Abstract

We provide a numerical study showing that a bottom reflector is indispensable to achieve unidirectional emission from a photonic-crystal (PhC) nanolaser. First, we study a PhC slab nanocavity suspended over a flat mirror formed by a dielectric or metal substrate. We find that the laser’s vertical emission can be enhanced by more than a factor of 6 compared with the device in the absence of the mirror. Then, we study the situation where the PhC nanocavity is in contact with a flat metal surface. The underlying metal substrate may serve as both an electrical current pathway and a heat sink, which would help achieve continuous-wave lasing operation at room temperature. The design of the laser emitting at 1.3 μm reveals that a relatively high cavity Q of over 1000 is achievable assuming room-temperature gold as a substrate. Furthermore, linearly polarized unidirectional vertical emission with the radiation efficiency over 50% can be achieved. Finally, we discuss how this hybrid design relates to various plasmonic cavities and propose a useful quantitative measure of the degree of the “plasmonic” character in a general metallic nanocavity.

© 2012 Optical Society of America

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  1. E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).
    [CrossRef]
  2. J.-M. Gérard and B. Gayral, “Strong Purcell effect for inas quantum boxes in three-dimensional solid-state microcavities,” J. Lightwave Technol. 17, 2089–2095 (1999).
    [CrossRef]
  3. H. Yokoyama, “Physics and device applications of optical microcavities,” Science 256, 66–70 (1992).
    [CrossRef]
  4. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
    [CrossRef]
  5. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
    [CrossRef]
  6. J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed.(Princeton University, 2008).
  7. P. Yeh, A. Yariv, and C. S. Hong, “Electromagnetic propagation in periodic stratified media. I. General theory,” J. Opt. Soc. Am. 67, 423–438 (1977).
    [CrossRef]
  8. J. L. Jewell, J. P. Harbison, A. Scherer, Y. H. Lee, and L. T. Florez, “Vertical-cavity surface-emitting lasers: design, growth, fabrication, characterization,” IEEE J. Quantum Electron. 27, 1332–1346 (1991).
    [CrossRef]
  9. O. Painter, R. K. Lee, A. Yariv, A. Scherer, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
    [CrossRef]
  10. 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]
  11. B. S. Song, S. Noda, T. Asano, and Y. Akahane, “Utra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater. 4, 207–210 (2005).
    [CrossRef]
  12. P. B. Deotare, M. W. McCutcheon, I. W. Frank, M. Khan, and M. Loncar, “High quality factor photonic crystal nanobeam cavities,” Appl. Phys. Lett. 94, 121106 (2009).
    [CrossRef]
  13. O. Painter, J. Vučkovič, and A. Scherer, “Defect modes of a two-dimensional photonic crystal in an optically thin dielectric slab,” J. Opt. Soc. Am. B 16, 275–285 (1999).
    [CrossRef]
  14. S. G. Johnson, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
    [CrossRef]
  15. 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]
  16. U. K. Khankhoje, S.-H. Kim, B. C. Richards, J. Hendrickson, J. Sweet, J. D. Olitzky, G. Khitrova, H. M. Gibbs, and A. Scherer, “Modelling and fabrication of GaAs photonic-crystal cavities for cavity quantum electrodynamics,” Nanotechnology 21, 065202 (2010).
    [CrossRef]
  17. E. A. Hinds, Cavity Quantum Electrodynamics (Academic, 1994).
  18. S.-H. Kim, M.-K. Seo, J.-Y. Kim, and Y.-H. Lee, “Effects of a bottom substrate on emission properties of a photonic crystal nanolaser,” in Proceedings of IEEE 19th International Conference on Indium Phosphide & Related Materials (IEEE, 2007), pp. 480–483.
  19. M. Toishi, D. Englund, A. Faraon, and J. Vučković, “High-brightness single photon source from a quantum dot in a directional-emission nanocavity,” Opt. Express 17, 14618–14626 (2009).
    [CrossRef]
  20. 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]
  21. M.-K. Seo, K.-Y. Jeong, J.-K. Yang, Y.-H. Lee, H.-G. Park, and S.-B. Kim, “Low threshold current single-cell hexapole mode photonic crystal laser,” Appl. Phys. Lett. 90, 171122 (2007).
    [CrossRef]
  22. T. Okumura, M. Kurokawa, M. Shirao, D. Kondo, H. Ito, N. Nishiyama, T. Maruyama, and S. Arai, “Lateral current injection GaInAsP/InP laser on semi-insulating substrate for membrane-based photonic circuits,” Opt. Express 17, 12564–12570 (2009).
    [CrossRef]
  23. B. Ellis, M. A. Mayer, G. Shambat, T. Sarmiento, J. Harris, E. E. Haller, and J. Vuckovic, “Ultralow-threshold electrically pumped quantum-dot photonic-crystal nanocavity laser,” Nat. Photon. 5, 297–300 (2011).
    [CrossRef]
  24. C. M. Long, A. V. Giannopoulos, and K. D. Choquette, “Lateral current injection photonic crystal membrane light emitting diodes,” J. Vac. Sci. Technol. B 28, 359–364 (2010).
    [CrossRef]
  25. K. Nozaki, S. Kita, and T. Baba, “Room temperature continuous wave operation and controlled spontaneous emission in ultrasmall photonic crystal nanolaser,” Opt. Express 15, 7506–7514 (2007).
    [CrossRef]
  26. S.-H. Kim, Y.-H. Lee, J. Huang, and A. Scherer, “Unidirectional vertical emission from photonic crystal nanolasers,” in Proceedings of 11th International IEEE Conference on Transparent Optical Networks (IEEE, 2009), pp. 1–4.
  27. M. L. Povinelli, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “Toward photonic-crystal metamaterials: creating magnetic emitters in photonic crystals,” Appl. Phys. Lett. 82, 1069–1071 (2003).
    [CrossRef]
  28. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
    [CrossRef]
  29. S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65, 235112 (2002).
    [CrossRef]
  30. J. P. Dowling, M. O. Scully, and F. DeMartini, “Radiation pattern of a classical dipole in a cavity,” Opt. Commun. 82, 415–419 (1991).
    [CrossRef]
  31. B. B. Bakir, C. Seassal, X. Letartre, P. Viktorovitch, M. Zussy, L. D. Cioccio, and J. M. Fedeli, “Surface-emitting microlaser combining two-dimensional photonic crystal membrane and vertical Bragg mirror,” Appl. Phys. Lett. 88, 081113 (2006).
    [CrossRef]
  32. T. Ochiai and K. Sakoda, “Dispersion relation and optical transmittance of a hexagonal photonic crystal slab,” Phys. Rev. B 63, 125107 (2001).
    [CrossRef]
  33. J.-H. Kang, M.-K. Seo, S.-K. Kim, S.-H. Kim, M.-K. Kim, H.-G. Park, K.-S. Kim, and Y.-H. Lee, “Polarized vertical beaming of an engineered hexapole mode laser,” Opt. Express 17, 6074–6081 (2009).
    [CrossRef]
  34. B. Min, E. Ostby, V. Sorger, E. Ulin-Avila, L. Yang, X. Zhang, and K. Vahala, “High-Q surface-plasmon-polarition whispering-gallery microcavity,” Nature (London) 457, 455–458 (2009).
    [CrossRef]
  35. R. F. Oulton, V. J. Sorger, T. Zentgaraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature (London) 461, 629–632 (2009).
    [CrossRef]
  36. M.-K. Seo, S.-H. Kwon, H.-S. Ee, and H.-G. Park, “Full three-dimensional subwavelength high-Q surface-plasmon-polariton cavity,” Nano Lett. 9, 4078–4082 (2009).
    [CrossRef]
  37. M. T. Hill, M. Marell, E. S. P. Leong, B. Smalbrugge, Y. Zhu, M. Sun, P. J. van Veldhoven, E. J. Geluk, F. Karouta, Y.-S. Oei, R. Nötzel, C.-Z. Ning, and M. K. Smit, “Lasing in metal-insulator-metal sub-wavelength plasmonic waveguides,” Opt. Express 17, 11107–11112 (2009).
    [CrossRef]
  38. J. Huang, S.-H. Kim, and A. Scherer, “Design of a surface-emitting, subwavelength metal-clad disk laser in the visible spectrum,” Opt. Express 18, 19581–19591 (2010).
    [CrossRef]
  39. M. T. Hill, “Status and prospects for metallic and plasmonic nano-lasers,” J. Opt. Soc. Am. B 27, B36–B44 (2010).
    [CrossRef]
  40. S.-W. Chang and S. L. Chuang, “Fundamental formulation for plasmonic nanolasers,” IEEE J. Quantum Electron. 45, 1014–1023 (2009).
    [CrossRef]
  41. S.-W. Chang and S. L. Chuang, “Normal modes for plasmonic nanolasers with dispersive and inhomogeneous media,” Opt. Lett. 34, 91–93 (2009).
    [CrossRef]
  42. J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1998).
  43. A. Tandaechanurat, S. Iwamoto, M. Nomura, N. Kumagai, and Y. Arakawa, “Increase of Q-factor in photonic crystal H1-defect nanocavities after closing of photonic bandgap with optimal slab thickness,” Opt. Express 16, 448–455 (2008).
    [CrossRef]
  44. A. Mizrahi, V. Lomakin, B. A. Slutsky, M. P. Nezhad, L. Feng, and Y. Fainman, “Low threshold gain metal coated laser nanoresonators,” Opt. Lett. 33, 1261–1263 (2008).
    [CrossRef]
  45. M. Ibanescu, S. G. Johnson, D. Roundy, Y. Fink, and J. D. Joannopoulos, “Microcavity confinement based on an anomalous zero group-velocity waveguide mode,” Opt. Lett. 30, 552–554 (2005).
    [CrossRef]
  46. S.-H. Kim, J. Huang, and A. Scherer, “A photonic crystal nanocavity laser in an optically very thick slab,” http://arxiv.org/abs/1111.4272 .
  47. D. Taillaert, W. Bogaerts, P. Bienstman, T. Krauss, P. Van Daele, I. Moerman, S. Verstuyft, K. De Mesel, and R. Baets, “An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron. 38, 949–955 (2002).
    [CrossRef]
  48. H. Altug, D. Englund, and J. Vučković, “Ultra-fast photonic crystal nanolasers,” Nat. Phys. 2, 484–488 (2006).
    [CrossRef]
  49. M. Fujita, A. Sakai, and T. Baba, “Ultrasmall and ultralow threshold GaInAsP-InP microdisk injection lasers: design, fabrication, lasing characteristics, and spontaneous emission factor,” IEEE J. Sel. Top. Quantum Electron. 5, 673–681 (1999).
    [CrossRef]
  50. I. Friedler, C. Sauvan, J. P. Hugonin, P. Lalanne, J. Claudon, and J. M. Gérard, “Solid-state single photon sources: the nanowire antenna,” Opt. Express 17, 2095–2110 (2009).
    [CrossRef]
  51. W.-D. Li, F. Ding, J. Hu, and S. Y. Chou, “Three-dimensional cavity nanoantenna coupled plasmonic nanodots for ultrahigh and uniform surface-enhanced Raman scattering over large area,” Opt. Express 19, 3925–3936 (2011).
    [CrossRef]
  52. J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature (London) 455, 376–379 (2008).
    [CrossRef]
  53. H.-J. Chang, S.-H. Kim, Y.-H. Lee, E. P. Kartalov, and A. Scherer, “A photonic-crystal optical antenna for extremely large local-field enhancement,” Opt. Express 18, 24163–24177 (2010).
    [CrossRef]
  54. M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: refractionlike behavior in the vicinity of the photonic band gap,” Phys. Rev. B 62, 10696–10705 (2000).
    [CrossRef]
  55. K. Ishizaki and S. Noda, “Manipulation of photons at the surface of three-dimensional photonic crystals,” Nature (London) 460, 367–370 (2009).
    [CrossRef]
  56. M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett. 93, 137404 (2004).
    [CrossRef]
  57. S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full three-dimensional photonic bandgap crystals at near-infrared wavelengths,” Science 289, 604–606 (2000).
    [CrossRef]
  58. C. Kittel, Introduction to Solid State Physics, 8th ed. (Wiley, 2005).
  59. M. Staffaroni, J. Conway, S. Vedantam, J. Tang, and E. Yablonovitch, “Circuit analysis in metal-optics,” http://arxiv.org/abs/1006.3126 .
  60. J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritions,” Rep. Prog. Phys. 70, 1–87 (2007).
    [CrossRef]
  61. A. M. Lakhani, M. ki Kim, E. K. Lau, and M. C. Wu, “Plasmonic crystal defect nanolaser,” Opt. Express 19, 18237–18245 (2011).
    [CrossRef]
  62. D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett. 90, 027402 (2003).
    [CrossRef]

