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," Nat. 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," Nat. 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

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," Nat. Photonics 2, 622-626 (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

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

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

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]

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]

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," Nat. Mater. 4, 207-210 (2005).
[CrossRef]

2004

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

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

2001

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," Nat. 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," Nat. 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," Nat. 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]

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]

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.-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]

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.-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]

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.

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]

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]

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]

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. 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," Nat. Photonics 2, 622-626 (2008).
[CrossRef]

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.

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," Nat. 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.

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]

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," Nat. 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," Nat. 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.

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," Nat. 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," Nat. 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]

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," Nat. 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.

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.

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]

Nat. Mater.

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

Nature

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 Photonics

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," Nat. Photonics 2, 622-626 (2008).
[CrossRef]

Opt. Express

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]

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]

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]

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]

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]

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]

Opt. Lett.

Phys. Rev. B

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.

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

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

Science

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

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.

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).

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

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

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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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