Abstract

We design photonic crystal microcavities in diamond films for applications in quantum information. Optimization of the cavity design by “gentle confinement” yields a high quality factor Q>66000 and small mode volume V≈1.1(λ/n)3. In view of experimental applications we consider the influence of material absorption on the cavity Q factors and present a simple interpretation in the framework of a one-dimensional cavity model.

© 2008 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
  3. R. Brouri, A. Beveratos, J.-Ph. Poizat, and P. Grangier, "Photon antibunching in the fluorescence of individual color centers in diamond," Opt. Lett. 25, 1294-1296 (2000).
    [CrossRef]
  4. F. Jelezko, T. Gaebel, I. Popa, A. Gruber, and J. Wrachtrup, "Observation of coherent oscillations in a single electron spin," Phys. Rev. Lett. 92, 076401 (2004).
    [CrossRef] [PubMed]
  5. F. Jelezko, T. Gaebel, I. Popa, M. Domhan, A. Gruber, and J. Wrachtrup, "Observation of coherent oscillation of a single nuclear spin and realization of a two-qubit conditional quantum gate," Phys. Rev. Lett. 93, 130501 (2004).
    [CrossRef] [PubMed]
  6. C. Santori, D. Fattal, S. M. Spillane, M. Fiorentino, R. G. Beausoleil, A. D. Greentree, P. Olivero, M. Draganski, J. R. Rabeau, P. Reichart, B.C. Gibson, S. Rubanov, D. N. Jamieson, and S. Prawer, "Coherent population trapping in diamond N-V centers at zero magnetic field," Opt. Express 14, 7986-7994 (2006).
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    [CrossRef]
  9. J. R. Rabeau, Y. L. Chin, S. Prawer, F. Jelezko, T. Gaebel, and J. Wrachtrup, "Fabrication of single nickel-nitrogen defects in diamond by chemical vapor deposition," Appl. Phys. Lett. 86, 131926 (2005).
    [CrossRef]
  10. E. Wu, V. Jacques, F. Treussart, H. Zeng, P. Grangier, and J.-F. Roch, "Single-photon emission in the near infrared from diamond colour centre," J. Lumin. 119-120, 19-23 (2006).
    [CrossRef]
  11. C. Wang, C. Kurtsiefer, H. Weinfurter, and B. Burchard, "Single photon emission from SiV centres in diamond produced by ion implantation," J. Phys. B: At. Mol. Opt. Phys. 39, 37-41 (2006).
    [CrossRef]
  12. L. Childress, J. M. Taylor, A. S. Sørensen, and M. D. Lukin, "Fault-tolerant quantum communication based on solid-state photon emitters," Phys. Rev. Lett. 96, 070504 (2006).
    [CrossRef] [PubMed]
  13. A. D. Greentree, J. Salzman, S. Prawer, and L. C. L. Hollenberg, "Quantum gate for Q-switching in monolithic photonic-band-gap cavities containing two-level atoms," Phys. Rev. A 73, 013818 (2006).
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  19. A. D. Greentree, P. Olivero, M. Draganski, E. Trajkov, J. R. Rabeau, P. Reichart, B. C. Gibson, S. Rubanov, S. T. Huntington, D. N. Jamieson, and S. Prawer, "Critical components for diamond-based quantum coherent devices," J. Phys.: Condens. Matter 18, S825-S842 (2006).
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    [CrossRef]
  22. C. F. Wang, Y-S. Choi, J. C. Lee, E. L. Hu, J. Yang, and J. E. Butler, "Observation of whispering gallery modes in nanocrystalline diamond microdisks," Appl. Phys. Lett. 90, 081110 (2007).
    [CrossRef]
  23. C. F. Wang, R. Hanson, D. D. Awschalom, E. L. Hu, T. Feygelson, J. Yang, and J. E. Butler, "Fabrication and characterization of two-dimensional photonic crystal microcavities in nanocrystalline diamond," Appl. Phys. Lett. 91, 201112 (2007).
    [CrossRef]
  24. Y. Akahane, T. Asano, B.-S. Song, and S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature (London) 425, 944-947 (2003).
    [CrossRef] [PubMed]
  25. Y. Akahane, T. Asano, B.-S. Song, and S. Noda, "Fine-tuned high-Q photonic-crystal nanocavity," Opt. Express 131202-1214 (2005).
    [CrossRef] [PubMed]
  26. P. Achatz, J. A. Garrido, M. Stutzmann, O. A. Williams, D. M. Gruen, A. Kromka, and D. Steinmuller, "Optical properties of nanocrystalline diamond thin films," Appl. Phys. Lett. 88, 101908 (2006).
    [CrossRef]
  27. J. P. Reithmaier, G. Se¸ k, A. Loffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, "Strong coupling in a single quantum dot semiconductor microcavity system," Nature (London) 432, 197-200 (2004).
    [CrossRef] [PubMed]
  28. T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, "Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity," Nature (London) 432, 200-203 (2004).
    [CrossRef] [PubMed]
  29. S. Johnson and J. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis," Opt. Express 8, 173-190 (2001).
    [CrossRef] [PubMed]
  30. K. Srinivasan and O. Painter, "Momentum space design of high-Q photonic crystal optical cavities," Opt. Express 10, 670-684 (2002).
    [PubMed]
  31. Z. Zhang and M. Qiu, "Small-volume waveguide-section high Q microcavities in 2D photonic crystal slabs," Opt. Express 12, 3988-3995 (2004).
    [CrossRef] [PubMed]
  32. B.-S. Song, S. Noda, T. Asano, and Y. Akahane, "Ultra-high-Q photonic double-heterostructure nanocavity," Nat. Maters. 4, 207-210 (2005).
    [CrossRef]
  33. D. Englund, I. Fushman, and J. Vuickoviic, "General recipe for designing photonic crystal cavities," Opt. Express 13, 5961-5975 (2005).
    [CrossRef] [PubMed]
  34. D. Englund and J. Vuickovic, "A direct analysis of photonic nanostructures," Opt. Express 14, 3472-3483 (2006).
    [CrossRef] [PubMed]
  35. A. Farjadpour, D. Roundy, A. Rodriguez, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, and G. W. Burr, "Improving accuracy by subpixel smoothing in the finite-difference time domain," Opt. Lett. 31, 2972-2974 (2006).
    [CrossRef] [PubMed]
  36. J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, "Optimization of the Q factor in photonic crystal microcavities," IEEE J. Quantum Electron. 38, 850-856 (2002).
    [CrossRef]
  37. I. Alvarado-Rodriguez and E. Yablonovitch, "Separation of radiation and absorption losses in two-dimensional photonic crystal single defect cavities," J. Appl. Phys. 92, 6399-6401 (2002).
    [CrossRef]
  38. T. Asano, B.-S. Song, and S. Noda, "Analysis of the experimental Q factors (~1 million) of photonic crystal nanocavities," Opt. Express 14, 1996-2002 (2006).
    [CrossRef] [PubMed]
  39. T. Xu, S. Yang, S. Selvakumar, V. Nair, and H.E. Ruda, "Nanowire-array-based photonic crystal cavity by finitedifference time-domain calculations," Phys. Rev. B 75, 125104 (2007).
    [CrossRef]

