vučković, A. Scherer, H. Chen, and D. Deppe, “High quality two-dimensional photonic crystal slab cavities,” Appl. Phys. Lett. 79, 4289–4291 (2001).
[CrossRef]

Chu, S. T.

B. E. Little, S. T. Chu, W. Pan, D. Ripin, T. Kaneko, Y. Kokubun, and E. Ippen, “Vertically Coupled Glass Microring Resonator Channel Dropping Filters,” IEEE Photonics Tech. Lett. 11, 215–217 (1999).
[CrossRef]

Chutinan, A.

S. Noda, A. Chutinan, and M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature 407, 608–610 (2000).
[CrossRef] [PubMed]

Dapkus, P. D.

O. Painter, K. Srinivasan, J. D. O’Brien, A. Scherer, and P. D. Dapkus, “Tailoring of the resonant mode properties of optical nanocavities in two-dimensional photonic crystal slab waveguides,” J. Opt. A 3, S161–S170 (2001).
[CrossRef]

O. J. Painter, A. Husain, A. Scherer, J. D. O’Brien, I. Kim, and P. D. Dapkus, “Room Temperature Photonic Crystal Defect Lasers at Near-Infrared Wavelengths in InGaAsP,” J. Lightwave Tech. 17, 2082–2088 (1999).
[CrossRef]

De la Rue, R.

C. Smith, R. De la Rue, M. Rattier, S. Olivier, H. Benisty, C. Weisbuch, T. Krauss, U. Oesterlé, and R. Houdré, “Coupled guide and cavity in a two-dimensional photonic crystal,” Appl. Phys. Lett. 78, 1487–1489 (2001).
[CrossRef]

Deppe, D.

T. Yoshie, J. Vučković, A. Scherer, H. Chen, and D. Deppe, “High quality two-dimensional photonic crystal slab cavities,” Appl. Phys. Lett. 79, 4289–4291 (2001).
[CrossRef]

Fan, S.

S. G. Johnson, S. Fan, A. Mekis, and J. D. Joannopoulos, “Multipole-cancellation mechanism for high-Q cavities in the absence of a complete photonic bandgap,” Appl. Phys. Lett. 78, 3388–3390 (2001).
[CrossRef]

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejaki, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
[CrossRef]

S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Channel drop filters in photonic crystals,” Opt. Express 3, 4–11 (1998), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-3-1-4.
[CrossRef] [PubMed]

Florez, L. T.

J. L. Jewell, J. P. Harbison, A. Scherer, Y. H. Lee, and L. T. Florez, “Vertical-Cavity Surface-Emitting Lasers: Design, Growth, Fabrication, Characterization,” IEEE J. Quan. Elec. 27, 1332–1346 (1991).
[CrossRef]

Gibbs, H. M.

G. Khitrova, H. M. Gibbs, F. Jahnke, M. Kira, and S. W. Koch, “Nonlinear optics of normal-mode-coupling semiconductor microcavities,” Rev. Mod. Phys. 71, 1591–1639 (1999).
[CrossRef]

Gmitter, T. J.

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopou-los, “Donor and acceptor modes in photonic band-structure,” Phys. Rev. Lett. 67, 3380–3383 (1991).
[CrossRef] [PubMed]

Harbison, J. P.

J. L. Jewell, J. P. Harbison, A. Scherer, Y. H. Lee, and L. T. Florez, “Vertical-Cavity Surface-Emitting Lasers: Design, Growth, Fabrication, Characterization,” IEEE J. Quan. Elec. 27, 1332–1346 (1991).
[CrossRef]

Houdré, R.

C. Smith, R. De la Rue, M. Rattier, S. Olivier, H. Benisty, C. Weisbuch, T. Krauss, U. Oesterlé, and R. Houdré, “Coupled guide and cavity in a two-dimensional photonic crystal,” Appl. Phys. Lett. 78, 1487–1489 (2001).
[CrossRef]

Husain, A.

O. J. Painter, A. Husain, A. Scherer, J. D. O’Brien, I. Kim, and P. D. Dapkus, “Room Temperature Photonic Crystal Defect Lasers at Near-Infrared Wavelengths in InGaAsP,” J. Lightwave Tech. 17, 2082–2088 (1999).
[CrossRef]

Imada, M.