2011 (3)

2010 (5)

H.-J. Chang, S.-H. Kim, Y.-H. Lee, E. P. Kartalov, and A. Scherer, “A photonic-crystal optical antenna for extremely large local-field enhancement,” Opt. Express 18, 24163–24177 (2010).
[CrossRef]

C. M. Long, A. V. Giannopoulos, and K. D. Choquette, “Lateral current injection photonic crystal membrane light emitting diodes,” J. Vac. Sci. Technol. B 28, 359–364 (2010).
[CrossRef]

J. Huang, S.-H. Kim, and A. Scherer, “Design of a surface-emitting, subwavelength metal-clad disk laser in the visible spectrum,” Opt. Express 18, 19581–19591 (2010).
[CrossRef]

M. T. Hill, “Status and prospects for metallic and plasmonic nano-lasers,” J. Opt. Soc. Am. B 27, B36–B44 (2010).
[CrossRef]

U. K. Khankhoje, S.-H. Kim, B. C. Richards, J. Hendrickson, J. Sweet, J. D. Olitzky, G. Khitrova, H. M. Gibbs, and A. Scherer, “Modelling and fabrication of GaAs photonic-crystal cavities for cavity quantum electrodynamics,” Nanotechnology 21, 065202 (2010).
[CrossRef]

2009 (12)

M. Toishi, D. Englund, A. Faraon, and J. Vučković, “High-brightness single photon source from a quantum dot in a directional-emission nanocavity,” Opt. Express 17, 14618–14626 (2009).
[CrossRef]

T. Okumura, M. Kurokawa, M. Shirao, D. Kondo, H. Ito, N. Nishiyama, T. Maruyama, and S. Arai, “Lateral current injection GaInAsP/InP laser on semi-insulating substrate for membrane-based photonic circuits,” Opt. Express 17, 12564–12570 (2009).
[CrossRef]

P. B. Deotare, M. W. McCutcheon, I. W. Frank, M. Khan, and M. Loncar, “High quality factor photonic crystal nanobeam cavities,” Appl. Phys. Lett. 94, 121106 (2009).
[CrossRef]

S.-W. Chang and S. L. Chuang, “Fundamental formulation for plasmonic nanolasers,” IEEE J. Quantum Electron. 45, 1014–1023 (2009).
[CrossRef]

S.-W. Chang and S. L. Chuang, “Normal modes for plasmonic nanolasers with dispersive and inhomogeneous media,” Opt. Lett. 34, 91–93 (2009).
[CrossRef]