2007

I. Bayn and J. Salzman, "High-Q photonic crystal nanocavities on diamond for quantum electrodynamics," Eur. Phys. J. Appl. Phys. 37, 19-24 (2007).
[CrossRef]

C. F. Wang, Y-S. Choi, J. C. Lee, E. L. Hu, J. Yang, and J. E. Butler, "Observation of whispering gallery modes in nanocrystalline diamond microdisks," Appl. Phys. Lett. 90, 081110 (2007).
[CrossRef]

C. F. Wang, R. Hanson, D. D. Awschalom, E. L. Hu, T. Feygelson, J. Yang, and J. E. Butler, "Fabrication and characterization of two-dimensional photonic crystal microcavities in nanocrystalline diamond," Appl. Phys. Lett. 91, 201112 (2007).
[CrossRef]

T. Xu, S. Yang, S. Selvakumar, V. Nair, and H.E. Ruda, "Nanowire-array-based photonic crystal cavity by finitedifference time-domain calculations," Phys. Rev. B 75, 125104 (2007).
[CrossRef]

2006

T. Asano, B.-S. Song, and S. Noda, "Analysis of the experimental Q factors (~1 million) of photonic crystal nanocavities," Opt. Express 14, 1996-2002 (2006).
[CrossRef] [PubMed]