S. Noda, A. Chutinan, and M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature 407, 608–610 (2000).
[CrossRef] [PubMed]

Ippen, E.

B. E. Little, S. T. Chu, W. Pan, D. Ripin, T. Kaneko, Y. Kokubun, and E. Ippen, “Vertically Coupled Glass Microring Resonator Channel Dropping Filters,” IEEE Photonics Tech. Lett. 11, 215–217 (1999).
[CrossRef]

Jahnke, F.

G. Khitrova, H. M. Gibbs, F. Jahnke, M. Kira, and S. W. Koch, “Nonlinear optics of normal-mode-coupling semiconductor microcavities,” Rev. Mod. Phys. 71, 1591–1639 (1999).
[CrossRef]

Jewell, J. L.

J. L. Jewell, J. P. Harbison, A. Scherer, Y. H. Lee, and L. T. Florez, “Vertical-Cavity Surface-Emitting Lasers: Design, Growth, Fabrication, Characterization,” IEEE J. Quan. Elec. 27, 1332–1346 (1991).
[CrossRef]

Joannopoulos, J. D.

S. G. Johnson, S. Fan, A. Mekis, and J. D. Joannopoulos, “Multipole-cancellation mechanism for high-Q cavities in the absence of a complete photonic bandgap,” Appl. Phys. Lett. 78, 3388–3390 (2001).
[CrossRef]

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejaki, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
[CrossRef]

S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Channel drop filters in photonic crystals,” Opt. Express 3, 4–11 (1998), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-3-1-4.
[CrossRef] [PubMed]

Joannopou-los, J. D.

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopou-los, “Donor and acceptor modes in photonic band-structure,” Phys. Rev. Lett. 67, 3380–3383 (1991).
[CrossRef] [PubMed]

Johnson, S. G.

S. G. Johnson, S. Fan, A. Mekis, and J. D. Joannopoulos, “Multipole-cancellation mechanism for high-Q cavities in the absence of a complete photonic bandgap,” Appl. Phys. Lett. 78, 3388–3390 (2001).
[CrossRef]

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejaki, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
[CrossRef]

Kaneko, T.

B. E. Little, S. T. Chu, W. Pan, D. Ripin, T. Kaneko, Y. Kokubun, and E. Ippen, “Vertically Coupled Glass Microring Resonator Channel Dropping Filters,” IEEE Photonics Tech. Lett. 11, 215–217 (1999).
[CrossRef]

Khitrova, G.

G. Khitrova, H. M. Gibbs, F. Jahnke, M. Kira, and S. W. Koch, “Nonlinear optics of normal-mode-coupling semiconductor microcavities,” Rev. Mod. Phys. 71, 1591–1639 (1999).
[CrossRef]

Kim, I.

O. J. Painter, A. Husain, A. Scherer, J. D. O’Brien, I. Kim, and P. D. Dapkus, “Room Temperature Photonic Crystal Defect Lasers at Near-Infrared Wavelengths in InGaAsP,” J. Lightwave Tech. 17, 2082–2088 (1999).
[CrossRef]

Kippenberg, T. J.

S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, “Ultralow-threshold Raman laser using spherical dielectric microcavity,” Nature 415, 621–623 (2002).
[CrossRef] [PubMed]

Kira, M.

G. Khitrova, H. M. Gibbs, F. Jahnke, M. Kira, and S. W. Koch, “Nonlinear optics of normal-mode-coupling semiconductor microcavities,” Rev. Mod. Phys. 71, 1591–1639 (1999).
[CrossRef]

Koch, S. W.

G. Khitrova, H. M. Gibbs, F. Jahnke, M. Kira, and S. W. Koch, “Nonlinear optics of normal-mode-coupling semiconductor microcavities,” Rev. Mod. Phys. 71, 1591–1639 (1999).
[CrossRef]

Kokubun, Y.

B. E. Little, S. T. Chu, W. Pan, D. Ripin, T. Kaneko, Y. Kokubun, and E. Ippen, “Vertically Coupled Glass Microring Resonator Channel Dropping Filters,” IEEE Photonics Tech. Lett. 11, 215–217 (1999).
[CrossRef]

Kolodziejaki, L. A.