K. Ishizaki and S. Noda, “Manipulation of photons at the surface of three-dimensional photonic crystals,” Nature (London) 460, 367–370 (2009).
[CrossRef]

I. Friedler, C. Sauvan, J. P. Hugonin, P. Lalanne, J. Claudon, and J. M. Gérard, “Solid-state single photon sources: the nanowire antenna,” Opt. Express 17, 2095–2110 (2009).
[CrossRef]

J.-H. Kang, M.-K. Seo, S.-K. Kim, S.-H. Kim, M.-K. Kim, H.-G. Park, K.-S. Kim, and Y.-H. Lee, “Polarized vertical beaming of an engineered hexapole mode laser,” Opt. Express 17, 6074–6081 (2009).
[CrossRef]

B. Min, E. Ostby, V. Sorger, E. Ulin-Avila, L. Yang, X. Zhang, and K. Vahala, “High-Q surface-plasmon-polarition whispering-gallery microcavity,” Nature (London) 457, 455–458 (2009).
[CrossRef]

R. F. Oulton, V. J. Sorger, T. Zentgaraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature (London) 461, 629–632 (2009).
[CrossRef]

M.-K. Seo, S.-H. Kwon, H.-S. Ee, and H.-G. Park, “Full three-dimensional subwavelength high-Q surface-plasmon-polariton cavity,” Nano Lett. 9, 4078–4082 (2009).
[CrossRef]

M. T. Hill, M. Marell, E. S. P. Leong, B. Smalbrugge, Y. Zhu, M. Sun, P. J. van Veldhoven, E. J. Geluk, F. Karouta, Y.-S. Oei, R. Nötzel, C.-Z. Ning, and M. K. Smit, “Lasing in metal-insulator-metal sub-wavelength plasmonic waveguides,” Opt. Express 17, 11107–11112 (2009).
[CrossRef]

2008 (3)

2007 (3)

K. Nozaki, S. Kita, and T. Baba, “Room temperature continuous wave operation and controlled spontaneous emission in ultrasmall photonic crystal nanolaser,” Opt. Express 15, 7506–7514 (2007).
[CrossRef]

M.-K. Seo, K.-Y. Jeong, J.-K. Yang, Y.-H. Lee, H.-G. Park, and S.-B. Kim, “Low threshold current single-cell hexapole mode photonic crystal laser,” Appl. Phys. Lett. 90, 171122 (2007).
[CrossRef]

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritions,” Rep. Prog. Phys. 70, 1–87 (2007).
[CrossRef]

2006 (3)

H. Altug, D. Englund, and J. Vučković, “Ultra-fast photonic crystal nanolasers,” Nat. Phys. 2, 484–488 (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]

B. B. Bakir, C. Seassal, X. Letartre, P. Viktorovitch, M. Zussy, L. D. Cioccio, and J. M. Fedeli, “Surface-emitting microlaser combining two-dimensional photonic crystal membrane and vertical Bragg mirror,” Appl. Phys. Lett. 88, 081113 (2006).
[CrossRef]

2005 (2)

M. Ibanescu, S. G. Johnson, D. Roundy, Y. Fink, and J. D. Joannopoulos, “Microcavity confinement based on an anomalous zero group-velocity waveguide mode,” Opt. Lett. 30, 552–554 (2005).
[CrossRef]

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

2004 (2)

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]

M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett. 93, 137404 (2004).
[CrossRef]

2003 (3)

D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett. 90, 027402 (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]

M. L. Povinelli, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “Toward photonic-crystal metamaterials: creating magnetic emitters in photonic crystals,” Appl. Phys. Lett. 82, 1069–1071 (2003).
[CrossRef]

2002 (2)

S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65, 235112 (2002).
[CrossRef]

D. Taillaert, W. Bogaerts, P. Bienstman, T. Krauss, P. Van Daele, I. Moerman, S. Verstuyft, K. De Mesel, and R. Baets, “An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron. 38, 949–955 (2002).
[CrossRef]

2001 (1)

T. Ochiai and K. Sakoda, “Dispersion relation and optical transmittance of a hexagonal photonic crystal slab,” Phys. Rev. B 63, 125107 (2001).
[CrossRef]

2000 (2)

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full three-dimensional photonic bandgap crystals at near-infrared wavelengths,” Science 289, 604–606 (2000).
[CrossRef]

M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: refractionlike behavior in the vicinity of the photonic band gap,” Phys. Rev. B 62, 10696–10705 (2000).
[CrossRef]

1999 (5)

M. Fujita, A. Sakai, and T. Baba, “Ultrasmall and ultralow threshold GaInAsP-InP microdisk injection lasers: design, fabrication, lasing characteristics, and spontaneous emission factor,” IEEE J. Sel. Top. Quantum Electron. 5, 673–681 (1999).
[CrossRef]

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

J.-M. Gérard and B. Gayral, “Strong Purcell effect for inas quantum boxes in three-dimensional solid-state microcavities,” J. Lightwave Technol. 17, 2089–2095 (1999).
[CrossRef]

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

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

1992 (1)

H. Yokoyama, “Physics and device applications of optical microcavities,” Science 256, 66–70 (1992).
[CrossRef]

1991 (2)

J. L. Jewell, J. P. Harbison, A. Scherer, Y. H. Lee, and L. T. Florez, “Vertical-cavity surface-emitting lasers: design, growth, fabrication, characterization,” IEEE J. Quantum Electron. 27, 1332–1346 (1991).
[CrossRef]

J. P. Dowling, M. O. Scully, and F. DeMartini, “Radiation pattern of a classical dipole in a cavity,” Opt. Commun. 82, 415–419 (1991).
[CrossRef]

1987 (2)

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

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[CrossRef]

1977 (1)

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

1946 (1)

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

Akahane, Y.

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

Altug, H.

H. Altug, D. Englund, and J. Vučković, “Ultra-fast photonic crystal nanolasers,” Nat. Phys. 2, 484–488 (2006).
[CrossRef]

Arai, S.

Arakawa, Y.

Asano, T.

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

Baba, T.

K. Nozaki, S. Kita, and T. Baba, “Room temperature continuous wave operation and controlled spontaneous emission in ultrasmall photonic crystal nanolaser,” Opt. Express 15, 7506–7514 (2007).
[CrossRef]

M. Fujita, A. Sakai, and T. Baba, “Ultrasmall and ultralow threshold GaInAsP-InP microdisk injection lasers: design, fabrication, lasing characteristics, and spontaneous emission factor,” IEEE J. Sel. Top. Quantum Electron. 5, 673–681 (1999).
[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]

Baets, R.

D. Taillaert, W. Bogaerts, P. Bienstman, T. Krauss, P. Van Daele, I. Moerman, S. Verstuyft, K. De Mesel, and R. Baets, “An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron. 38, 949–955 (2002).
[CrossRef]

Bakir, B. B.

B. B. Bakir, C. Seassal, X. Letartre, P. Viktorovitch, M. Zussy, L. D. Cioccio, and J. M. Fedeli, “Surface-emitting microlaser combining two-dimensional photonic crystal membrane and vertical Bragg mirror,” Appl. Phys. Lett. 88, 081113 (2006).
[CrossRef]

Bartal, G.

R. F. Oulton, V. J. Sorger, T. Zentgaraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature (London) 461, 629–632 (2009).
[CrossRef]

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature (London) 455, 376–379 (2008).
[CrossRef]

Bergman, D. J.

D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett. 90, 027402 (2003).
[CrossRef]

Bienstman, P.

