Abstract

We investigate the dependence of quality factor Q of dipole modes in photonic crystal H1-defect nanocavity on the slab thickness and observe an increase of Q even after closing of the photonic bandgap both in numerical simulation and experimentation. This counter intuitive behavior results from the weak coupling between the cavity mode and the 2nd-guided mode in the photonic crystal slab. This is confirmed by computing the overlap between them in the momentum space.

© 2008 Optical Society of America

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References

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  1. E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).
  2. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
    [Crossref] [PubMed]
  3. O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
    [Crossref] [PubMed]
  4. H. Y. Ryu, H. G. Park, and Y. H. Lee, “Two-dimensional photonic crystal semiconductor lasers: computational design, fabrication, and characterization,” IEEE J. Sel. Top. Quantum Electron. 8, 891–908 (2002).
    [Crossref]
  5. J. Vučković, M. Lončar, H. Mabuchi, and A. Scherer, “Optimization of the Q factor in photonic crystal microcavities,” IEEE J. Quantum Electron. 38, 850–856 (2002).
    [Crossref]
  6. D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vučković, “Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal,” Phys. Rev. Lett. 95, 013904 (2005).
    [Crossref] [PubMed]
  7. D. Englund and J. Vučković, “A direct analysis of photonic nanostructures,” Opt. Express 14, 3472–3483 (2006), http://www.opticsexpress.org/abstract.cfm?URI=oe-14-8-3472
    [Crossref] [PubMed]
  8. Y. Akahane, T. Asano, B. S. Song, and S. Noda, “High-Q photonic nanocavity in two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
    [Crossref] [PubMed]
  9. Y. Akahane, T. Asano, B. S. Song, and S. Noda, “Fine-tuned high-Q photonic-crystal nanocavity,” Opt. Express 13, 1202–1214 (2005), http://www.opticsexpress.org/abstract.cfm?URI=oe-13-4-1202
    [Crossref] [PubMed]
  10. J. Vučković and Y. Yamamoto, “Photonic crystal microcavities for cavity quantum electrodynamics with a single quantum dot,” Appl. Phys. Lett. 82, 2374–2376 (2003).
    [Crossref]
  11. H. G. Park, J. K. Hwang, J. Huh, H. Y. Ryu, S. H. Kim, J. S. Kim, and Y.H. Lee, “Characteristics of modified single-defect two-dimensional photonic crystal lasers,” IEEE J. Quantum Electron. 38, 1353–1365 (2002).
    [Crossref]
  12. B. S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nature Mat. 4, 207–210 (2005).
    [Crossref]
  13. E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, and T. Tanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88, 041112 (2006).
    [Crossref]
  14. 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), http://www.opticsexpress.org/abstract.cfm?URI=oe-14-5-1996
    [Crossref] [PubMed]
  15. T. Tanabe, M. Notomi, and E. Kuramochi, “Measurement of ultra-high-Q photonic crystal nanocavity using single-sideband frequency modulator,” Electron. Lett. 43, 187–188 (2007).
    [Crossref]
  16. S. G. Johnson, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
    [Crossref]
  17. T. M. Stace, G. J. Milburn, and C. H. W. Barnes, “Entangled two-photon source using biexciton emission of an asymmetric quantum dot in a cavity,” Phys. Rev. B 67, 085317 (2003).
    [Crossref]
  18. F. Troiani, J. I. Perea, and C. Tejedor, “Cavity-assisted generation of entangled photon pairs by a quantum-dot cascade decay,” Phys. Rev. B 74, 235310 (2006).
    [Crossref]
  19. K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propagat. AP-14, 302–307 (1966).
  20. J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
    [Crossref]
  21. O. Painter, J. Vučković, and A. Sherer, “Defect modes of a two-dimensional photonic crystal in an optically thin dielectric slab,” J. Opt. Soc. Am. B 16, 275–285 (1999).
    [Crossref]
  22. J. S. Foresi, P.R. Villeneuve, J. Ferrera, E.R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
    [Crossref]
  23. H. Y. Ryu, J. K. Hwang, and Y. H. Lee, “The smallest possible whispering-gallery-like mode in the square lattice photonic crystal slab single-defect cavity,” IEEE J. Quantum Electron. 39, 314–322 (2003).
    [Crossref]
  24. K. Srinivasan and O. Painter, “Momentum space design of high-Q photonic crystal optical cavities,” Opt. Express 10, 670–684 (2002), http://www.opticsexpress.org/ abstract.cfm?URI=oe-10-15-670
    [PubMed]

