Abstract

We demonstrate new types of dielectric-band photonic crystal lasers in a two-dimensional modified single-cell cavity with enlarged air holes. Finite-difference time-domain simulations performed in real and Fourier spaces show that the dielectric-band cavity modes originating from the first band edge point in the dielectric band have mode patterns that are distinguishable from conventional air-band cavity modes. In our experiment, the observed multimode lasing peaks are identified as the hexapole and the monopole dielectric-band cavity modes through the spectral positions and mode images. The thresholds of these lasers are measured as ~340 μW and ~450 μW, respectively, at room temperature. In addition, using the simulation based on the actual fabricated structures, quality factors and mode volumes are computed as 4900 and 1.09 (λ/n)3 for the hexapole mode, and 4300 and 2.27 (λ/n)3 for the monopole mode, respectively.

© 2009 Optical Society of America

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  1. Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
    [Crossref] [PubMed]
  2. B.-S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nature Mater.  4, 207–210 (2005).
    [Crossref]
  3. T. Tanabe, A. Shinya, E. Kuramochi, S. Kondo, H. Taniyama, and M. Notomi, “Single point defect photonic crystal nanocavity with ultrahigh quality factor achieved by using hexapole mode,” Appl. Phys. Lett.  91, 021110 (2007).
    [Crossref]
  4. K. Nozaki and T. Baba, “Laser characteristics with ultimate-small modal volume in photonic crystal slab point-shift nanolasers,” Appl. Phys. Lett.  88, 211101 (2006).
    [Crossref]
  5. H.-S. Ee, K.-Y. Jeong, M.-K. Seo, Y.-H. Lee, and H.-G. Park, “Ultrasmall square-lattice zero-cell photonic crystal laser,” Appl. Phys. Lett.  93, 011104 (2008).
    [Crossref]
  6. G.-H. Kim, Y.-H. Lee, A. Shinya, and M. Notomi, “Coupling of small, low-loss hexapole mode with photonic crystal slab waveguide mode,” Opt. Express 12, 6624–6631 (2004).
    [Crossref] [PubMed]
  7. S.-H. Kwon, T. Sünner, M. Kamp, and A. Forchel, “Ultrahigh-Q photonic crystal cavity created by modulating air hole radius of a waveguide,” Opt. Express 16, 4605–4614 (2008).
    [Crossref] [PubMed]
  8. H.-G. Park, C. J. Barrelet, Y. Wu, B. Tian, F. Qian, and C. M. Lieber, “A wavelength-selective photonic-crystal waveguide coupled to a nanowire light source,” Nature Photonics 2, 622–626 (2008).
    [Crossref]
  9. T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, and E. Kuramochi, “Fast bistable all-optical switch and memory on a silicon photonic crystal on-chip,” Opt. Lett.  30, 2575–2577 (2005).
    [Crossref] [PubMed]
  10. J. M. Gerard and B. Gayral, “Toward high-efficiency quantum-dot single-photon sources,” Proc. SPIE 5361, 88 (2004).
    [Crossref]
  11. 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 432, 200–203 (2004).
    [Crossref] [PubMed]
  12. J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University Press, New Jersey, 2008).
  13. H.-G. Park, S.-H. Kim, S.-H. Kwon, Y.-G. Ju, J.-K. Yang, J.-H. Baek, S.-B. Kim, and Y.-H. Lee, “Electrically Driven Single-Cell Photonic Crystal Laser,” Science 305, 1444–1447 (2004).
    [Crossref] [PubMed]
  14. K. Srinivasan and O. Painter, “Momentum space design of high-Q photonic crystal optical cavities,” Opt. Express 10, 670–684 (2002).
    [PubMed]
  15. K. Srinivasan and O. Painter, “Fourier space design of high-Q cavities in standard and compressed hexagonal lattice photonic crystals,” Opt. Express 11, 579–593 (2003).
    [Crossref] [PubMed]
  16. Z. Zhang and M. Qiu, “Compact in-plane channel drop filter design using a single cavity with two degenerate modes in 2D photonic crystal slabs,” Opt. Express 13, 2596–2604 (2005).
    [Crossref] [PubMed]
  17. D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vuckovic, “Controlling the Spontaneous Emission Rate of Single Quantum Dots in a Two-Dimensional Photonic Crystal,” Phys. Rev. Lett.  95, 013904 (2005).
    [Crossref] [PubMed]
  18. This single-cell cavity is advantageous to the demonstration of the electrically driven laser by introducing a small central post underneath the cavity.
  19. K. Srinivasan, P. E. Barclay, and O. Painter, “Fabrication-tolerant high quality factor photonic crystal microcavities,” Opt. Express 12, 1458–1463 (2004).
    [Crossref] [PubMed]
  20. 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]
  21. S.-H. Kim and Y.-H. Lee, “Symmetry Relations of Two-Dimensional Photonic Crystal Cavity Modes,” IEEE J. Quantum Electron.  39, 1081–1085 (2003).
    [Crossref]
  22. S.-H. Kim, S.-K. Kim, and Y.-H. Lee, “Vertical beaming of wavelength-scale photonic crystal resonators,” Phys. Rev. B  73, 235117 (2006).
    [Crossref]
  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 band gap,” Appl. Phys. Lett.  78, 3388–3390 (2001).
    [Crossref]
  24. H.-Y. Ryu, M. Notomi, and Y.-H. Lee, “High-quality-factor and small-mode-volume hexapole modes in photonic-crystal-slab nanocavities,” Appl. Phys. Lett.  83, 4294–4296 (2003).
    [Crossref]
  25. S.-H. Kwon, S.-H. Kim, S.-K. Kim, and Y.-H. Lee, “Small, low-loss heterogeneous photonic bandedge laser,” Opt. Express 12, 5356–5361 (2004).
    [Crossref] [PubMed]
  26. A higher-order band edge mode with the wavelength of 1597 nm is observed in Fig. 7(a) (D).
  27. S.-K. Kim, G.-H. Kim, S.-H. Kim, S.-B. Kim, I. Kim, and Y.-H. Lee, “Loss management using parity-selective barriers for single-mode, single-cell photonic crystal resonators,” Appl. Phys. Lett.  88, 161119 (2006).
    [Crossref]
  28. D. Englund and J. Vuckovic, “A direct analysis of photonic nanostructures,” Opt. Express 14, 3472–3483 (2006).
    [Crossref] [PubMed]
  29. The band edge laser is observed with more increased pumping power. Threshold of the band edge laser is ~650 μW in the PhC cavity of Fig. 6.
  30. M.-K. Seo, H.-G. Park, J.-K. Yang, J.-Y. Kim, S.-H. Kim, and Y.-H. Lee, “Controlled sub-nanometer tuning of photonic crystal resonator by carbonaceous nano-dots,” Opt. Express 16, 9829–9837 (2008).
    [Crossref] [PubMed]