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejaki, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
[CrossRef]

Krauss, T.

C. Smith, R. De la Rue, M. Rattier, S. Olivier, H. Benisty, C. Weisbuch, T. Krauss, U. Oesterlé, and R. Houdré, “Coupled guide and cavity in a two-dimensional photonic crystal,” Appl. Phys. Lett. 78, 1487–1489 (2001).
[CrossRef]

Lee, R. K.

Lee, Y. H.

J. L. Jewell, J. P. Harbison, A. Scherer, Y. H. Lee, and L. T. Florez, “Vertical-Cavity Surface-Emitting Lasers: Design, Growth, Fabrication, Characterization,” IEEE J. Quan. Elec. 27, 1332–1346 (1991).
[CrossRef]

Levi, A. F. J.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode lasers,” Appl. Phys. Lett. 60, 289–291 (1992).
[CrossRef]

Little, B. E.

B. E. Little, S. T. Chu, W. Pan, D. Ripin, T. Kaneko, Y. Kokubun, and E. Ippen, “Vertically Coupled Glass Microring Resonator Channel Dropping Filters,” IEEE Photonics Tech. Lett. 11, 215–217 (1999).
[CrossRef]

Logan, R. A.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode lasers,” Appl. Phys. Lett. 60, 289–291 (1992).
[CrossRef]

Loncar, M.

J. Vučković, M. Lončar, H. Mabuchi, and A. Scherer, “Design of photonic crystal microcavities for cavity QED,” Phys. Rev. E 65 (2002).

Mabuchi, H.

J. Vučković, M. Lončar, H. Mabuchi, and A. Scherer, “Design of photonic crystal microcavities for cavity QED,” Phys. Rev. E 65 (2002).

McCall, S. L.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode lasers,” Appl. Phys. Lett. 60, 289–291 (1992).
[CrossRef]

Meade, R. D.

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopou-los, “Donor and acceptor modes in photonic band-structure,” Phys. Rev. Lett. 67, 3380–3383 (1991).
[CrossRef] [PubMed]

Mekis, A.

S. G. Johnson, S. Fan, A. Mekis, and J. D. Joannopoulos, “Multipole-cancellation mechanism for high-Q cavities in the absence of a complete photonic bandgap,” Appl. Phys. Lett. 78, 3388–3390 (2001).
[CrossRef]

Noda, S.

S. Noda, A. Chutinan, and M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature 407, 608–610 (2000).
[CrossRef] [PubMed]

O’Brien, J. D.

O. Painter, K. Srinivasan, J. D. O’Brien, A. Scherer, and P. D. Dapkus, “Tailoring of the resonant mode properties of optical nanocavities in two-dimensional photonic crystal slab waveguides,” J. Opt. A 3, S161–S170 (2001).
[CrossRef]

O. J. Painter, A. Husain, A. Scherer, J. D. O’Brien, I. Kim, and P. D. Dapkus, “Room Temperature Photonic Crystal Defect Lasers at Near-Infrared Wavelengths in InGaAsP,” J. Lightwave Tech. 17, 2082–2088 (1999).
[CrossRef]

Oesterlé, U.

C. Smith, R. De la Rue, M. Rattier, S. Olivier, H. Benisty, C. Weisbuch, T. Krauss, U. Oesterlé, and R. Houdré, “Coupled guide and cavity in a two-dimensional photonic crystal,” Appl. Phys. Lett. 78, 1487–1489 (2001).
[CrossRef]

Olivier, S.

C. Smith, R. De la Rue, M. Rattier, S. Olivier, H. Benisty, C. Weisbuch, T. Krauss, U. Oesterlé, and R. Houdré, “Coupled guide and cavity in a two-dimensional photonic crystal,” Appl. Phys. Lett. 78, 1487–1489 (2001).
[CrossRef]

Painter, O.

O. Painter and K. Srinivasan, “Localized defect states in two-dimensional photonic crystal slab waveguides: a simple model based upon symmetry analysis,” submitted to Phys. Rev. B (2002).