2007 (1)

T. Tanabe, M. Notomi, and E. Kuramochi, “Measurement of ultra-high-Q photonic crystal nanocavity using single-sideband frequency modulator,” Electron. Lett. 43, 187–188 (2007).
[Crossref]

2006 (4)

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, and T. Tanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88, 041112 (2006).
[Crossref]

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), http://www.opticsexpress.org/abstract.cfm?URI=oe-14-5-1996
[Crossref] [PubMed]

D. Englund and J. Vučković, “A direct analysis of photonic nanostructures,” Opt. Express 14, 3472–3483 (2006), http://www.opticsexpress.org/abstract.cfm?URI=oe-14-8-3472
[Crossref] [PubMed]

F. Troiani, J. I. Perea, and C. Tejedor, “Cavity-assisted generation of entangled photon pairs by a quantum-dot cascade decay,” Phys. Rev. B 74, 235310 (2006).
[Crossref]

2005 (3)

D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vučković, “Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal,” Phys. Rev. Lett. 95, 013904 (2005).
[Crossref] [PubMed]

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “Fine-tuned high-Q photonic-crystal nanocavity,” Opt. Express 13, 1202–1214 (2005), http://www.opticsexpress.org/abstract.cfm?URI=oe-13-4-1202
[Crossref] [PubMed]

B. S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nature Mat. 4, 207–210 (2005).
[Crossref]

2003 (4)

T. M. Stace, G. J. Milburn, and C. H. W. Barnes, “Entangled two-photon source using biexciton emission of an asymmetric quantum dot in a cavity,” Phys. Rev. B 67, 085317 (2003).
[Crossref]

J. Vučković and Y. Yamamoto, “Photonic crystal microcavities for cavity quantum electrodynamics with a single quantum dot,” Appl. Phys. Lett. 82, 2374–2376 (2003).
[Crossref]

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

H. Y. Ryu, J. K. Hwang, and Y. H. Lee, “The smallest possible whispering-gallery-like mode in the square lattice photonic crystal slab single-defect cavity,” IEEE J. Quantum Electron. 39, 314–322 (2003).
[Crossref]

2002 (4)

K. Srinivasan and O. Painter, “Momentum space design of high-Q photonic crystal optical cavities,” Opt. Express 10, 670–684 (2002), http://www.opticsexpress.org/ abstract.cfm?URI=oe-10-15-670
[PubMed]

H. Y. Ryu, H. G. Park, and Y. H. Lee, “Two-dimensional photonic crystal semiconductor lasers: computational design, fabrication, and characterization,” IEEE J. Sel. Top. Quantum Electron. 8, 891–908 (2002).
[Crossref]

J. Vučković, M. Lončar, H. Mabuchi, and A. Scherer, “Optimization of the Q factor in photonic crystal microcavities,” IEEE J. Quantum Electron. 38, 850–856 (2002).
[Crossref]

H. G. Park, J. K. Hwang, J. Huh, H. Y. Ryu, S. H. Kim, J. S. Kim, and Y.H. Lee, “Characteristics of modified single-defect two-dimensional photonic crystal lasers,” IEEE J. Quantum Electron. 38, 1353–1365 (2002).
[Crossref]

1999 (3)

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

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[Crossref] [PubMed]

O. Painter, J. Vučković, and A. Sherer, “Defect modes of a two-dimensional photonic crystal in an optically thin dielectric slab,” J. Opt. Soc. Am. B 16, 275–285 (1999).
[Crossref]

1997 (1)

J. S. Foresi, P.R. Villeneuve, J. Ferrera, E.R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
[Crossref]

1994 (1)

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
[Crossref]

1987 (1)

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

1966 (1)

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propagat. AP-14, 302–307 (1966).

1946 (1)

E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).

Akahane, Y.

B. S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nature Mat. 4, 207–210 (2005).
[Crossref]

Y. Akahane, T. Asano, B. S. Song, and S. Noda, “Fine-tuned high-Q photonic-crystal nanocavity,” Opt. Express 13, 1202–1214 (2005), http://www.opticsexpress.org/abstract.cfm?URI=oe-13-4-1202
[Crossref] [PubMed]

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

Arakawa, Y.

D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vučković, “Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal,” Phys. Rev. Lett. 95, 013904 (2005).
[Crossref] [PubMed]

Asano, T.

Barnes, C. H. W.

T. M. Stace, G. J. Milburn, and C. H. W. Barnes, “Entangled two-photon source using biexciton emission of an asymmetric quantum dot in a cavity,” Phys. Rev. B 67, 085317 (2003).
[Crossref]

Berenger, J. P.