P. Achatz, J. A. Garrido, M. Stutzmann, O. A. Williams, D. M. Gruen, A. Kromka, and D. Steinmuller, "Optical properties of nanocrystalline diamond thin films," Appl. Phys. Lett. 88, 101908 (2006).
[CrossRef]

D. Englund and J. Vuickovic, "A direct analysis of photonic nanostructures," Opt. Express 14, 3472-3483 (2006).
[CrossRef] [PubMed]

A. Farjadpour, D. Roundy, A. Rodriguez, M. Ibanescu, P. Bermel, J. D. Joannopoulos, S. G. Johnson, and G. W. Burr, "Improving accuracy by subpixel smoothing in the finite-difference time domain," Opt. Lett. 31, 2972-2974 (2006).
[CrossRef] [PubMed]

J. Wrachtrup and F. Jelezko, "Processing quantum information in diamond," J. Phys.: Condens. Matter 18, S807- S824 (2006).
[CrossRef]

E. Wu, V. Jacques, F. Treussart, H. Zeng, P. Grangier, and J.-F. Roch, "Single-photon emission in the near infrared from diamond colour centre," J. Lumin. 119-120, 19-23 (2006).
[CrossRef]

C. Wang, C. Kurtsiefer, H. Weinfurter, and B. Burchard, "Single photon emission from SiV centres in diamond produced by ion implantation," J. Phys. B: At. Mol. Opt. Phys. 39, 37-41 (2006).
[CrossRef]

L. Childress, J. M. Taylor, A. S. Sørensen, and M. D. Lukin, "Fault-tolerant quantum communication based on solid-state photon emitters," Phys. Rev. Lett. 96, 070504 (2006).
[CrossRef] [PubMed]

A. D. Greentree, J. Salzman, S. Prawer, and L. C. L. Hollenberg, "Quantum gate for Q-switching in monolithic photonic-band-gap cavities containing two-level atoms," Phys. Rev. A 73, 013818 (2006).
[CrossRef]

Y. L. Lim, S. D. Barrett, A. Beige, P. Kok, and L. C. Kwek, "Repeat-until-success quantum computing using stationary and flying qubits," Phys. Rev. A 73, 012304 (2006).
[CrossRef]

A. D. Greentree, C. Tahan, J. H. Cole, and L. C. L. Hollenberg, "Quantum phase transitions of light," Nat. Phys. 2, 856-861 (2006).
[CrossRef]

C. Santori, D. Fattal, S. M. Spillane, M. Fiorentino, R. G. Beausoleil, A. D. Greentree, P. Olivero, M. Draganski, J. R. Rabeau, P. Reichart, B.C. Gibson, S. Rubanov, D. N. Jamieson, and S. Prawer, "Coherent population trapping in diamond N-V centers at zero magnetic field," Opt. Express 14, 7986-7994 (2006).
[CrossRef] [PubMed]

A. D. Greentree, P. Olivero, M. Draganski, E. Trajkov, J. R. Rabeau, P. Reichart, B. C. Gibson, S. Rubanov, S. T. Huntington, D. N. Jamieson, and S. Prawer, "Critical components for diamond-based quantum coherent devices," J. Phys.: Condens. Matter 18, S825-S842 (2006).
[CrossRef]

S. Tomljenovic-Hanic, M. J. Steel, C. Martijn de Sterke, and J. Salzman, "Diamond based photonic crystal microcavities," Opt. Express 14, 3556-3562 (2006).
[CrossRef] [PubMed]

2005

Y. L. Lim, A. Beige, and L. C. Kwek, "Repeat-until-success linear optics distributed quantum computing," Phys. Rev. Lett. 95, 030505 (2005).
[CrossRef] [PubMed]

J. R. Rabeau, Y. L. Chin, S. Prawer, F. Jelezko, T. Gaebel, and J. Wrachtrup, "Fabrication of single nickel-nitrogen defects in diamond by chemical vapor deposition," Appl. Phys. Lett. 86, 131926 (2005).
[CrossRef]

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, "Fine-tuned high-Q photonic-crystal nanocavity," Opt. Express 131202-1214 (2005).
[CrossRef] [PubMed]

B.-S. Song, S. Noda, T. Asano, and Y. Akahane, "Ultra-high-Q photonic double-heterostructure nanocavity," Nat. Maters. 4, 207-210 (2005).
[CrossRef]