O. Painter, K. Srinivasan, J. D. O’Brien, A. Scherer, and P. D. Dapkus, “Tailoring of the resonant mode properties of optical nanocavities in two-dimensional photonic crystal slab waveguides,” J. Opt. A 3, S161–S170 (2001).
[CrossRef]

O. Painter, J. Vučković, and A. Scherer, “Defect Modes of a Two-Dimensional Photonic Crystal in an Optically Thin Dielectric Slab,” J. Opt. Soc. Am. B 16, 275–285 (1999).
[CrossRef]

Painter, O. J.

O. J. Painter, A. Husain, A. Scherer, J. D. O’Brien, I. Kim, and P. D. Dapkus, “Room Temperature Photonic Crystal Defect Lasers at Near-Infrared Wavelengths in InGaAsP,” J. Lightwave Tech. 17, 2082–2088 (1999).
[CrossRef]

Pan, W.

B. E. Little, S. T. Chu, W. Pan, D. Ripin, T. Kaneko, Y. Kokubun, and E. Ippen, “Vertically Coupled Glass Microring Resonator Channel Dropping Filters,” IEEE Photonics Tech. Lett. 11, 215–217 (1999).
[CrossRef]

Pearton, S. J.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode lasers,” Appl. Phys. Lett. 60, 289–291 (1992).
[CrossRef]

Rappe, A. M.

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopou-los, “Donor and acceptor modes in photonic band-structure,” Phys. Rev. Lett. 67, 3380–3383 (1991).
[CrossRef] [PubMed]

Rattier, M.

C. Smith, R. De la Rue, M. Rattier, S. Olivier, H. Benisty, C. Weisbuch, T. Krauss, U. Oesterlé, and R. Houdré, “Coupled guide and cavity in a two-dimensional photonic crystal,” Appl. Phys. Lett. 78, 1487–1489 (2001).
[CrossRef]

Ripin, D.

B. E. Little, S. T. Chu, W. Pan, D. Ripin, T. Kaneko, Y. Kokubun, and E. Ippen, “Vertically Coupled Glass Microring Resonator Channel Dropping Filters,” IEEE Photonics Tech. Lett. 11, 215–217 (1999).
[CrossRef]

Roberts, P. J.

D. M. Atkin, P. S. J. Russell, T. A. Birks, and P. J. Roberts, “Photonic bandstructure of guided Bloch modes in high index films fully etched through with periodic microstructure,” J. Mod. Opt. 43, 1035–1053 (1996).
[CrossRef]

Russell, P. S. J.

D. M. Atkin, P. S. J. Russell, T. A. Birks, and P. J. Roberts, “Photonic bandstructure of guided Bloch modes in high index films fully etched through with periodic microstructure,” J. Mod. Opt. 43, 1035–1053 (1996).
[CrossRef]

Sakoda, K.

K. Sakoda, Optical Properties of Photonic Crystals (Springer-Verlag, Berlin, Germany, 2001).

Scherer, A.

J. Vučković, M. Lončar, H. Mabuchi, and A. Scherer, “Design of photonic crystal microcavities for cavity QED,” Phys. Rev. E 65 (2002).

T. Yoshie, J. Vučković, A. Scherer, H. Chen, and D. Deppe, “High quality two-dimensional photonic crystal slab cavities,” Appl. Phys. Lett. 79, 4289–4291 (2001).
[CrossRef]

O. Painter, K. Srinivasan, J. D. O’Brien, A. Scherer, and P. D. Dapkus, “Tailoring of the resonant mode properties of optical nanocavities in two-dimensional photonic crystal slab waveguides,” J. Opt. A 3, S161–S170 (2001).
[CrossRef]

O. Painter, J. Vučković, and A. Scherer, “Defect Modes of a Two-Dimensional Photonic Crystal in an Optically Thin Dielectric Slab,” J. Opt. Soc. Am. B 16, 275–285 (1999).
[CrossRef]

O. J. Painter, A. Husain, A. Scherer, J. D. O’Brien, I. Kim, and P. D. Dapkus, “Room Temperature Photonic Crystal Defect Lasers at Near-Infrared Wavelengths in InGaAsP,” J. Lightwave Tech. 17, 2082–2088 (1999).
[CrossRef]

A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, “Coupled-resonator optical waveguide: a proposal andanalysis,” Opt. Lett. 24, 711–713 (1999).
[CrossRef]

J. L. Jewell, J. P. Harbison, A. Scherer, Y. H. Lee, and L. T. Florez, “Vertical-Cavity Surface-Emitting Lasers: Design, Growth, Fabrication, Characterization,” IEEE J. Quan. Elec. 27, 1332–1346 (1991).
[CrossRef]

Slusher, R. E.