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comput. Phys. 114, 185–200 (1994).
[Crossref]

Dapkus, P. D.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[Crossref] [PubMed]

Englund, D.

D. Englund and J. Vučković, “A direct analysis of photonic nanostructures,” Opt. Express 14, 3472–3483 (2006), http://www.opticsexpress.org/abstract.cfm?URI=oe-14-8-3472
[Crossref] [PubMed]

D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vučković, “Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal,” Phys. Rev. Lett. 95, 013904 (2005).
[Crossref] [PubMed]

Fan, S.

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

J. S. Foresi, P.R. Villeneuve, J. Ferrera, E.R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
[Crossref]

Fattal, D.

D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vučković, “Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal,” Phys. Rev. Lett. 95, 013904 (2005).
[Crossref] [PubMed]

Ferrera, J.

J. S. Foresi, P.R. Villeneuve, J. Ferrera, E.R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
[Crossref]

Foresi, J. S.

J. S. Foresi, P.R. Villeneuve, J. Ferrera, E.R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
[Crossref]

Huh, J.

H. G. Park, J. K. Hwang, J. Huh, H. Y. Ryu, S. H. Kim, J. S. Kim, and Y.H. Lee, “Characteristics of modified single-defect two-dimensional photonic crystal lasers,” IEEE J. Quantum Electron. 38, 1353–1365 (2002).
[Crossref]

Hwang, J. K.

H. Y. Ryu, J. K. Hwang, and Y. H. Lee, “The smallest possible whispering-gallery-like mode in the square lattice photonic crystal slab single-defect cavity,” IEEE J. Quantum Electron. 39, 314–322 (2003).
[Crossref]

H. G. Park, J. K. Hwang, J. Huh, H. Y. Ryu, S. H. Kim, J. S. Kim, and Y.H. Lee, “Characteristics of modified single-defect two-dimensional photonic crystal lasers,” IEEE J. Quantum Electron. 38, 1353–1365 (2002).
[Crossref]

Ippen, E. P.

J. S. Foresi, P.R. Villeneuve, J. Ferrera, E.R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
[Crossref]

Joannopoulos, J. D.

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

J. S. Foresi, P.R. Villeneuve, J. Ferrera, E.R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
[Crossref]

Johnson, S. G.

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

Kim, I.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[Crossref] [PubMed]

Kim, J. S.

H. G. Park, J. K. Hwang, J. Huh, H. Y. Ryu, S. H. Kim, J. S. Kim, and Y.H. Lee, “Characteristics of modified single-defect two-dimensional photonic crystal lasers,” IEEE J. Quantum Electron. 38, 1353–1365 (2002).
[Crossref]

Kim, S. H.

H. G. Park, J. K. Hwang, J. Huh, H. Y. Ryu, S. H. Kim, J. S. Kim, and Y.H. Lee, “Characteristics of modified single-defect two-dimensional photonic crystal lasers,” IEEE J. Quantum Electron. 38, 1353–1365 (2002).
[Crossref]

Kimerling, L. C.

J. S. Foresi, P.R. Villeneuve, J. Ferrera, E.R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
[Crossref]

Kuramochi, E.

T. Tanabe, M. Notomi, and E. Kuramochi, “Measurement of ultra-high-Q photonic crystal nanocavity using single-sideband frequency modulator,” Electron. Lett. 43, 187–188 (2007).
[Crossref]

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, and T. Tanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88, 041112 (2006).
[Crossref]

Lee, R. K.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[Crossref] [PubMed]

Lee, Y. H.

H. Y. Ryu, J. K. Hwang, and Y. H. Lee, “The smallest possible whispering-gallery-like mode in the square lattice photonic crystal slab single-defect cavity,” IEEE J. Quantum Electron. 39, 314–322 (2003).
[Crossref]

H. Y. Ryu, H. G. Park, and Y. H. Lee, “Two-dimensional photonic crystal semiconductor lasers: computational design, fabrication, and characterization,” IEEE J. Sel. Top. Quantum Electron. 8, 891–908 (2002).
[Crossref]

Lee, Y.H.

H. G. Park, J. K. Hwang, J. Huh, H. Y. Ryu, S. H. Kim, J. S. Kim, and Y.H. Lee, “Characteristics of modified single-defect two-dimensional photonic crystal lasers,” IEEE J. Quantum Electron. 38, 1353–1365 (2002).
[Crossref]

Loncar, M.