2008 (4)

H.-G. Park, C. J. Barrelet, Y. Wu, B. Tian, F. Qian, and C. M. Lieber, “A wavelength-selective photonic-crystal waveguide coupled to a nanowire light source,” Nature Photonics 2, 622–626 (2008).
[Crossref]

H.-S. Ee, K.-Y. Jeong, M.-K. Seo, Y.-H. Lee, and H.-G. Park, “Ultrasmall square-lattice zero-cell photonic crystal laser,” Appl. Phys. Lett.  93, 011104 (2008).
[Crossref]

S.-H. Kwon, T. Sünner, M. Kamp, and A. Forchel, “Ultrahigh-Q photonic crystal cavity created by modulating air hole radius of a waveguide,” Opt. Express 16, 4605–4614 (2008).
[Crossref] [PubMed]

M.-K. Seo, H.-G. Park, J.-K. Yang, J.-Y. Kim, S.-H. Kim, and Y.-H. Lee, “Controlled sub-nanometer tuning of photonic crystal resonator by carbonaceous nano-dots,” Opt. Express 16, 9829–9837 (2008).
[Crossref] [PubMed]

2007 (1)

T. Tanabe, A. Shinya, E. Kuramochi, S. Kondo, H. Taniyama, and M. Notomi, “Single point defect photonic crystal nanocavity with ultrahigh quality factor achieved by using hexapole mode,” Appl. Phys. Lett.  91, 021110 (2007).
[Crossref]

2006 (5)

K. Nozaki and T. Baba, “Laser characteristics with ultimate-small modal volume in photonic crystal slab point-shift nanolasers,” Appl. Phys. Lett.  88, 211101 (2006).
[Crossref]

S.-H. Kim, S.-K. Kim, and Y.-H. Lee, “Vertical beaming of wavelength-scale photonic crystal resonators,” Phys. Rev. B  73, 235117 (2006).
[Crossref]

S.-K. Kim, G.-H. Kim, S.-H. Kim, S.-B. Kim, I. Kim, and Y.-H. Lee, “Loss management using parity-selective barriers for single-mode, single-cell photonic crystal resonators,” Appl. Phys. Lett.  88, 161119 (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).
[Crossref] [PubMed]

D. Englund and J. Vuckovic, “A direct analysis of photonic nanostructures,” Opt. Express 14, 3472–3483 (2006).
[Crossref] [PubMed]

2005 (4)

Z. Zhang and M. Qiu, “Compact in-plane channel drop filter design using a single cavity with two degenerate modes in 2D photonic crystal slabs,” Opt. Express 13, 2596–2604 (2005).
[Crossref] [PubMed]

D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vuckovic, “Controlling the Spontaneous Emission Rate of Single Quantum Dots in a Two-Dimensional Photonic Crystal,” Phys. Rev. Lett.  95, 013904 (2005).
[Crossref] [PubMed]

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

T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, and E. Kuramochi, “Fast bistable all-optical switch and memory on a silicon photonic crystal on-chip,” Opt. Lett.  30, 2575–2577 (2005).
[Crossref] [PubMed]

2004 (6)

J. M. Gerard and B. Gayral, “Toward high-efficiency quantum-dot single-photon sources,” Proc. SPIE 5361, 88 (2004).
[Crossref]

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 432, 200–203 (2004).
[Crossref] [PubMed]

H.-G. Park, S.-H. Kim, S.-H. Kwon, Y.-G. Ju, J.-K. Yang, J.-H. Baek, S.-B. Kim, and Y.-H. Lee, “Electrically Driven Single-Cell Photonic Crystal Laser,” Science 305, 1444–1447 (2004).
[Crossref] [PubMed]

G.-H. Kim, Y.-H. Lee, A. Shinya, and M. Notomi, “Coupling of small, low-loss hexapole mode with photonic crystal slab waveguide mode,” Opt. Express 12, 6624–6631 (2004).
[Crossref] [PubMed]