D. Englund, I. Fushman, and J. Vuickoviic, "General recipe for designing photonic crystal cavities," Opt. Express 13, 5961-5975 (2005).
[CrossRef] [PubMed]

2004

Z. Zhang and M. Qiu, "Small-volume waveguide-section high Q microcavities in 2D photonic crystal slabs," Opt. Express 12, 3988-3995 (2004).
[CrossRef] [PubMed]

J. P. Reithmaier, G. Se¸ k, A. Loffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, "Strong coupling in a single quantum dot semiconductor microcavity system," Nature (London) 432, 197-200 (2004).
[CrossRef] [PubMed]

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, "Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity," Nature (London) 432, 200-203 (2004).
[CrossRef] [PubMed]

F. Jelezko, T. Gaebel, I. Popa, A. Gruber, and J. Wrachtrup, "Observation of coherent oscillations in a single electron spin," Phys. Rev. Lett. 92, 076401 (2004).
[CrossRef] [PubMed]

F. Jelezko, T. Gaebel, I. Popa, M. Domhan, A. Gruber, and J. Wrachtrup, "Observation of coherent oscillation of a single nuclear spin and realization of a two-qubit conditional quantum gate," Phys. Rev. Lett. 93, 130501 (2004).
[CrossRef] [PubMed]

T. Gaebel, I. Popa, A. Gruber, M. Domhan, F. Jelezko, and J. Wrachtrup, "Stable single-photon source in the near infrared," New J. Phys. 6, 98 (2004).
[CrossRef]

2003

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

2002

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

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, "Optimization of the Q factor in photonic crystal microcavities," IEEE J. Quantum Electron. 38, 850-856 (2002).
[CrossRef]

I. Alvarado-Rodriguez and E. Yablonovitch, "Separation of radiation and absorption losses in two-dimensional photonic crystal single defect cavities," J. Appl. Phys. 92, 6399-6401 (2002).
[CrossRef]

2001

S. Johnson and J. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis," Opt. Express 8, 173-190 (2001).
[CrossRef] [PubMed]

J. Vuickovic, M . Lonicar, H . Mabuchi, and A . Scherer, "Design of photonic crystal microcavities for cavity QED," Phys. Rev. E 65, 016608 (2001).
[CrossRef]

2000

C. Kurtsiefer, S. Mayer, P. Zarda, and H. Weinfurter, "Stable solid-state source of single photons," Phys. Rev. Lett. 85, 290-293 (2000).
[CrossRef] [PubMed]

R. Brouri, A. Beveratos, J.-Ph. Poizat, and P. Grangier, "Photon antibunching in the fluorescence of individual color centers in diamond," Opt. Lett. 25, 1294-1296 (2000).
[CrossRef]

1996

A.V. Turukhin, C.-H. Liu, A. A. Gorokhovsky, R. R. Alfano, and W. Phillips, "Picosecond photoluminescence decay of Si-doped chemical-vapor-deposited diamond films," Phys. Rev. B 54, 16448-16451 (1996).
[CrossRef]

Appl. Phys. Lett.

J. R. Rabeau, Y. L. Chin, S. Prawer, F. Jelezko, T. Gaebel, and J. Wrachtrup, "Fabrication of single nickel-nitrogen defects in diamond by chemical vapor deposition," Appl. Phys. Lett. 86, 131926 (2005).
[CrossRef]

C. F. Wang, Y-S. Choi, J. C. Lee, E. L. Hu, J. Yang, and J. E. Butler, "Observation of whispering gallery modes in nanocrystalline diamond microdisks," Appl. Phys. Lett. 90, 081110 (2007).
[CrossRef]

C. F. Wang, R. Hanson, D. D. Awschalom, E. L. Hu, T. Feygelson, J. Yang, and J. E. Butler, "Fabrication and characterization of two-dimensional photonic crystal microcavities in nanocrystalline diamond," Appl. Phys. Lett. 91, 201112 (2007).
[CrossRef]

P. Achatz, J. A. Garrido, M. Stutzmann, O. A. Williams, D. M. Gruen, A. Kromka, and D. Steinmuller, "Optical properties of nanocrystalline diamond thin films," Appl. Phys. Lett. 88, 101908 (2006).
[CrossRef]

Eur. Phys. J. Appl. Phys.

I. Bayn and J. Salzman, "High-Q photonic crystal nanocavities on diamond for quantum electrodynamics," Eur. Phys. J. Appl. Phys. 37, 19-24 (2007).
[CrossRef]

IEEE J. Quantum Electron.