J. Vučković, M. Lončar, H. Mabuchi, and A. Scherer, “Optimization of the Q factor in photonic crystal microcavities,” IEEE J. Quantum Electron. 38, 850–856 (2002).
[Crossref]

Mabuchi, H.

J. Vučković, M. Lončar, H. Mabuchi, and A. Scherer, “Optimization of the Q factor in photonic crystal microcavities,” IEEE J. Quantum Electron. 38, 850–856 (2002).
[Crossref]

Milburn, G. J.

T. M. Stace, G. J. Milburn, and C. H. W. Barnes, “Entangled two-photon source using biexciton emission of an asymmetric quantum dot in a cavity,” Phys. Rev. B 67, 085317 (2003).
[Crossref]

Mitsugi, S.

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, and T. Tanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88, 041112 (2006).
[Crossref]

Nakaoka, T.

D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vučković, “Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal,” Phys. Rev. Lett. 95, 013904 (2005).
[Crossref] [PubMed]

Noda, S.

Notomi, M.

T. Tanabe, M. Notomi, and E. Kuramochi, “Measurement of ultra-high-Q photonic crystal nanocavity using single-sideband frequency modulator,” Electron. Lett. 43, 187–188 (2007).
[Crossref]

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, and T. Tanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88, 041112 (2006).
[Crossref]

O’Brien, J. D.

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[Crossref] [PubMed]

Painter, O.

Park, H. G.

H. Y. Ryu, H. G. Park, and Y. H. Lee, “Two-dimensional photonic crystal semiconductor lasers: computational design, fabrication, and characterization,” IEEE J. Sel. Top. Quantum Electron. 8, 891–908 (2002).
[Crossref]

H. G. Park, J. K. Hwang, J. Huh, H. Y. Ryu, S. H. Kim, J. S. Kim, and Y.H. Lee, “Characteristics of modified single-defect two-dimensional photonic crystal lasers,” IEEE J. Quantum Electron. 38, 1353–1365 (2002).
[Crossref]

Perea, J. I.

F. Troiani, J. I. Perea, and C. Tejedor, “Cavity-assisted generation of entangled photon pairs by a quantum-dot cascade decay,” Phys. Rev. B 74, 235310 (2006).
[Crossref]

Purcell, E. M.

E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).

Ryu, H. Y.

H. Y. Ryu, J. K. Hwang, and Y. H. Lee, “The smallest possible whispering-gallery-like mode in the square lattice photonic crystal slab single-defect cavity,” IEEE J. Quantum Electron. 39, 314–322 (2003).
[Crossref]

H. Y. Ryu, H. G. Park, and Y. H. Lee, “Two-dimensional photonic crystal semiconductor lasers: computational design, fabrication, and characterization,” IEEE J. Sel. Top. Quantum Electron. 8, 891–908 (2002).
[Crossref]

H. G. Park, J. K. Hwang, J. Huh, H. Y. Ryu, S. H. Kim, J. S. Kim, and Y.H. Lee, “Characteristics of modified single-defect two-dimensional photonic crystal lasers,” IEEE J. Quantum Electron. 38, 1353–1365 (2002).
[Crossref]

Scherer, A.

J. Vučković, M. Lončar, H. Mabuchi, and A. Scherer, “Optimization of the Q factor in photonic crystal microcavities,” IEEE J. Quantum Electron. 38, 850–856 (2002).
[Crossref]

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[Crossref] [PubMed]

Sherer, A.

Shinya, A.

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, and T. Tanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88, 041112 (2006).
[Crossref]

Smith, H. I.

J. S. Foresi, P.R. Villeneuve, J. Ferrera, E.R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
[Crossref]

Solomon, G.

D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vučković, “Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal,” Phys. Rev. Lett. 95, 013904 (2005).
[Crossref] [PubMed]

Song, B. S.

Srinivasan, K.

Stace, T. M.

T. M. Stace, G. J. Milburn, and C. H. W. Barnes, “Entangled two-photon source using biexciton emission of an asymmetric quantum dot in a cavity,” Phys. Rev. B 67, 085317 (2003).
[Crossref]

Steinmeyer, G.

J. S. Foresi, P.R. Villeneuve, J. Ferrera, E.R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
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E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, and T. Tanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88, 041112 (2006).
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F. Troiani, J. I. Perea, and C. Tejedor, “Cavity-assisted generation of entangled photon pairs by a quantum-dot cascade decay,” Phys. Rev. B 74, 235310 (2006).
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Thoen, E.R.

