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] [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 (3)

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).

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).
[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]

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)

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]

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. 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]

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).
[CrossRef]

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)

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]

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]

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] [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]

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
[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)

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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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