K. Srinivasan, P. E. Barclay, and O. Painter, “Fabrication-tolerant high quality factor photonic crystal microcavities,” Opt. Express 12, 1458–1463 (2004).
[Crossref] [PubMed]

S.-H. Kwon, S.-H. Kim, S.-K. Kim, and Y.-H. Lee, “Small, low-loss heterogeneous photonic bandedge laser,” Opt. Express 12, 5356–5361 (2004).
[Crossref] [PubMed]

2003 (4)

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

S.-H. Kim and Y.-H. Lee, “Symmetry Relations of Two-Dimensional Photonic Crystal Cavity Modes,” IEEE J. Quantum Electron.  39, 1081–1085 (2003).
[Crossref]

H.-Y. Ryu, M. Notomi, and Y.-H. Lee, “High-quality-factor and small-mode-volume hexapole modes in photonic-crystal-slab nanocavities,” Appl. Phys. Lett.  83, 4294–4296 (2003).
[Crossref]

K. Srinivasan and O. Painter, “Fourier space design of high-Q cavities in standard and compressed hexagonal lattice photonic crystals,” Opt. Express 11, 579–593 (2003).
[Crossref] [PubMed]

2002 (1)

2001 (1)

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 band gap,” Appl. Phys. Lett.  78, 3388–3390 (2001).
[Crossref]

Akahane, Y.

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

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “High-Q photonic nanocavity in a 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. Vuckovic, “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.

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]

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

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

Baba, T.

K. Nozaki and T. Baba, “Laser characteristics with ultimate-small modal volume in photonic crystal slab point-shift nanolasers,” Appl. Phys. Lett.  88, 211101 (2006).
[Crossref]

Baek, J.-H.

H.-G. Park, S.-H. Kim, S.-H. Kwon, Y.-G. Ju, J.-K. Yang, J.-H. Baek, S.-B. Kim, and Y.-H. Lee, “Electrically Driven Single-Cell Photonic Crystal Laser,” Science 305, 1444–1447 (2004).
[Crossref] [PubMed]

Barclay, P. E.

Barrelet, C. J.

H.-G. Park, C. J. Barrelet, Y. Wu, B. Tian, F. Qian, and C. M. Lieber, “A wavelength-selective photonic-crystal waveguide coupled to a nanowire light source,” Nature Photonics 2, 622–626 (2008).
[Crossref]

Deppe, D. G.

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 432, 200–203 (2004).
[Crossref] [PubMed]

Ee, H.-S.

H.-S. Ee, K.-Y. Jeong, M.-K. Seo, Y.-H. Lee, and H.-G. Park, “Ultrasmall square-lattice zero-cell photonic crystal laser,” Appl. Phys. Lett.  93, 011104 (2008).
[Crossref]

Ell, C.

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 432, 200–203 (2004).
[Crossref] [PubMed]

Englund, D.

D. Englund and J. Vuckovic, “A direct analysis of photonic nanostructures,” Opt. Express 14, 3472–3483 (2006).
[Crossref] [PubMed]

D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vuckovic, “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, A. Mekis, and J. D. Joannopoulos, “Multipole-cancellation mechanism for high-Q cavities in the absence of a complete photonic band gap,” Appl. Phys. Lett.  78, 3388–3390 (2001).
[Crossref]

Fattal, D.

D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vuckovic, “Controlling the Spontaneous Emission Rate of Single Quantum Dots in a Two-Dimensional Photonic Crystal,” Phys. Rev. Lett.  95, 013904 (2005).
[Crossref] [PubMed]

Forchel, A.

Gayral, B.

J. M. Gerard and B. Gayral, “Toward high-efficiency quantum-dot single-photon sources,” Proc. SPIE 5361, 88 (2004).
[Crossref]

Gerard, J. M.

J. M. Gerard and B. Gayral, “Toward high-efficiency quantum-dot single-photon sources,” Proc. SPIE 5361, 88 (2004).
[Crossref]

Gibbs, H. M.

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 432, 200–203 (2004).
[Crossref] [PubMed]

Hendrickson, J.

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 432, 200–203 (2004).
[Crossref] [PubMed]

Jeong, K.-Y.

H.-S. Ee, K.-Y. Jeong, M.-K. Seo, Y.-H. Lee, and H.-G. Park, “Ultrasmall square-lattice zero-cell photonic crystal laser,” Appl. Phys. Lett.  93, 011104 (2008).
[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 band gap,” Appl. Phys. Lett.  78, 3388–3390 (2001).
[Crossref]

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University Press, New Jersey, 2008).

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 band gap,” Appl. Phys. Lett.  78, 3388–3390 (2001).
[Crossref]

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University Press, New Jersey, 2008).

Ju, Y.-G.

H.-G. Park, S.-H. Kim, S.-H. Kwon, Y.-G. Ju, J.-K. Yang, J.-H. Baek, S.-B. Kim, and Y.-H. Lee, “Electrically Driven Single-Cell Photonic Crystal Laser,” Science 305, 1444–1447 (2004).
[Crossref] [PubMed]

Kamp, M.

Khitrova, G.

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 432, 200–203 (2004).
[Crossref] [PubMed]

Kim, G.-H.