J. S. Foresi, P.R. Villeneuve, J. Ferrera, E.R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
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F. Troiani, J. I. Perea, and C. Tejedor, “Cavity-assisted generation of entangled photon pairs by a quantum-dot cascade decay,” Phys. Rev. B 74, 235310 (2006).
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J. S. Foresi, P.R. Villeneuve, J. Ferrera, E.R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
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D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vučković, “Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal,” Phys. Rev. Lett. 95, 013904 (2005).
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D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vučković, “Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal,” Phys. Rev. Lett. 95, 013904 (2005).
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Appl. Phys. Lett. (2)

J. Vučković and Y. Yamamoto, “Photonic crystal microcavities for cavity quantum electrodynamics with a single quantum dot,” Appl. Phys. Lett. 82, 2374–2376 (2003).
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E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, and T. Tanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88, 041112 (2006).
[Crossref]

Electron. Lett. (1)

T. Tanabe, M. Notomi, and E. Kuramochi, “Measurement of ultra-high-Q photonic crystal nanocavity using single-sideband frequency modulator,” Electron. Lett. 43, 187–188 (2007).
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IEEE J. Quantum Electron. (3)

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H. Y. Ryu, H. G. Park, and Y. H. Lee, “Two-dimensional photonic crystal semiconductor lasers: computational design, fabrication, and characterization,” IEEE J. Sel. Top. Quantum Electron. 8, 891–908 (2002).
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IEEE Trans. Antennas Propagat. (1)

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J. S. Foresi, P.R. Villeneuve, J. Ferrera, E.R. Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
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Nature Mat. (1)

B. S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nature Mat. 4, 207–210 (2005).
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Opt. Express (4)

Phys. Rev. (1)

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Phys. Rev. B (3)

S. G. Johnson, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
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T. M. Stace, G. J. Milburn, and C. H. W. Barnes, “Entangled two-photon source using biexciton emission of an asymmetric quantum dot in a cavity,” Phys. Rev. B 67, 085317 (2003).
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F. Troiani, J. I. Perea, and C. Tejedor, “Cavity-assisted generation of entangled photon pairs by a quantum-dot cascade decay,” Phys. Rev. B 74, 235310 (2006).
[Crossref]

Phys. Rev. Lett. (2)

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

D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vučković, “Controlling the spontaneous emission rate of single quantum dots in a two-dimensional photonic crystal,” Phys. Rev. Lett. 95, 013904 (2005).
[Crossref] [PubMed]

Science (1)

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[Crossref] [PubMed]

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Figures (7)

Fig. 1.
Fig. 1.

Field distributions at the center of the slab of (a) Ey component of x-dipole mode and (b) Ex component of y-dipole mode. The circular lines show boundaries of air holes.

Fig. 2.
Fig. 2.

Dependence of Q-factor on slab thickness for the x-dipole mode in H1-defect cavity with r=0.40a. The total Q-factor (square), the vertical Q-factor (circle) and the in-plane Q-factor (triangle) are plotted separately.

Fig. 3.
Fig. 3.

Band diagram for the structure with d=1.35a and r=0.40a. The x-dipole mode with normalized frequency of 0.292 overlaps with the 2nd-guided mode.

Fig. 4.
Fig. 4.

Ey -field distributions in momentum space for the cavity mode in the cavities with (a) d=1.35a and (b) d=1.75a including light lines (solid circles) and EFC of 2nd-guided modes at the cavity mode frequencies (dotted circles). (c) Q and amounts of overlap between the cavity mode and the EFC of the 2nd-guided mode of each structure with the slab thickness from 1.20 to 1.75a.

Fig. 5.
Fig. 5.

(a) Scanning electron micrograph of the fabricated H1-defect nanocavity with the slab thickness of 390 nm viewed in (a) Cross sectional view and (b) Top view.

Fig. 6.
Fig. 6.

PL spectra from the PCS nanocavities with d=1.345a and the polarization dependence of the dipole modes.

Fig. 7.
Fig. 7.

Dependence of measured-Q (square) on slab thickness compared with calculated-Q (triangle) for (a) x-dipole mode and (b) y-dipole mode.

Equations (4)

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

U ( t ) = U ( 0 ) exp [ ( ω t ) Q ] ,
1 Q total = 1 Q + 1 Q = P ω U + P ω U = P ω U ,
V eff = ε ( r ) E ( r ) 2 dV max [ ε ( r ) E ( r ) 2 ] ,
n eff = ε ( r ) E ( r ) 2 dV E ( r ) 2 dV ,

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