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode lasers,” Appl. Phys. Lett. 60, 289–291 (1992).
[CrossRef]

Smith, C.

C. Smith, R. De la Rue, M. Rattier, S. Olivier, H. Benisty, C. Weisbuch, T. Krauss, U. Oesterlé, and R. Houdré, “Coupled guide and cavity in a two-dimensional photonic crystal,” Appl. Phys. Lett. 78, 1487–1489 (2001).
[CrossRef]

Spillane, S. M.

S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, “Ultralow-threshold Raman laser using spherical dielectric microcavity,” Nature 415, 621–623 (2002).
[CrossRef] [PubMed]

Srinivasan, K.

O. Painter and K. Srinivasan, “Localized defect states in two-dimensional photonic crystal slab waveguides: a simple model based upon symmetry analysis,” submitted to Phys. Rev. B (2002).

O. Painter, K. Srinivasan, J. D. O’Brien, A. Scherer, and P. D. Dapkus, “Tailoring of the resonant mode properties of optical nanocavities in two-dimensional photonic crystal slab waveguides,” J. Opt. A 3, S161–S170 (2001).
[CrossRef]

Tinkham, M.

M. Tinkham, Group Theory and Quantum Mechanics, International Series in Pure and Applied Physics (McGaw-Hill, Inc., New York, NY, 1964).

Vahala, K. J.

S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, “Ultralow-threshold Raman laser using spherical dielectric microcavity,” Nature 415, 621–623 (2002).
[CrossRef] [PubMed]

Villeneuve, P. R.

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejaki, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
[CrossRef]

S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Channel drop filters in photonic crystals,” Opt. Express 3, 4–11 (1998), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-3-1-4.
[CrossRef] [PubMed]

Vuckovic, J.

J. Vučković, M. Lončar, H. Mabuchi, and A. Scherer, “Design of photonic crystal microcavities for cavity QED,” Phys. Rev. E 65 (2002).

T. Yoshie, J. Vučković, A. Scherer, H. Chen, and D. Deppe, “High quality two-dimensional photonic crystal slab cavities,” Appl. Phys. Lett. 79, 4289–4291 (2001).
[CrossRef]

O. Painter, J. Vučković, and A. Scherer, “Defect Modes of a Two-Dimensional Photonic Crystal in an Optically Thin Dielectric Slab,” J. Opt. Soc. Am. B 16, 275–285 (1999).
[CrossRef]

Weisbuch, C.

C. Smith, R. De la Rue, M. Rattier, S. Olivier, H. Benisty, C. Weisbuch, T. Krauss, U. Oesterlé, and R. Houdré, “Coupled guide and cavity in a two-dimensional photonic crystal,” Appl. Phys. Lett. 78, 1487–1489 (2001).
[CrossRef]

Xu, Y.

Yablonovitch, E.

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopou-los, “Donor and acceptor modes in photonic band-structure,” Phys. Rev. Lett. 67, 3380–3383 (1991).
[CrossRef] [PubMed]

Yariv, A.

Yokoyama, H.

H. Yokoyama, “Physics and Device Application of Optical Microcavities,” Science 256, 66–70 (1992).
[CrossRef] [PubMed]

Yoshie, T.

