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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  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]
  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]
  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).
  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).
  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]
  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]
  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]
  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]
  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).
  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]
  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).
  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).
  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).
  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

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]

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]

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]

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]

2005 (3)

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]

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]

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)

J. Vučković and Y. Yamamoto, "Photonic crystal microcavities for cavity quantum electrodynamics with a single quantum dot," Appl. Phys. Lett. 82, 2374-2376 (2003).

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]

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]

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).

2002 (3)

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]

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).

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).

1999 (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]

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, 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).

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).

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]

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).

Appl. Phys. Lett. (2)

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]

J. Vučković and Y. Yamamoto, "Photonic crystal microcavities for cavity quantum electrodynamics with a single quantum dot," Appl. Phys. Lett. 82, 2374-2376 (2003).

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).
[CrossRef]

IEEE J. Quantum Electron. (3)

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).

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]

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).

IEEE J. Sel. Top. Quantum Electron. (1)

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).

IEEE Trans. Antennas Propagat. (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).

J. Comput. Phys. (1)

J. P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," J. Comput. Phys. 114, 185-200 (1994).
[CrossRef]

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

Nature (2)

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]

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).

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).
[CrossRef]

Opt. Express (3)

Phys. Rev. (1)

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

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).
[CrossRef]

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]

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]

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]

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]

Other (1)

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

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