D. Taillaert, W. Bogaerts, P. Bienstman, T. Krauss, P. Van Daele, I. Moerman, S. Verstuyft, K. De Mesel, and R. Baets, “An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron. 38, 949–955 (2002).
[CrossRef]

Bogaerts, W.

D. Taillaert, W. Bogaerts, P. Bienstman, T. Krauss, P. Van Daele, I. Moerman, S. Verstuyft, K. De Mesel, and R. Baets, “An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron. 38, 949–955 (2002).
[CrossRef]

Chang, H.-J.

Chang, S.-W.

S.-W. Chang and S. L. Chuang, “Normal modes for plasmonic nanolasers with dispersive and inhomogeneous media,” Opt. Lett. 34, 91–93 (2009).
[CrossRef]

S.-W. Chang and S. L. Chuang, “Fundamental formulation for plasmonic nanolasers,” IEEE J. Quantum Electron. 45, 1014–1023 (2009).
[CrossRef]

Choquette, K. D.

C. M. Long, A. V. Giannopoulos, and K. D. Choquette, “Lateral current injection photonic crystal membrane light emitting diodes,” J. Vac. Sci. Technol. B 28, 359–364 (2010).
[CrossRef]

Chou, S. Y.

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Chuang, S. L.

S.-W. Chang and S. L. Chuang, “Fundamental formulation for plasmonic nanolasers,” IEEE J. Quantum Electron. 45, 1014–1023 (2009).
[CrossRef]

S.-W. Chang and S. L. Chuang, “Normal modes for plasmonic nanolasers with dispersive and inhomogeneous media,” Opt. Lett. 34, 91–93 (2009).
[CrossRef]

Chulkov, E. V.

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritions,” Rep. Prog. Phys. 70, 1–87 (2007).
[CrossRef]

Chutinan, A.

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full three-dimensional photonic bandgap crystals at near-infrared wavelengths,” Science 289, 604–606 (2000).
[CrossRef]

Cioccio, L. D.

B. B. Bakir, C. Seassal, X. Letartre, P. Viktorovitch, M. Zussy, L. D. Cioccio, and J. M. Fedeli, “Surface-emitting microlaser combining two-dimensional photonic crystal membrane and vertical Bragg mirror,” Appl. Phys. Lett. 88, 081113 (2006).
[CrossRef]

Claudon, J.

Dai, L.

R. F. Oulton, V. J. Sorger, T. Zentgaraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature (London) 461, 629–632 (2009).
[CrossRef]

Dapkus, P. D.

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

De Mesel, K.

D. Taillaert, W. Bogaerts, P. Bienstman, T. Krauss, P. Van Daele, I. Moerman, S. Verstuyft, K. De Mesel, and R. Baets, “An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron. 38, 949–955 (2002).
[CrossRef]

DeMartini, F.

J. P. Dowling, M. O. Scully, and F. DeMartini, “Radiation pattern of a classical dipole in a cavity,” Opt. Commun. 82, 415–419 (1991).
[CrossRef]

Deotare, P. B.

P. B. Deotare, M. W. McCutcheon, I. W. Frank, M. Khan, and M. Loncar, “High quality factor photonic crystal nanobeam cavities,” Appl. Phys. Lett. 94, 121106 (2009).
[CrossRef]

Ding, F.

Dowling, J. P.

J. P. Dowling, M. O. Scully, and F. DeMartini, “Radiation pattern of a classical dipole in a cavity,” Opt. Commun. 82, 415–419 (1991).
[CrossRef]

Echenique, P. M.

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritions,” Rep. Prog. Phys. 70, 1–87 (2007).
[CrossRef]

Ee, H.-S.

M.-K. Seo, S.-H. Kwon, H.-S. Ee, and H.-G. Park, “Full three-dimensional subwavelength high-Q surface-plasmon-polariton cavity,” Nano Lett. 9, 4078–4082 (2009).
[CrossRef]

Ellis, B.

B. Ellis, M. A. Mayer, G. Shambat, T. Sarmiento, J. Harris, E. E. Haller, and J. Vuckovic, “Ultralow-threshold electrically pumped quantum-dot photonic-crystal nanocavity laser,” Nat. Photon. 5, 297–300 (2011).
[CrossRef]

Englund, D.

Fainman, Y.

Fan, S.

S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65, 235112 (2002).
[CrossRef]

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

Faraon, A.

Fedeli, J. M.

B. B. Bakir, C. Seassal, X. Letartre, P. Viktorovitch, M. Zussy, L. D. Cioccio, and J. M. Fedeli, “Surface-emitting microlaser combining two-dimensional photonic crystal membrane and vertical Bragg mirror,” Appl. Phys. Lett. 88, 081113 (2006).
[CrossRef]

Feng, L.

Fink, Y.

Florez, L. T.

J. L. Jewell, J. P. Harbison, A. Scherer, Y. H. Lee, and L. T. Florez, “Vertical-cavity surface-emitting lasers: design, growth, fabrication, characterization,” IEEE J. Quantum Electron. 27, 1332–1346 (1991).
[CrossRef]

Frank, I. W.

P. B. Deotare, M. W. McCutcheon, I. W. Frank, M. Khan, and M. Loncar, “High quality factor photonic crystal nanobeam cavities,” Appl. Phys. Lett. 94, 121106 (2009).
[CrossRef]

Friedler, I.

Fujita, M.

M. Fujita, A. Sakai, and T. Baba, “Ultrasmall and ultralow threshold GaInAsP-InP microdisk injection lasers: design, fabrication, lasing characteristics, and spontaneous emission factor,” IEEE J. Sel. Top. Quantum Electron. 5, 673–681 (1999).
[CrossRef]

Gayral, B.

Geluk, E. J.

Genov, D. A.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature (London) 455, 376–379 (2008).
[CrossRef]

Gérard, J. M.

Gérard, J.-M.

Giannopoulos, A. V.

C. M. Long, A. V. Giannopoulos, and K. D. Choquette, “Lateral current injection photonic crystal membrane light emitting diodes,” J. Vac. Sci. Technol. B 28, 359–364 (2010).
[CrossRef]

Gibbs, H. M.

U. K. Khankhoje, S.-H. Kim, B. C. Richards, J. Hendrickson, J. Sweet, J. D. Olitzky, G. Khitrova, H. M. Gibbs, and A. Scherer, “Modelling and fabrication of GaAs photonic-crystal cavities for cavity quantum electrodynamics,” Nanotechnology 21, 065202 (2010).
[CrossRef]

Gladden, C.

R. F. Oulton, V. J. Sorger, T. Zentgaraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature (London) 461, 629–632 (2009).
[CrossRef]

Haller, E. E.

B. Ellis, M. A. Mayer, G. Shambat, T. Sarmiento, J. Harris, E. E. Haller, and J. Vuckovic, “Ultralow-threshold electrically pumped quantum-dot photonic-crystal nanocavity laser,” Nat. Photon. 5, 297–300 (2011).
[CrossRef]

Harbison, J. P.

J. L. Jewell, J. P. Harbison, A. Scherer, Y. H. Lee, and L. T. Florez, “Vertical-cavity surface-emitting lasers: design, growth, fabrication, characterization,” IEEE J. Quantum Electron. 27, 1332–1346 (1991).
[CrossRef]

Harris, J.

B. Ellis, M. A. Mayer, G. Shambat, T. Sarmiento, J. Harris, E. E. Haller, and J. Vuckovic, “Ultralow-threshold electrically pumped quantum-dot photonic-crystal nanocavity laser,” Nat. Photon. 5, 297–300 (2011).
[CrossRef]

Hendrickson, J.