T. Yoshie, J. Vučković, A. Scherer, H. Chen, and D. Deppe, “High quality two-dimensional photonic crystal slab cavities,” Appl. Phys. Lett. 79, 4289–4291 (2001).
[CrossRef]

Appl. Phys. Lett. (4)

S. L. McCall, A. F. J. Levi, R. E. Slusher, S. J. Pearton, and R. A. Logan, “Whispering-gallery mode lasers,” Appl. Phys. Lett. 60, 289–291 (1992).
[CrossRef]

C. Smith, R. De la Rue, M. Rattier, S. Olivier, H. Benisty, C. Weisbuch, T. Krauss, U. Oesterlé, and R. Houdré, “Coupled guide and cavity in a two-dimensional photonic crystal,” Appl. Phys. Lett. 78, 1487–1489 (2001).
[CrossRef]

T. Yoshie, J. Vučković, A. Scherer, H. Chen, and D. Deppe, “High quality two-dimensional photonic crystal slab cavities,” Appl. Phys. Lett. 79, 4289–4291 (2001).
[CrossRef]

S. G. Johnson, S. Fan, A. Mekis, and J. D. Joannopoulos, “Multipole-cancellation mechanism for high-Q cavities in the absence of a complete photonic bandgap,” Appl. Phys. Lett. 78, 3388–3390 (2001).
[CrossRef]

IEEE J. Quan. Elec. (1)

J. L. Jewell, J. P. Harbison, A. Scherer, Y. H. Lee, and L. T. Florez, “Vertical-Cavity Surface-Emitting Lasers: Design, Growth, Fabrication, Characterization,” IEEE J. Quan. Elec. 27, 1332–1346 (1991).
[CrossRef]

IEEE Photonics Tech. Lett. (1)

B. E. Little, S. T. Chu, W. Pan, D. Ripin, T. Kaneko, Y. Kokubun, and E. Ippen, “Vertically Coupled Glass Microring Resonator Channel Dropping Filters,” IEEE Photonics Tech. Lett. 11, 215–217 (1999).
[CrossRef]

J. Lightwave Tech. (1)

O. J. Painter, A. Husain, A. Scherer, J. D. O’Brien, I. Kim, and P. D. Dapkus, “Room Temperature Photonic Crystal Defect Lasers at Near-Infrared Wavelengths in InGaAsP,” J. Lightwave Tech. 17, 2082–2088 (1999).
[CrossRef]

J. Mod. Opt. (1)

D. M. Atkin, P. S. J. Russell, T. A. Birks, and P. J. Roberts, “Photonic bandstructure of guided Bloch modes in high index films fully etched through with periodic microstructure,” J. Mod. Opt. 43, 1035–1053 (1996).
[CrossRef]

J. Opt. A (1)

O. Painter, K. Srinivasan, J. D. O’Brien, A. Scherer, and P. D. Dapkus, “Tailoring of the resonant mode properties of optical nanocavities in two-dimensional photonic crystal slab waveguides,” J. Opt. A 3, S161–S170 (2001).
[CrossRef]

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

Nature (2)

S. Noda, A. Chutinan, and M. Imada, “Trapping and emission of photons by a single defect in a photonic bandgap structure,” Nature 407, 608–610 (2000).
[CrossRef] [PubMed]

S. M. Spillane, T. J. Kippenberg, and K. J. Vahala, “Ultralow-threshold Raman laser using spherical dielectric microcavity,” Nature 415, 621–623 (2002).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. B (1)

S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejaki, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
[CrossRef]

Phys. Rev. E (1)

J. Vučković, M. Lončar, H. Mabuchi, and A. Scherer, “Design of photonic crystal microcavities for cavity QED,” Phys. Rev. E 65 (2002).

Phys. Rev. Lett. (1)

E. Yablonovitch, T. J. Gmitter, R. D. Meade, A. M. Rappe, K. D. Brommer, and J. D. Joannopou-los, “Donor and acceptor modes in photonic band-structure,” Phys. Rev. Lett. 67, 3380–3383 (1991).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

G. Khitrova, H. M. Gibbs, F. Jahnke, M. Kira, and S. W. Koch, “Nonlinear optics of normal-mode-coupling semiconductor microcavities,” Rev. Mod. Phys. 71, 1591–1639 (1999).
[CrossRef]

Science (1)

H. Yokoyama, “Physics and Device Application of Optical Microcavities,” Science 256, 66–70 (1992).
[CrossRef] [PubMed]

submitted to Phys. Rev. B (1)

O. Painter and K. Srinivasan, “Localized defect states in two-dimensional photonic crystal slab waveguides: a simple model based upon symmetry analysis,” submitted to Phys. Rev. B (2002).