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, "Optimization of the Q factor in photonic crystal microcavities," IEEE J. Quantum Electron. 38, 850-856 (2002).
[CrossRef]

J. Appl. Phys.

I. Alvarado-Rodriguez and E. Yablonovitch, "Separation of radiation and absorption losses in two-dimensional photonic crystal single defect cavities," J. Appl. Phys. 92, 6399-6401 (2002).
[CrossRef]

J. Lumin.

E. Wu, V. Jacques, F. Treussart, H. Zeng, P. Grangier, and J.-F. Roch, "Single-photon emission in the near infrared from diamond colour centre," J. Lumin. 119-120, 19-23 (2006).
[CrossRef]

J. Phys. B: At. Mol. Opt. Phys.

C. Wang, C. Kurtsiefer, H. Weinfurter, and B. Burchard, "Single photon emission from SiV centres in diamond produced by ion implantation," J. Phys. B: At. Mol. Opt. Phys. 39, 37-41 (2006).
[CrossRef]

J. Phys.: Condens. Matter

J. Wrachtrup and F. Jelezko, "Processing quantum information in diamond," J. Phys.: Condens. Matter 18, S807- S824 (2006).
[CrossRef]

A. D. Greentree, P. Olivero, M. Draganski, E. Trajkov, J. R. Rabeau, P. Reichart, B. C. Gibson, S. Rubanov, S. T. Huntington, D. N. Jamieson, and S. Prawer, "Critical components for diamond-based quantum coherent devices," J. Phys.: Condens. Matter 18, S825-S842 (2006).
[CrossRef]

Nat. Phys.

A. D. Greentree, C. Tahan, J. H. Cole, and L. C. L. Hollenberg, "Quantum phase transitions of light," Nat. Phys. 2, 856-861 (2006).
[CrossRef]

Nature (London)

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

J. P. Reithmaier, G. Se¸ k, A. Loffler, C. Hofmann, S. Kuhn, S. Reitzenstein, L. V. Keldysh, V. D. Kulakovskii, T. L. Reinecke, and A. Forchel, "Strong coupling in a single quantum dot semiconductor microcavity system," Nature (London) 432, 197-200 (2004).
[CrossRef] [PubMed]

T. Yoshie, A. Scherer, J. Hendrickson, G. Khitrova, H. M. Gibbs, G. Rupper, C. Ell, O. B. Shchekin, and D. G. Deppe, "Vacuum Rabi splitting with a single quantum dot in a photonic crystal nanocavity," Nature (London) 432, 200-203 (2004).
[CrossRef] [PubMed]

Nature Materials

B.-S. Song, S. Noda, T. Asano, and Y. Akahane, "Ultra-high-Q photonic double-heterostructure nanocavity," Nat. Maters. 4, 207-210 (2005).
[CrossRef]

New J. Phys.

T. Gaebel, I. Popa, A. Gruber, M. Domhan, F. Jelezko, and J. Wrachtrup, "Stable single-photon source in the near infrared," New J. Phys. 6, 98 (2004).
[CrossRef]

Opt. Express

C. Santori, D. Fattal, S. M. Spillane, M. Fiorentino, R. G. Beausoleil, A. D. Greentree, P. Olivero, M. Draganski, J. R. Rabeau, P. Reichart, B.C. Gibson, S. Rubanov, D. N. Jamieson, and S. Prawer, "Coherent population trapping in diamond N-V centers at zero magnetic field," Opt. Express 14, 7986-7994 (2006).
[CrossRef] [PubMed]

D. Englund, I. Fushman, and J. Vuickoviic, "General recipe for designing photonic crystal cavities," Opt. Express 13, 5961-5975 (2005).
[CrossRef] [PubMed]

D. Englund and J. Vuickovic, "A direct analysis of photonic nanostructures," Opt. Express 14, 3472-3483 (2006).
[CrossRef] [PubMed]

S. Johnson and J. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis," Opt. Express 8, 173-190 (2001).
[CrossRef] [PubMed]

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

Z. Zhang and M. Qiu, "Small-volume waveguide-section high Q microcavities in 2D photonic crystal slabs," Opt. Express 12, 3988-3995 (2004).
[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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Opt. Lett.