U. K. Khankhoje, S.-H. Kim, B. C. Richards, J. Hendrickson, J. Sweet, J. D. Olitzky, G. Khitrova, H. M. Gibbs, and A. Scherer, “Modelling and fabrication of GaAs photonic-crystal cavities for cavity quantum electrodynamics,” Nanotechnology 21, 065202 (2010).
[CrossRef]

Hill, M. T.

Hinds, E. A.

E. A. Hinds, Cavity Quantum Electrodynamics (Academic, 1994).

Hong, C. S.

Hu, J.

Huang, J.

J. Huang, S.-H. Kim, and A. Scherer, “Design of a surface-emitting, subwavelength metal-clad disk laser in the visible spectrum,” Opt. Express 18, 19581–19591 (2010).
[CrossRef]

S.-H. Kim, Y.-H. Lee, J. Huang, and A. Scherer, “Unidirectional vertical emission from photonic crystal nanolasers,” in Proceedings of 11th International IEEE Conference on Transparent Optical Networks (IEEE, 2009), pp. 1–4.

Hugonin, J. P.

Ibanescu, M.

Ishizaki, K.

K. Ishizaki and S. Noda, “Manipulation of photons at the surface of three-dimensional photonic crystals,” Nature (London) 460, 367–370 (2009).
[CrossRef]

Ito, H.

Iwamoto, S.

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1998).

Jeong, K.-Y.

M.-K. Seo, K.-Y. Jeong, J.-K. Yang, Y.-H. Lee, H.-G. Park, and S.-B. Kim, “Low threshold current single-cell hexapole mode photonic crystal laser,” Appl. Phys. Lett. 90, 171122 (2007).
[CrossRef]

Jewell, J. L.

J. L. Jewell, J. P. Harbison, A. Scherer, Y. H. Lee, and L. T. Florez, “Vertical-cavity surface-emitting lasers: design, growth, fabrication, characterization,” IEEE J. Quantum Electron. 27, 1332–1346 (1991).
[CrossRef]

Joannopoulos, J. D.

M. Ibanescu, S. G. Johnson, D. Roundy, Y. Fink, and J. D. Joannopoulos, “Microcavity confinement based on an anomalous zero group-velocity waveguide mode,” Opt. Lett. 30, 552–554 (2005).
[CrossRef]

M. L. Povinelli, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “Toward photonic-crystal metamaterials: creating magnetic emitters in photonic crystals,” Appl. Phys. Lett. 82, 1069–1071 (2003).
[CrossRef]

S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65, 235112 (2002).
[CrossRef]

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

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed.(Princeton University, 2008).

John, S.

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[CrossRef]

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Johnson, S. G.

M. Ibanescu, S. G. Johnson, D. Roundy, Y. Fink, and J. D. Joannopoulos, “Microcavity confinement based on an anomalous zero group-velocity waveguide mode,” Opt. Lett. 30, 552–554 (2005).
[CrossRef]

M. L. Povinelli, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “Toward photonic-crystal metamaterials: creating magnetic emitters in photonic crystals,” Appl. Phys. Lett. 82, 1069–1071 (2003).
[CrossRef]

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

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed.(Princeton University, 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]

Kang, J.-H.

Karouta, F.

Kartalov, E. P.

Khan, M.

P. B. Deotare, M. W. McCutcheon, I. W. Frank, M. Khan, and M. Loncar, “High quality factor photonic crystal nanobeam cavities,” Appl. Phys. Lett. 94, 121106 (2009).
[CrossRef]

Khankhoje, U. K.

U. K. Khankhoje, S.-H. Kim, B. C. Richards, J. Hendrickson, J. Sweet, J. D. Olitzky, G. Khitrova, H. M. Gibbs, and A. Scherer, “Modelling and fabrication of GaAs photonic-crystal cavities for cavity quantum electrodynamics,” Nanotechnology 21, 065202 (2010).
[CrossRef]

Khitrova, G.

U. K. Khankhoje, S.-H. Kim, B. C. Richards, J. Hendrickson, J. Sweet, J. D. Olitzky, G. Khitrova, H. M. Gibbs, and A. Scherer, “Modelling and fabrication of GaAs photonic-crystal cavities for cavity quantum electrodynamics,” Nanotechnology 21, 065202 (2010).
[CrossRef]

ki Kim, M.

Kim, I.

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

Kim, J.-Y.

S.-H. Kim, M.-K. Seo, J.-Y. Kim, and Y.-H. Lee, “Effects of a bottom substrate on emission properties of a photonic crystal nanolaser,” in Proceedings of IEEE 19th International Conference on Indium Phosphide & Related Materials (IEEE, 2007), pp. 480–483.

Kim, K.-S.

Kim, M.-K.

Kim, S.-B.

M.-K. Seo, K.-Y. Jeong, J.-K. Yang, Y.-H. Lee, H.-G. Park, and S.-B. Kim, “Low threshold current single-cell hexapole mode photonic crystal laser,” Appl. Phys. Lett. 90, 171122 (2007).
[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]

Kim, S.-H.

U. K. Khankhoje, S.-H. Kim, B. C. Richards, J. Hendrickson, J. Sweet, J. D. Olitzky, G. Khitrova, H. M. Gibbs, and A. Scherer, “Modelling and fabrication of GaAs photonic-crystal cavities for cavity quantum electrodynamics,” Nanotechnology 21, 065202 (2010).
[CrossRef]

H.-J. Chang, S.-H. Kim, Y.-H. Lee, E. P. Kartalov, and A. Scherer, “A photonic-crystal optical antenna for extremely large local-field enhancement,” Opt. Express 18, 24163–24177 (2010).
[CrossRef]

J. Huang, S.-H. Kim, and A. Scherer, “Design of a surface-emitting, subwavelength metal-clad disk laser in the visible spectrum,” Opt. Express 18, 19581–19591 (2010).
[CrossRef]

J.-H. Kang, M.-K. Seo, S.-K. Kim, S.-H. Kim, M.-K. Kim, H.-G. Park, K.-S. Kim, and Y.-H. Lee, “Polarized vertical beaming of an engineered hexapole mode laser,” Opt. Express 17, 6074–6081 (2009).
[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]

S.-H. Kim, M.-K. Seo, J.-Y. Kim, and Y.-H. Lee, “Effects of a bottom substrate on emission properties of a photonic crystal nanolaser,” in Proceedings of IEEE 19th International Conference on Indium Phosphide & Related Materials (IEEE, 2007), pp. 480–483.

S.-H. Kim, Y.-H. Lee, J. Huang, and A. Scherer, “Unidirectional vertical emission from photonic crystal nanolasers,” in Proceedings of 11th International IEEE Conference on Transparent Optical Networks (IEEE, 2009), pp. 1–4.

Kim, S.-K.

Kita, S.

Kittel, C.

C. Kittel, Introduction to Solid State Physics, 8th ed. (Wiley, 2005).

Kolodziejski, L. A.

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

Kondo, D.

Krauss, T.

D. Taillaert, W. Bogaerts, P. Bienstman, T. Krauss, P. Van Daele, I. Moerman, S. Verstuyft, K. De Mesel, and R. Baets, “An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron. 38, 949–955 (2002).
[CrossRef]

Kumagai, N.

Kurokawa, M.

Kwon, S.-H.

M.-K. Seo, S.-H. Kwon, H.-S. Ee, and H.-G. Park, “Full three-dimensional subwavelength high-Q surface-plasmon-polariton cavity,” Nano Lett. 9, 4078–4082 (2009).
[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]

Lakhani, A. M.

Lalanne, P.

Lau, E. K.

Lee, R. K.

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

Lee, Y. H.

J. L. Jewell, J. P. Harbison, A. Scherer, Y. H. Lee, and L. T. Florez, “Vertical-cavity surface-emitting lasers: design, growth, fabrication, characterization,” IEEE J. Quantum Electron. 27, 1332–1346 (1991).
[CrossRef]

Lee, Y.-H.