Other (3)

This can be viewed in the far-field as elimination of lower-order multi-pole radiation components[23].

M. Tinkham, Group Theory and Quantum Mechanics, International Series in Pure and Applied Physics (McGaw-Hill, Inc., New York, NY, 1964).

K. Sakoda, Optical Properties of Photonic Crystals (Springer-Verlag, Berlin, Germany, 2001).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1.
Fig. 1.

2D hexagonal PC slab waveguide structure and cladding light cone.

Fig. 2.
Fig. 2.

Real and reciprocal space lattices of (a) a 2D hexagonal lattice, and(b) a 2D square lattice. For the hexagonal lattice: |a1| = |a2| = a, |G1| = |G2| = 4π/√3a, |k x | = 2π/√3a, |k J | = 4π/3a. For the square lattice: |a1| = |a2| = a, |G1| =|G2| = 2π/a, |k x | = π/a, |k M | = √2π/a.

Fig. 3.
Fig. 3.

Spatial FT of x-dipole donor mode in a hexagonal lattice (r/a = 0.30) with a central missing air hole. (a) in 2D, (b) along the ky direction with kx = 0.

Fig. 4.
Fig. 4.

Fundamental TE-like (even) guided mode bandstructure for hexagonal and square lattices, calculated using a 2D plane-wave expansion method with an effective index for the vertical guiding: (a) hexagonal lattice with r/a = 0.36, n slab = n eff = 2.65, (b) square lattice with r/a = 0.40, n slab = n eff = 2.65.

Fig. 5.
Fig. 5.

Illustration showing the mode coupling for the B e,d1 A 2 , mode in k-space through the Δη̃ perturbation.

Fig. 6.
Fig. 6.

Δη̃(k ) for dielectric structure of Table 7.

Fig. 7.
Fig. 7.

Properties of the graded square lattice.

Tables (8)

Tables Icon

Table 1. Symmetry classification and dominant Fourier components for the B-field of conduction band donor modes in a hexagonal lattice.

Tables Icon

Table 2. Symmetry classification and dominant Fourier components for the B-field of valence band acceptor modes in a hexagonal lattice.

Tables Icon

Table 3. Symmetry classification and dominant Fourier components for the B-field of conduction band donor modes in a square lattice.

Tables Icon

Table 4. Symmetry classification and dominant Fourier components for the B-field of valence band acceptor modes in a square lattice.

Tables Icon

Table 5. Candidate donor and acceptor modes in a square lattice.

Tables Icon

Table 6. Characteristics of the B a,a1 A2 resonant mode in a hexagonal lattice (images are for a PC cavity with r/a = 0.35, r′/a = 0.45, d/a = 0.75, and n slab = 3.4).

Tables Icon

Table 7. Characteristics of the B e,d1 A 2 resonant mode in a square lattice (images are for a PC cavity with r/a = 0.30, r′/a = 0.28, d/a = 0.75, and n slab = 3.4).

Tables Icon

Table 8. Field characteristics of graded square lattice shown in figure 7(a).

Equations (6)

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

B A 2 a , a 1 = z ̂ ( cos ( k J 1 r a ) + cos ( k J 3 r a ) + cos ( k J 5 r a ) ) ,
d 3 r ( H o lcm ( r ) ) * ( × ( Δ η ( r ) × H o d ( r ) ) ) ~ d 2 k ( 2 π ) 4 ( B ˜ z , o lcm ) * ( [ Δη ˜ ( k 2 B ˜ z , o d ) ]
+ [ ( k x Δ η ˜ ) ( k x B ˜ z , o d ) ] + [ ( k y Δ η ˜ ) ( k y B ˜ z , o d ) ] )
Δ η ˜ ( k x ( k 1 c + Δ x ) , k y ± k X 1 ( k 1 c + Δ y ) ) coupling to light cone ,
Δ η ˜ k x ± k X 2 Δ x , k y Δ y ) coupling to leaky M point .
Δ η ˜ ( k ) = F ( k ; r , r ) cos ( k y a 2 ) ,

Metrics