S.-K. Kim, G.-H. Kim, S.-H. Kim, S.-B. Kim, I. Kim, and Y.-H. Lee, “Loss management using parity-selective barriers for single-mode, single-cell photonic crystal resonators,” Appl. Phys. Lett.  88, 161119 (2006).
[Crossref]

G.-H. Kim, Y.-H. Lee, A. Shinya, and M. Notomi, “Coupling of small, low-loss hexapole mode with photonic crystal slab waveguide mode,” Opt. Express 12, 6624–6631 (2004).
[Crossref] [PubMed]

Kim, I.

S.-K. Kim, G.-H. Kim, S.-H. Kim, S.-B. Kim, I. Kim, and Y.-H. Lee, “Loss management using parity-selective barriers for single-mode, single-cell photonic crystal resonators,” Appl. Phys. Lett.  88, 161119 (2006).
[Crossref]

Kim, J.-Y.

Kim, S.-B.

S.-K. Kim, G.-H. Kim, S.-H. Kim, S.-B. Kim, I. Kim, and Y.-H. Lee, “Loss management using parity-selective barriers for single-mode, single-cell photonic crystal resonators,” Appl. Phys. Lett.  88, 161119 (2006).
[Crossref]

H.-G. Park, S.-H. Kim, S.-H. Kwon, Y.-G. Ju, J.-K. Yang, J.-H. Baek, S.-B. Kim, and Y.-H. Lee, “Electrically Driven Single-Cell Photonic Crystal Laser,” Science 305, 1444–1447 (2004).
[Crossref] [PubMed]

Kim, S.-H.

M.-K. Seo, H.-G. Park, J.-K. Yang, J.-Y. Kim, S.-H. Kim, and Y.-H. Lee, “Controlled sub-nanometer tuning of photonic crystal resonator by carbonaceous nano-dots,” Opt. Express 16, 9829–9837 (2008).
[Crossref] [PubMed]

S.-K. Kim, G.-H. Kim, S.-H. Kim, S.-B. Kim, I. Kim, and Y.-H. Lee, “Loss management using parity-selective barriers for single-mode, single-cell photonic crystal resonators,” Appl. Phys. Lett.  88, 161119 (2006).
[Crossref]

S.-H. Kim, S.-K. Kim, and Y.-H. Lee, “Vertical beaming of wavelength-scale photonic crystal resonators,” Phys. Rev. B  73, 235117 (2006).
[Crossref]

H.-G. Park, S.-H. Kim, S.-H. Kwon, Y.-G. Ju, J.-K. Yang, J.-H. Baek, S.-B. Kim, and Y.-H. Lee, “Electrically Driven Single-Cell Photonic Crystal Laser,” Science 305, 1444–1447 (2004).
[Crossref] [PubMed]

S.-H. Kwon, S.-H. Kim, S.-K. Kim, and Y.-H. Lee, “Small, low-loss heterogeneous photonic bandedge laser,” Opt. Express 12, 5356–5361 (2004).
[Crossref] [PubMed]

S.-H. Kim and Y.-H. Lee, “Symmetry Relations of Two-Dimensional Photonic Crystal Cavity Modes,” IEEE J. Quantum Electron.  39, 1081–1085 (2003).
[Crossref]

Kim, S.-K.

S.-H. Kim, S.-K. Kim, and Y.-H. Lee, “Vertical beaming of wavelength-scale photonic crystal resonators,” Phys. Rev. B  73, 235117 (2006).
[Crossref]

S.-K. Kim, G.-H. Kim, S.-H. Kim, S.-B. Kim, I. Kim, and Y.-H. Lee, “Loss management using parity-selective barriers for single-mode, single-cell photonic crystal resonators,” Appl. Phys. Lett.  88, 161119 (2006).
[Crossref]

S.-H. Kwon, S.-H. Kim, S.-K. Kim, and Y.-H. Lee, “Small, low-loss heterogeneous photonic bandedge laser,” Opt. Express 12, 5356–5361 (2004).
[Crossref] [PubMed]

Kondo, S.

T. Tanabe, A. Shinya, E. Kuramochi, S. Kondo, H. Taniyama, and M. Notomi, “Single point defect photonic crystal nanocavity with ultrahigh quality factor achieved by using hexapole mode,” Appl. Phys. Lett.  91, 021110 (2007).
[Crossref]

Kuramochi, E.

T. Tanabe, A. Shinya, E. Kuramochi, S. Kondo, H. Taniyama, and M. Notomi, “Single point defect photonic crystal nanocavity with ultrahigh quality factor achieved by using hexapole mode,” Appl. Phys. Lett.  91, 021110 (2007).
[Crossref]

T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, and E. Kuramochi, “Fast bistable all-optical switch and memory on a silicon photonic crystal on-chip,” Opt. Lett.  30, 2575–2577 (2005).
[Crossref] [PubMed]

Kwon, S.-H.

Lee, Y.-H.