H.-J. Chang, S.-H. Kim, Y.-H. Lee, E. P. Kartalov, and A. Scherer, “A photonic-crystal optical antenna for extremely large local-field enhancement,” Opt. Express 18, 24163–24177 (2010).
[CrossRef]

J.-H. Kang, M.-K. Seo, S.-K. Kim, S.-H. Kim, M.-K. Kim, H.-G. Park, K.-S. Kim, and Y.-H. Lee, “Polarized vertical beaming of an engineered hexapole mode laser,” Opt. Express 17, 6074–6081 (2009).
[CrossRef]

M.-K. Seo, K.-Y. Jeong, J.-K. Yang, Y.-H. Lee, H.-G. Park, and S.-B. Kim, “Low threshold current single-cell hexapole mode photonic crystal laser,” Appl. Phys. Lett. 90, 171122 (2007).
[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]

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.-H. Kim, M.-K. Seo, J.-Y. Kim, and Y.-H. Lee, “Effects of a bottom substrate on emission properties of a photonic crystal nanolaser,” in Proceedings of IEEE 19th International Conference on Indium Phosphide & Related Materials (IEEE, 2007), pp. 480–483.

S.-H. Kim, Y.-H. Lee, J. Huang, and A. Scherer, “Unidirectional vertical emission from photonic crystal nanolasers,” in Proceedings of 11th International IEEE Conference on Transparent Optical Networks (IEEE, 2009), pp. 1–4.

Leong, E. S. P.

Letartre, X.

B. B. Bakir, C. Seassal, X. Letartre, P. Viktorovitch, M. Zussy, L. D. Cioccio, and J. M. Fedeli, “Surface-emitting microlaser combining two-dimensional photonic crystal membrane and vertical Bragg mirror,” Appl. Phys. Lett. 88, 081113 (2006).
[CrossRef]

Li, W.-D.

Lomakin, V.

Loncar, M.

P. B. Deotare, M. W. McCutcheon, I. W. Frank, M. Khan, and M. Loncar, “High quality factor photonic crystal nanobeam cavities,” Appl. Phys. Lett. 94, 121106 (2009).
[CrossRef]

Long, C. M.

C. M. Long, A. V. Giannopoulos, and K. D. Choquette, “Lateral current injection photonic crystal membrane light emitting diodes,” J. Vac. Sci. Technol. B 28, 359–364 (2010).
[CrossRef]

Ma, R. M.

R. F. Oulton, V. J. Sorger, T. Zentgaraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature (London) 461, 629–632 (2009).
[CrossRef]

Marell, M.

Maruyama, T.

Mayer, M. A.

B. Ellis, M. A. Mayer, G. Shambat, T. Sarmiento, J. Harris, E. E. Haller, and J. Vuckovic, “Ultralow-threshold electrically pumped quantum-dot photonic-crystal nanocavity laser,” Nat. Photon. 5, 297–300 (2011).
[CrossRef]

McCutcheon, M. W.

P. B. Deotare, M. W. McCutcheon, I. W. Frank, M. Khan, and M. Loncar, “High quality factor photonic crystal nanobeam cavities,” Appl. Phys. Lett. 94, 121106 (2009).
[CrossRef]

Meade, R. D.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed.(Princeton University, 2008).

Min, B.

B. Min, E. Ostby, V. Sorger, E. Ulin-Avila, L. Yang, X. Zhang, and K. Vahala, “High-Q surface-plasmon-polarition whispering-gallery microcavity,” Nature (London) 457, 455–458 (2009).
[CrossRef]

Mizrahi, A.

Moerman, I.

D. Taillaert, W. Bogaerts, P. Bienstman, T. Krauss, P. Van Daele, I. Moerman, S. Verstuyft, K. De Mesel, and R. Baets, “An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron. 38, 949–955 (2002).
[CrossRef]

Nezhad, M. P.

Ning, C.-Z.

Nishiyama, N.

Noda, S.

K. Ishizaki and S. Noda, “Manipulation of photons at the surface of three-dimensional photonic crystals,” Nature (London) 460, 367–370 (2009).
[CrossRef]

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

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full three-dimensional photonic bandgap crystals at near-infrared wavelengths,” Science 289, 604–606 (2000).
[CrossRef]

Nomura, M.

Notomi, M.

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]

M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: refractionlike behavior in the vicinity of the photonic band gap,” Phys. Rev. B 62, 10696–10705 (2000).
[CrossRef]

Nötzel, R.

Nozaki, K.

O’Brien, J. D.

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

Ochiai, T.

T. Ochiai and K. Sakoda, “Dispersion relation and optical transmittance of a hexagonal photonic crystal slab,” Phys. Rev. B 63, 125107 (2001).
[CrossRef]

Oei, Y.-S.

Okumura, T.

Olitzky, J. D.

U. K. Khankhoje, S.-H. Kim, B. C. Richards, J. Hendrickson, J. Sweet, J. D. Olitzky, G. Khitrova, H. M. Gibbs, and A. Scherer, “Modelling and fabrication of GaAs photonic-crystal cavities for cavity quantum electrodynamics,” Nanotechnology 21, 065202 (2010).
[CrossRef]

Ostby, E.

B. Min, E. Ostby, V. Sorger, E. Ulin-Avila, L. Yang, X. Zhang, and K. Vahala, “High-Q surface-plasmon-polarition whispering-gallery microcavity,” Nature (London) 457, 455–458 (2009).
[CrossRef]

Oulton, R. F.

R. F. Oulton, V. J. Sorger, T. Zentgaraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature (London) 461, 629–632 (2009).
[CrossRef]

Painter, O.

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

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

Park, H.-G.

J.-H. Kang, M.-K. Seo, S.-K. Kim, S.-H. Kim, M.-K. Kim, H.-G. Park, K.-S. Kim, and Y.-H. Lee, “Polarized vertical beaming of an engineered hexapole mode laser,” Opt. Express 17, 6074–6081 (2009).
[CrossRef]

M.-K. Seo, S.-H. Kwon, H.-S. Ee, and H.-G. Park, “Full three-dimensional subwavelength high-Q surface-plasmon-polariton cavity,” Nano Lett. 9, 4078–4082 (2009).
[CrossRef]

M.-K. Seo, K.-Y. Jeong, J.-K. Yang, Y.-H. Lee, H.-G. Park, and S.-B. Kim, “Low threshold current single-cell hexapole mode photonic crystal laser,” Appl. Phys. Lett. 90, 171122 (2007).
[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]

Pendry, J. B.

M. L. Povinelli, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “Toward photonic-crystal metamaterials: creating magnetic emitters in photonic crystals,” Appl. Phys. Lett. 82, 1069–1071 (2003).
[CrossRef]

Pitarke, J. M.

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritions,” Rep. Prog. Phys. 70, 1–87 (2007).
[CrossRef]

Povinelli, M. L.

M. L. Povinelli, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “Toward photonic-crystal metamaterials: creating magnetic emitters in photonic crystals,” Appl. Phys. Lett. 82, 1069–1071 (2003).
[CrossRef]

Purcell, E. M.

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

Richards, B. C.

U. K. Khankhoje, S.-H. Kim, B. C. Richards, J. Hendrickson, J. Sweet, J. D. Olitzky, G. Khitrova, H. M. Gibbs, and A. Scherer, “Modelling and fabrication of GaAs photonic-crystal cavities for cavity quantum electrodynamics,” Nanotechnology 21, 065202 (2010).
[CrossRef]

Roundy, D.

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]

Sakai, A.