Phys. Rev. A

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[CrossRef]

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[CrossRef]

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Figures (8)

Fig. 1.
Fig. 1.

Gap map of TE-modes in a two-dimensional photonic crystal consisting of a lattice of air holes in diamond (ε=5.76, infinite extension in z-direction), as function of relative air hole radius. (a) square lattice, (b) triangular lattice. Black data points (squares): lower edge of fundamental band gap; red data points (circles): upper edge of fundamental band gap.

Fig. 2.
Fig. 2.

Projected band diagram of TE-like modes in a two-dimensional photonic crystal consisting of a triangular lattice of air holes in a diamond slab (ε=5.76). (a) Air hole radius R=0.4 a, slab thickness h=0.75 a (b) R=0.29 a, h=0.91 a. Also shown: light line (red) and frequency of optimized cavity mode (black line), see Sec.2.4.

Fig. 3.
Fig. 3.

Schematic layout of M1 cavity built around one missing air hole. Holes A are the air holes of the regular lattice with radius R, all other parameters are explained in the text.

Fig. 4.
Fig. 4.

Quality factor Q of the M1 cavity for variations of the next-neighbor hole dimensions and displacements. (a) Q vs. RB and d. Other parameters are: R=0.29 a, h=0.93 a, m=0, RC =0.23 a, RD =0.29 a. (b) Q vs. RC and m. Other parameters are: R=0.29 a, h=0.93 a, d=0.19 a, RB =0.25 a, RD =0.29 a.

Fig. 5.
Fig. 5.

(a) Electric field (Ex ) amplitude and (b) magnetic field (Hz ) amplitude of the optimized M1 cavity resonant mode in the center plane of the slab (z=0). Color scale: grey: diamond, white: air, blue and red: positive and negative field amplitudes, respectively.

Fig. 6.
Fig. 6.

k-space intensity distribution I for resonant mode of (a) optimized M1 cavity (parameter set III) and (b) non-optimized M1 cavity (parameters: R=0.28 a, h=0.77 a, d=0.21 a, RB =0.28 a, m=0, RC =0.22 a, RD =0.28 a, Q≈25000). The white circle shows the light cone boundary k k 0.

Fig. 7.
Fig. 7.

Real and imaginary part of model dielectric function used to introduce material absorption into FDTD calculations. Parameters (see eq. (4)) are: ε =5.76, ωc =0.384, γ=0.4, Δε=0.005. The dashed red line shows the frequency of the resonant cavity mode, the solid red curve the Gaussian frequency distribution of the source used to excite the cavity mode in the FDTD calculations.

Fig. 8.
Fig. 8.

Quality factor Q of M1 cavity (geometry given by parameter set II) vs. material absorption coefficient α. Black squares show Q-factors calculated from FDTD simulations including material losses. The solid curve is a plot of eqs. (6,9) with parameters nr =2.4 and λ=740 nm.

Tables (3)

Tables Icon

Table 1. M1 cavity parameters used as starting point for cavity optimization (Parameter Set I). Numbers are given in units of lattice constant a.

Tables Icon

Table 2. Second iteration of M1 cavity parameters (Parameter Set II). Numbers are given in units of lattice constant a.

Tables Icon

Table 3. M1 cavity parameters for optimum quality factor Q (Parameter Set III). Numbers are given in units of lattice constant a.

Equations (9)

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F = 3 Q 4 π 2 ( λ n ) 3 V ,
V = ε ( r ) E ( r ) 2 d 3 r max [ ε ( r ) E ( r ) 2 ] .
P k k 0 I dk x dk y with I = FT 2 ( H y ) + 1 η FT 2 ( E x ) 2 + FT 2 ( H x ) 1 η FT 2 ( E y ) 2
ε ( ω , r ) = ε ( r ) + ω c 2 Δ ε ω c 2 ω 2 i ω γ
α ( ω ) = k 0 n ω c 2 Δ ε ω γ ( ω c 2 ω 2 ) 2 + ω 2 γ 2
1 Q = 1 Q 0 + 1 Q abs
ϕ ( t ) = exp ( t τ c ) ϕ ( 0 ) exp ( ω t Q ) ϕ ( 0 ) .
ϕ abs ( t ) = exp ( α ω t k ) ϕ ( 0 ) exp ( ω t Q abs ) ϕ ( 0 ) .
Q abs = k α = n r 2 n i .

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