H.-S. Ee, K.-Y. Jeong, M.-K. Seo, Y.-H. Lee, and H.-G. Park, “Ultrasmall square-lattice zero-cell photonic crystal laser,” Appl. Phys. Lett.  93, 011104 (2008).
[Crossref]

M.-K. Seo, H.-G. Park, J.-K. Yang, J.-Y. Kim, S.-H. Kim, and Y.-H. Lee, “Controlled sub-nanometer tuning of photonic crystal resonator by carbonaceous nano-dots,” Opt. Express 16, 9829–9837 (2008).
[Crossref] [PubMed]

S.-K. Kim, G.-H. Kim, S.-H. Kim, S.-B. Kim, I. Kim, and Y.-H. Lee, “Loss management using parity-selective barriers for single-mode, single-cell photonic crystal resonators,” Appl. Phys. Lett.  88, 161119 (2006).
[Crossref]

S.-H. Kim, S.-K. Kim, and Y.-H. Lee, “Vertical beaming of wavelength-scale photonic crystal resonators,” Phys. Rev. B  73, 235117 (2006).
[Crossref]

H.-G. Park, S.-H. Kim, S.-H. Kwon, Y.-G. Ju, J.-K. Yang, J.-H. Baek, S.-B. Kim, and Y.-H. Lee, “Electrically Driven Single-Cell Photonic Crystal Laser,” Science 305, 1444–1447 (2004).
[Crossref] [PubMed]

G.-H. Kim, Y.-H. Lee, A. Shinya, and M. Notomi, “Coupling of small, low-loss hexapole mode with photonic crystal slab waveguide mode,” Opt. Express 12, 6624–6631 (2004).
[Crossref] [PubMed]

S.-H. Kwon, S.-H. Kim, S.-K. Kim, and Y.-H. Lee, “Small, low-loss heterogeneous photonic bandedge laser,” Opt. Express 12, 5356–5361 (2004).
[Crossref] [PubMed]

S.-H. Kim and Y.-H. Lee, “Symmetry Relations of Two-Dimensional Photonic Crystal Cavity Modes,” IEEE J. Quantum Electron.  39, 1081–1085 (2003).
[Crossref]

H.-Y. Ryu, M. Notomi, and Y.-H. Lee, “High-quality-factor and small-mode-volume hexapole modes in photonic-crystal-slab nanocavities,” Appl. Phys. Lett.  83, 4294–4296 (2003).
[Crossref]

Lieber, C. M.

H.-G. Park, C. J. Barrelet, Y. Wu, B. Tian, F. Qian, and C. M. Lieber, “A wavelength-selective photonic-crystal waveguide coupled to a nanowire light source,” Nature Photonics 2, 622–626 (2008).
[Crossref]

Meade, R. D.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University Press, New Jersey, 2008).

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 band gap,” Appl. Phys. Lett.  78, 3388–3390 (2001).
[Crossref]

Mitsugi, S.

T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, and E. Kuramochi, “Fast bistable all-optical switch and memory on a silicon photonic crystal on-chip,” Opt. Lett.  30, 2575–2577 (2005).
[Crossref] [PubMed]

Nakaoka, T.

D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vuckovic, “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.

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]

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

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

Notomi, M.

T. Tanabe, A. Shinya, E. Kuramochi, S. Kondo, H. Taniyama, and M. Notomi, “Single point defect photonic crystal nanocavity with ultrahigh quality factor achieved by using hexapole mode,” Appl. Phys. Lett.  91, 021110 (2007).
[Crossref]

T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, and E. Kuramochi, “Fast bistable all-optical switch and memory on a silicon photonic crystal on-chip,” Opt. Lett.  30, 2575–2577 (2005).
[Crossref] [PubMed]

G.-H. Kim, Y.-H. Lee, A. Shinya, and M. Notomi, “Coupling of small, low-loss hexapole mode with photonic crystal slab waveguide mode,” Opt. Express 12, 6624–6631 (2004).
[Crossref] [PubMed]

H.-Y. Ryu, M. Notomi, and Y.-H. Lee, “High-quality-factor and small-mode-volume hexapole modes in photonic-crystal-slab nanocavities,” Appl. Phys. Lett.  83, 4294–4296 (2003).
[Crossref]

Nozaki, K.

K. Nozaki and T. Baba, “Laser characteristics with ultimate-small modal volume in photonic crystal slab point-shift nanolasers,” Appl. Phys. Lett.  88, 211101 (2006).
[Crossref]

Painter, O.

Park, H.-G.

M.-K. Seo, H.-G. Park, J.-K. Yang, J.-Y. Kim, S.-H. Kim, and Y.-H. Lee, “Controlled sub-nanometer tuning of photonic crystal resonator by carbonaceous nano-dots,” Opt. Express 16, 9829–9837 (2008).
[Crossref] [PubMed]

H.-S. Ee, K.-Y. Jeong, M.-K. Seo, Y.-H. Lee, and H.-G. Park, “Ultrasmall square-lattice zero-cell photonic crystal laser,” Appl. Phys. Lett.  93, 011104 (2008).
[Crossref]

H.-G. Park, C. J. Barrelet, Y. Wu, B. Tian, F. Qian, and C. M. Lieber, “A wavelength-selective photonic-crystal waveguide coupled to a nanowire light source,” Nature Photonics 2, 622–626 (2008).
[Crossref]

H.-G. Park, S.-H. Kim, S.-H. Kwon, Y.-G. Ju, J.-K. Yang, J.-H. Baek, S.-B. Kim, and Y.-H. Lee, “Electrically Driven Single-Cell Photonic Crystal Laser,” Science 305, 1444–1447 (2004).
[Crossref] [PubMed]

Qian, F.

H.-G. Park, C. J. Barrelet, Y. Wu, B. Tian, F. Qian, and C. M. Lieber, “A wavelength-selective photonic-crystal waveguide coupled to a nanowire light source,” Nature Photonics 2, 622–626 (2008).
[Crossref]

Qiu, M.

Rupper, G.