M. Fujita, A. Sakai, and T. Baba, “Ultrasmall and ultralow threshold GaInAsP-InP microdisk injection lasers: design, fabrication, lasing characteristics, and spontaneous emission factor,” IEEE J. Sel. Top. Quantum Electron. 5, 673–681 (1999).
[CrossRef]

Sakoda, K.

T. Ochiai and K. Sakoda, “Dispersion relation and optical transmittance of a hexagonal photonic crystal slab,” Phys. Rev. B 63, 125107 (2001).
[CrossRef]

Sarmiento, T.

B. Ellis, M. A. Mayer, G. Shambat, T. Sarmiento, J. Harris, E. E. Haller, and J. Vuckovic, “Ultralow-threshold electrically pumped quantum-dot photonic-crystal nanocavity laser,” Nat. Photon. 5, 297–300 (2011).
[CrossRef]

Sauvan, C.

Scherer, A.

J. Huang, S.-H. Kim, and A. Scherer, “Design of a surface-emitting, subwavelength metal-clad disk laser in the visible spectrum,” Opt. Express 18, 19581–19591 (2010).
[CrossRef]

H.-J. Chang, S.-H. Kim, Y.-H. Lee, E. P. Kartalov, and A. Scherer, “A photonic-crystal optical antenna for extremely large local-field enhancement,” Opt. Express 18, 24163–24177 (2010).
[CrossRef]

U. K. Khankhoje, S.-H. Kim, B. C. Richards, J. Hendrickson, J. Sweet, J. D. Olitzky, G. Khitrova, H. M. Gibbs, and A. Scherer, “Modelling and fabrication of GaAs photonic-crystal cavities for cavity quantum electrodynamics,” Nanotechnology 21, 065202 (2010).
[CrossRef]

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

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

J. L. Jewell, J. P. Harbison, A. Scherer, Y. H. Lee, and L. T. Florez, “Vertical-cavity surface-emitting lasers: design, growth, fabrication, characterization,” IEEE J. Quantum Electron. 27, 1332–1346 (1991).
[CrossRef]

S.-H. Kim, Y.-H. Lee, J. Huang, and A. Scherer, “Unidirectional vertical emission from photonic crystal nanolasers,” in Proceedings of 11th International IEEE Conference on Transparent Optical Networks (IEEE, 2009), pp. 1–4.

Scully, M. O.

J. P. Dowling, M. O. Scully, and F. DeMartini, “Radiation pattern of a classical dipole in a cavity,” Opt. Commun. 82, 415–419 (1991).
[CrossRef]

Seassal, C.

B. B. Bakir, C. Seassal, X. Letartre, P. Viktorovitch, M. Zussy, L. D. Cioccio, and J. M. Fedeli, “Surface-emitting microlaser combining two-dimensional photonic crystal membrane and vertical Bragg mirror,” Appl. Phys. Lett. 88, 081113 (2006).
[CrossRef]

Seo, M.-K.

M.-K. Seo, S.-H. Kwon, H.-S. Ee, and H.-G. Park, “Full three-dimensional subwavelength high-Q surface-plasmon-polariton cavity,” Nano Lett. 9, 4078–4082 (2009).
[CrossRef]

J.-H. Kang, M.-K. Seo, S.-K. Kim, S.-H. Kim, M.-K. Kim, H.-G. Park, K.-S. Kim, and Y.-H. Lee, “Polarized vertical beaming of an engineered hexapole mode laser,” Opt. Express 17, 6074–6081 (2009).
[CrossRef]

M.-K. Seo, K.-Y. Jeong, J.-K. Yang, Y.-H. Lee, H.-G. Park, and S.-B. Kim, “Low threshold current single-cell hexapole mode photonic crystal laser,” Appl. Phys. Lett. 90, 171122 (2007).
[CrossRef]

S.-H. Kim, M.-K. Seo, J.-Y. Kim, and Y.-H. Lee, “Effects of a bottom substrate on emission properties of a photonic crystal nanolaser,” in Proceedings of IEEE 19th International Conference on Indium Phosphide & Related Materials (IEEE, 2007), pp. 480–483.

Shambat, G.

B. Ellis, M. A. Mayer, G. Shambat, T. Sarmiento, J. Harris, E. E. Haller, and J. Vuckovic, “Ultralow-threshold electrically pumped quantum-dot photonic-crystal nanocavity laser,” Nat. Photon. 5, 297–300 (2011).
[CrossRef]

Shirao, M.

Silkin, V. M.

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritions,” Rep. Prog. Phys. 70, 1–87 (2007).
[CrossRef]

Slutsky, B. A.

Smalbrugge, B.

Smit, M. K.

Song, B. S.

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

Sorger, V.

B. Min, E. Ostby, V. Sorger, E. Ulin-Avila, L. Yang, X. Zhang, and K. Vahala, “High-Q surface-plasmon-polarition whispering-gallery microcavity,” Nature (London) 457, 455–458 (2009).
[CrossRef]

Sorger, V. J.

R. F. Oulton, V. J. Sorger, T. Zentgaraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature (London) 461, 629–632 (2009).
[CrossRef]

Stockman, M. I.

M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett. 93, 137404 (2004).
[CrossRef]

D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett. 90, 027402 (2003).
[CrossRef]

Sun, M.

Sweet, J.

U. K. Khankhoje, S.-H. Kim, B. C. Richards, J. Hendrickson, J. Sweet, J. D. Olitzky, G. Khitrova, H. M. Gibbs, and A. Scherer, “Modelling and fabrication of GaAs photonic-crystal cavities for cavity quantum electrodynamics,” Nanotechnology 21, 065202 (2010).
[CrossRef]

Taillaert, D.

D. Taillaert, W. Bogaerts, P. Bienstman, T. Krauss, P. Van Daele, I. Moerman, S. Verstuyft, K. De Mesel, and R. Baets, “An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron. 38, 949–955 (2002).
[CrossRef]

Tandaechanurat, A.

Toishi, M.

Tomoda, K.

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full three-dimensional photonic bandgap crystals at near-infrared wavelengths,” Science 289, 604–606 (2000).
[CrossRef]

Ulin-Avila, E.

B. Min, E. Ostby, V. Sorger, E. Ulin-Avila, L. Yang, X. Zhang, and K. Vahala, “High-Q surface-plasmon-polarition whispering-gallery microcavity,” Nature (London) 457, 455–458 (2009).
[CrossRef]

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature (London) 455, 376–379 (2008).
[CrossRef]

Vahala, K.

B. Min, E. Ostby, V. Sorger, E. Ulin-Avila, L. Yang, X. Zhang, and K. Vahala, “High-Q surface-plasmon-polarition whispering-gallery microcavity,” Nature (London) 457, 455–458 (2009).
[CrossRef]

Valentine, J.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature (London) 455, 376–379 (2008).
[CrossRef]

Van Daele, P.

D. Taillaert, W. Bogaerts, P. Bienstman, T. Krauss, P. Van Daele, I. Moerman, S. Verstuyft, K. De Mesel, and R. Baets, “An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron. 38, 949–955 (2002).
[CrossRef]

van Veldhoven, P. J.

Verstuyft, S.

D. Taillaert, W. Bogaerts, P. Bienstman, T. Krauss, P. Van Daele, I. Moerman, S. Verstuyft, K. De Mesel, and R. Baets, “An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron. 38, 949–955 (2002).
[CrossRef]

Viktorovitch, P.

B. B. Bakir, C. Seassal, X. Letartre, P. Viktorovitch, M. Zussy, L. D. Cioccio, and J. M. Fedeli, “Surface-emitting microlaser combining two-dimensional photonic crystal membrane and vertical Bragg mirror,” Appl. Phys. Lett. 88, 081113 (2006).
[CrossRef]

Villeneuve, P. R.