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 432, 200–203 (2004).
[Crossref] [PubMed]

Ryu, H.-Y.

H.-Y. Ryu, M. Notomi, and Y.-H. Lee, “High-quality-factor and small-mode-volume hexapole modes in photonic-crystal-slab nanocavities,” Appl. Phys. Lett.  83, 4294–4296 (2003).
[Crossref]

Scherer, A.

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 432, 200–203 (2004).
[Crossref] [PubMed]

Seo, M.-K.

H.-S. Ee, K.-Y. Jeong, M.-K. Seo, Y.-H. Lee, and H.-G. Park, “Ultrasmall square-lattice zero-cell photonic crystal laser,” Appl. Phys. Lett.  93, 011104 (2008).
[Crossref]

M.-K. Seo, H.-G. Park, J.-K. Yang, J.-Y. Kim, S.-H. Kim, and Y.-H. Lee, “Controlled sub-nanometer tuning of photonic crystal resonator by carbonaceous nano-dots,” Opt. Express 16, 9829–9837 (2008).
[Crossref] [PubMed]

Shchekin, O. B.

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 432, 200–203 (2004).
[Crossref] [PubMed]

Shinya, A.

T. Tanabe, A. Shinya, E. Kuramochi, S. Kondo, H. Taniyama, and M. Notomi, “Single point defect photonic crystal nanocavity with ultrahigh quality factor achieved by using hexapole mode,” Appl. Phys. Lett.  91, 021110 (2007).
[Crossref]

T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, and E. Kuramochi, “Fast bistable all-optical switch and memory on a silicon photonic crystal on-chip,” Opt. Lett.  30, 2575–2577 (2005).
[Crossref] [PubMed]

G.-H. Kim, Y.-H. Lee, A. Shinya, and M. Notomi, “Coupling of small, low-loss hexapole mode with photonic crystal slab waveguide mode,” Opt. Express 12, 6624–6631 (2004).
[Crossref] [PubMed]

Solomon, G.

D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vuckovic, “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.

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]

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

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

Srinivasan, K.

Sünner, T.

Tanabe, T.

T. Tanabe, A. Shinya, E. Kuramochi, S. Kondo, H. Taniyama, and M. Notomi, “Single point defect photonic crystal nanocavity with ultrahigh quality factor achieved by using hexapole mode,” Appl. Phys. Lett.  91, 021110 (2007).
[Crossref]

T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, and E. Kuramochi, “Fast bistable all-optical switch and memory on a silicon photonic crystal on-chip,” Opt. Lett.  30, 2575–2577 (2005).
[Crossref] [PubMed]

Taniyama, H.

T. Tanabe, A. Shinya, E. Kuramochi, S. Kondo, H. Taniyama, and M. Notomi, “Single point defect photonic crystal nanocavity with ultrahigh quality factor achieved by using hexapole mode,” Appl. Phys. Lett.  91, 021110 (2007).
[Crossref]

Tian, B.

H.-G. Park, C. J. Barrelet, Y. Wu, B. Tian, F. Qian, and C. M. Lieber, “A wavelength-selective photonic-crystal waveguide coupled to a nanowire light source,” Nature Photonics 2, 622–626 (2008).
[Crossref]

Vuckovic, J.

D. Englund and J. Vuckovic, “A direct analysis of photonic nanostructures,” Opt. Express 14, 3472–3483 (2006).
[Crossref] [PubMed]

D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vuckovic, “Controlling the Spontaneous Emission Rate of Single Quantum Dots in a Two-Dimensional Photonic Crystal,” Phys. Rev. Lett.  95, 013904 (2005).
[Crossref] [PubMed]

Waks, E.

D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vuckovic, “Controlling the Spontaneous Emission Rate of Single Quantum Dots in a Two-Dimensional Photonic Crystal,” Phys. Rev. Lett.  95, 013904 (2005).
[Crossref] [PubMed]

Winn, J. N.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University Press, New Jersey, 2008).

Wu, Y.

H.-G. Park, C. J. Barrelet, Y. Wu, B. Tian, F. Qian, and C. M. Lieber, “A wavelength-selective photonic-crystal waveguide coupled to a nanowire light source,” Nature Photonics 2, 622–626 (2008).
[Crossref]

Yamamoto, Y.

D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vuckovic, “Controlling the Spontaneous Emission Rate of Single Quantum Dots in a Two-Dimensional Photonic Crystal,” Phys. Rev. Lett.  95, 013904 (2005).
[Crossref] [PubMed]

Yang, J.-K.

M.-K. Seo, H.-G. Park, J.-K. Yang, J.-Y. Kim, S.-H. Kim, and Y.-H. Lee, “Controlled sub-nanometer tuning of photonic crystal resonator by carbonaceous nano-dots,” Opt. Express 16, 9829–9837 (2008).
[Crossref] [PubMed]

H.-G. Park, S.-H. Kim, S.-H. Kwon, Y.-G. Ju, J.-K. Yang, J.-H. Baek, S.-B. Kim, and Y.-H. Lee, “Electrically Driven Single-Cell Photonic Crystal Laser,” Science 305, 1444–1447 (2004).
[Crossref] [PubMed]

Yoshie, T.

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 432, 200–203 (2004).
[Crossref] [PubMed]

Zhang, B.

D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vuckovic, “Controlling the Spontaneous Emission Rate of Single Quantum Dots in a Two-Dimensional Photonic Crystal,” Phys. Rev. Lett.  95, 013904 (2005).
[Crossref] [PubMed]

Zhang, Z.

Appl. Phys. Lett (6)

T. Tanabe, A. Shinya, E. Kuramochi, S. Kondo, H. Taniyama, and M. Notomi, “Single point defect photonic crystal nanocavity with ultrahigh quality factor achieved by using hexapole mode,” Appl. Phys. Lett.  91, 021110 (2007).
[Crossref]

K. Nozaki and T. Baba, “Laser characteristics with ultimate-small modal volume in photonic crystal slab point-shift nanolasers,” Appl. Phys. Lett.  88, 211101 (2006).
[Crossref]

H.-S. Ee, K.-Y. Jeong, M.-K. Seo, Y.-H. Lee, and H.-G. Park, “Ultrasmall square-lattice zero-cell photonic crystal laser,” Appl. Phys. Lett.  93, 011104 (2008).
[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 band gap,” Appl. Phys. Lett.  78, 3388–3390 (2001).
[Crossref]

H.-Y. Ryu, M. Notomi, and Y.-H. Lee, “High-quality-factor and small-mode-volume hexapole modes in photonic-crystal-slab nanocavities,” Appl. Phys. Lett.  83, 4294–4296 (2003).
[Crossref]

S.-K. Kim, G.-H. Kim, S.-H. Kim, S.-B. Kim, I. Kim, and Y.-H. Lee, “Loss management using parity-selective barriers for single-mode, single-cell photonic crystal resonators,” Appl. Phys. Lett.  88, 161119 (2006).
[Crossref]

IEEE J. Quantum Electron (1)

S.-H. Kim and Y.-H. Lee, “Symmetry Relations of Two-Dimensional Photonic Crystal Cavity Modes,” IEEE J. Quantum Electron.  39, 1081–1085 (2003).
[Crossref]

Nature (2)

Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425, 944–947 (2003).
[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 432, 200–203 (2004).
[Crossref] [PubMed]

Nature Mater (1)

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

Nature Photonics (1)

H.-G. Park, C. J. Barrelet, Y. Wu, B. Tian, F. Qian, and C. M. Lieber, “A wavelength-selective photonic-crystal waveguide coupled to a nanowire light source,” Nature Photonics 2, 622–626 (2008).
[Crossref]

Opt. Express (10)

G.-H. Kim, Y.-H. Lee, A. Shinya, and M. Notomi, “Coupling of small, low-loss hexapole mode with photonic crystal slab waveguide mode,” Opt. Express 12, 6624–6631 (2004).
[Crossref] [PubMed]

S.-H. Kwon, T. Sünner, M. Kamp, and A. Forchel, “Ultrahigh-Q photonic crystal cavity created by modulating air hole radius of a waveguide,” Opt. Express 16, 4605–4614 (2008).
[Crossref] [PubMed]

K. Srinivasan, P. E. Barclay, and O. Painter, “Fabrication-tolerant high quality factor photonic crystal microcavities,” Opt. Express 12, 1458–1463 (2004).
[Crossref] [PubMed]

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]

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

K. Srinivasan and O. Painter, “Fourier space design of high-Q cavities in standard and compressed hexagonal lattice photonic crystals,” Opt. Express 11, 579–593 (2003).
[Crossref] [PubMed]

Z. Zhang and M. Qiu, “Compact in-plane channel drop filter design using a single cavity with two degenerate modes in 2D photonic crystal slabs,” Opt. Express 13, 2596–2604 (2005).
[Crossref] [PubMed]

D. Englund and J. Vuckovic, “A direct analysis of photonic nanostructures,” Opt. Express 14, 3472–3483 (2006).
[Crossref] [PubMed]

S.-H. Kwon, S.-H. Kim, S.-K. Kim, and Y.-H. Lee, “Small, low-loss heterogeneous photonic bandedge laser,” Opt. Express 12, 5356–5361 (2004).
[Crossref] [PubMed]

M.-K. Seo, H.-G. Park, J.-K. Yang, J.-Y. Kim, S.-H. Kim, and Y.-H. Lee, “Controlled sub-nanometer tuning of photonic crystal resonator by carbonaceous nano-dots,” Opt. Express 16, 9829–9837 (2008).
[Crossref] [PubMed]

Opt. Lett (1)

T. Tanabe, M. Notomi, S. Mitsugi, A. Shinya, and E. Kuramochi, “Fast bistable all-optical switch and memory on a silicon photonic crystal on-chip,” Opt. Lett.  30, 2575–2577 (2005).
[Crossref] [PubMed]

Phys. Rev (1)

S.-H. Kim, S.-K. Kim, and Y.-H. Lee, “Vertical beaming of wavelength-scale photonic crystal resonators,” Phys. Rev. B  73, 235117 (2006).
[Crossref]

Phys. Rev. Lett (1)

D. Englund, D. Fattal, E. Waks, G. Solomon, B. Zhang, T. Nakaoka, Y. Arakawa, Y. Yamamoto, and J. Vuckovic, “Controlling the Spontaneous Emission Rate of Single Quantum Dots in a Two-Dimensional Photonic Crystal,” Phys. Rev. Lett.  95, 013904 (2005).
[Crossref] [PubMed]

Proc. SPIE (1)

J. M. Gerard and B. Gayral, “Toward high-efficiency quantum-dot single-photon sources,” Proc. SPIE 5361, 88 (2004).
[Crossref]

Science (1)

H.-G. Park, S.-H. Kim, S.-H. Kwon, Y.-G. Ju, J.-K. Yang, J.-H. Baek, S.-B. Kim, and Y.-H. Lee, “Electrically Driven Single-Cell Photonic Crystal Laser,” Science 305, 1444–1447 (2004).
[Crossref] [PubMed]

Other (4)

The band edge laser is observed with more increased pumping power. Threshold of the band edge laser is ~650 μW in the PhC cavity of Fig. 6.

A higher-order band edge mode with the wavelength of 1597 nm is observed in Fig. 7(a) (D).

This single-cell cavity is advantageous to the demonstration of the electrically driven laser by introducing a small central post underneath the cavity.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light (Princeton University Press, New Jersey, 2008).

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Figures (10)

Fig. 1.
Fig. 1.

(a). Calculated TE-like band diagram of the triangular lattice PhC slab structure. The first band edge point (K1) and the second band edge point (M2) are denoted by blue and red circles, respectively. Gray and black regions indicate photonic band gap and leaky modes, respectively. The inset shows the irreducible Brillouin zone of the triangular lattice PhC structure. (b)-(c) The electric field intensity profiles of (b) the K1 band edge mode, and (c) the M2 band edge mode.

Fig. 2.
Fig. 2.

The modified single-cell PhC cavities for (a) the dielectric-band and (b) the air-band cavity modes. In (a), one missing air hole at the center is surrounded by four layers of air holes with linearly decreasing radii (r 1 to r 4). The air holes with same radii are indicated by the same hexagons. In (b), the six nearest neighbor air holes (r m) are reduced and pushed away from the cavity center.

Fig. 3.
Fig. 3.

The calculated mode patterns of the dielectric-band cavity modes. (a)-(b) The electric field intensity profiles (linear-scale) of (a) the hexapole, and (b) the monopole modes. The dielectric confinement factors, defined as the ratio of the energy in the dielectric to the whole energy of the mode, of the hexapole and the monopole modes are computed to 85.0 % and 86.2 %, respectively. (c)-(d) Fourier space intensity profiles (log-scale) of (c) the hexapole and (d) the monopole modes. The dotted white circle represents a light cone. The inset in (c) indicates the directions of wavevectors.

Fig. 4.
Fig. 4.

The calculated mode patterns of the air-band cavity modes. (a)-(b) The electric field intensity profiles (linear-scale) of (a) the hexapole, and (b) the monopole modes. The dielectric confinement factors of the hexapole and the monopole modes are computed to 79.2 % and 83.2 %, respectively. (c)-(d) Fourier space intensity profiles (log-scale) of (c) the hexapole, and (d) the monopole modes. The dotted white circle represents a light cone. The inset in (c) indicates the directions of wavevectors.

Fig. 5.
Fig. 5.

Calculated Q factors and mode volumes of (a) the hexapole and (b) the monopole dielectric-band cavity modes as a function of the radius of the nearest neighboring holes (r 1) in the PhC cavity of Fig. 2(a). The regular air hole radius r 5 is fixed to 0.3a. Other air hole radii are determined by the following simple equation (linearly-graded air hole radius): ri = r 5 + (5 - i)(r 1 - r 5)/4, where i =1, 2, 3, and 4.

Fig. 6.
Fig. 6.

(a). The SEM image of a fabricated laser structure. The scale bar is 3 μm. (b) The magnified SEM image. The radii of air holes enclosed by each hexagon are denoted by r 1, r 2, r 3, r 4, and r 5. The scale bar is 1 μm.

Fig. 7.
Fig. 7.

(a). Typical above-threshold PL spectra (log-scale) measured in four different samples (A) to (D). Air hole sizes increase from samples (A) to (D). (b) The resonant wavelength of each mode is plotted as a function of air filling fraction. The resonances in each sample are grouped by the gray dotted line. The measured resonances are indicated by dots and the calculated resonances by lines. The black, red, and blue dots are the resonant wavelengths of the hexapole, monopole and band edge modes, respectively.

Fig. 8.
Fig. 8.

Lasing mode images of (a) hexapole, (b) monopole, and (c) band edge modes, captured by an IR camera. All scale bars are 5 μm. Only a single-lasing mode is observed in each image. The pumping powers and the central wavelengths of the bandpass filters are (a) 426 μW and 1509 nm, (b) 527 μW and 1530 nm, and (c) 850 μW and 1564 nm. In (c), the effective transparent region is increased due to the relatively high pumping power.

Fig. 9.
Fig. 9.

(a). PL spectra at different incident pump powers of 426 μW (top) and 527 μW (bottom). Only the hexapole-mode lasing is observed at 426 μW; however, the monopole-mode lasing peak is additionally observed at 527 μW. (b)-(c) Lasing peak intensity vs. incident pump power for (b) the hexapole mode, and (c) the monopole mode. Threshold pump powers of the hexapole-mode and the monopole-mode lasers are ~340 μW and ~450 μW, respectively.

Fig. 10.
Fig. 10.

(a). Cavity structure transformed from the SEM image of the fabricated sample in Fig. 6. (b) The electric field intensity profiles (top) and Hz-field profiles (bottom) of the hexapole (left) and the monopole modes (right). The mode profiles of each mode agreed well with the profiles of the corresponding ideal structure.

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