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

Vuckovic, J.

B. Ellis, M. A. Mayer, G. Shambat, T. Sarmiento, J. Harris, E. E. Haller, and J. Vuckovic, “Ultralow-threshold electrically pumped quantum-dot photonic-crystal nanocavity laser,” Nat. Photon. 5, 297–300 (2011).
[CrossRef]

M. Toishi, D. Englund, A. Faraon, and J. Vučković, “High-brightness single photon source from a quantum dot in a directional-emission nanocavity,” Opt. Express 17, 14618–14626 (2009).
[CrossRef]

H. Altug, D. Englund, and J. Vučković, “Ultra-fast photonic crystal nanolasers,” Nat. Phys. 2, 484–488 (2006).
[CrossRef]

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

Winn, J. N.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed.(Princeton University, 2008).

Wu, M. C.

Yablonovitch, E.

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

Yamamoto, N.

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full three-dimensional photonic bandgap crystals at near-infrared wavelengths,” Science 289, 604–606 (2000).
[CrossRef]

Yang, J.-K.

M.-K. Seo, K.-Y. Jeong, J.-K. Yang, Y.-H. Lee, H.-G. Park, and S.-B. Kim, “Low threshold current single-cell hexapole mode photonic crystal laser,” Appl. Phys. Lett. 90, 171122 (2007).
[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]

Yang, L.

B. Min, E. Ostby, V. Sorger, E. Ulin-Avila, L. Yang, X. Zhang, and K. Vahala, “High-Q surface-plasmon-polarition whispering-gallery microcavity,” Nature (London) 457, 455–458 (2009).
[CrossRef]

Yariv, A.

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

P. Yeh, A. Yariv, and C. S. Hong, “Electromagnetic propagation in periodic stratified media. I. General theory,” J. Opt. Soc. Am. 67, 423–438 (1977).
[CrossRef]

Yeh, P.

Yokoyama, H.

H. Yokoyama, “Physics and device applications of optical microcavities,” Science 256, 66–70 (1992).
[CrossRef]

Zentgaraf, T.

R. F. Oulton, V. J. Sorger, T. Zentgaraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature (London) 461, 629–632 (2009).
[CrossRef]

Zentgraf, T.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature (London) 455, 376–379 (2008).
[CrossRef]

Zhang, S.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature (London) 455, 376–379 (2008).
[CrossRef]

Zhang, X.

B. Min, E. Ostby, V. Sorger, E. Ulin-Avila, L. Yang, X. Zhang, and K. Vahala, “High-Q surface-plasmon-polarition whispering-gallery microcavity,” Nature (London) 457, 455–458 (2009).
[CrossRef]

R. F. Oulton, V. J. Sorger, T. Zentgaraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature (London) 461, 629–632 (2009).
[CrossRef]

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature (London) 455, 376–379 (2008).
[CrossRef]

Zhu, Y.

Zussy, M.

B. B. Bakir, C. Seassal, X. Letartre, P. Viktorovitch, M. Zussy, L. D. Cioccio, and J. M. Fedeli, “Surface-emitting microlaser combining two-dimensional photonic crystal membrane and vertical Bragg mirror,” Appl. Phys. Lett. 88, 081113 (2006).
[CrossRef]

Appl. Phys. Lett. (5)

P. B. Deotare, M. W. McCutcheon, I. W. Frank, M. Khan, and M. Loncar, “High quality factor photonic crystal nanobeam cavities,” Appl. Phys. Lett. 94, 121106 (2009).
[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]

M.-K. Seo, K.-Y. Jeong, J.-K. Yang, Y.-H. Lee, H.-G. Park, and S.-B. Kim, “Low threshold current single-cell hexapole mode photonic crystal laser,” Appl. Phys. Lett. 90, 171122 (2007).
[CrossRef]

M. L. Povinelli, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “Toward photonic-crystal metamaterials: creating magnetic emitters in photonic crystals,” Appl. Phys. Lett. 82, 1069–1071 (2003).
[CrossRef]

B. B. Bakir, C. Seassal, X. Letartre, P. Viktorovitch, M. Zussy, L. D. Cioccio, and J. M. Fedeli, “Surface-emitting microlaser combining two-dimensional photonic crystal membrane and vertical Bragg mirror,” Appl. Phys. Lett. 88, 081113 (2006).
[CrossRef]

IEEE J. Quantum Electron. (3)

J. L. Jewell, J. P. Harbison, A. Scherer, Y. H. Lee, and L. T. Florez, “Vertical-cavity surface-emitting lasers: design, growth, fabrication, characterization,” IEEE J. Quantum Electron. 27, 1332–1346 (1991).
[CrossRef]

S.-W. Chang and S. L. Chuang, “Fundamental formulation for plasmonic nanolasers,” IEEE J. Quantum Electron. 45, 1014–1023 (2009).
[CrossRef]

D. Taillaert, W. Bogaerts, P. Bienstman, T. Krauss, P. Van Daele, I. Moerman, S. Verstuyft, K. De Mesel, and R. Baets, “An out-of-plane grating coupler for efficient butt-coupling between compact planar waveguides and single-mode fibers,” IEEE J. Quantum Electron. 38, 949–955 (2002).
[CrossRef]

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

M. Fujita, A. Sakai, and T. Baba, “Ultrasmall and ultralow threshold GaInAsP-InP microdisk injection lasers: design, fabrication, lasing characteristics, and spontaneous emission factor,” IEEE J. Sel. Top. Quantum Electron. 5, 673–681 (1999).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (2)

J. Vac. Sci. Technol. B (1)

C. M. Long, A. V. Giannopoulos, and K. D. Choquette, “Lateral current injection photonic crystal membrane light emitting diodes,” J. Vac. Sci. Technol. B 28, 359–364 (2010).
[CrossRef]

Nano Lett. (1)

M.-K. Seo, S.-H. Kwon, H.-S. Ee, and H.-G. Park, “Full three-dimensional subwavelength high-Q surface-plasmon-polariton cavity,” Nano Lett. 9, 4078–4082 (2009).
[CrossRef]

Nanotechnology (1)

U. K. Khankhoje, S.-H. Kim, B. C. Richards, J. Hendrickson, J. Sweet, J. D. Olitzky, G. Khitrova, H. M. Gibbs, and A. Scherer, “Modelling and fabrication of GaAs photonic-crystal cavities for cavity quantum electrodynamics,” Nanotechnology 21, 065202 (2010).
[CrossRef]

Nat. Mater. (1)

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

Nat. Photon. (1)

B. Ellis, M. A. Mayer, G. Shambat, T. Sarmiento, J. Harris, E. E. Haller, and J. Vuckovic, “Ultralow-threshold electrically pumped quantum-dot photonic-crystal nanocavity laser,” Nat. Photon. 5, 297–300 (2011).
[CrossRef]

Nat. Phys. (1)

H. Altug, D. Englund, and J. Vučković, “Ultra-fast photonic crystal nanolasers,” Nat. Phys. 2, 484–488 (2006).
[CrossRef]

Nature (London) (4)

K. Ishizaki and S. Noda, “Manipulation of photons at the surface of three-dimensional photonic crystals,” Nature (London) 460, 367–370 (2009).
[CrossRef]

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature (London) 455, 376–379 (2008).
[CrossRef]

B. Min, E. Ostby, V. Sorger, E. Ulin-Avila, L. Yang, X. Zhang, and K. Vahala, “High-Q surface-plasmon-polarition whispering-gallery microcavity,” Nature (London) 457, 455–458 (2009).
[CrossRef]

R. F. Oulton, V. J. Sorger, T. Zentgaraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature (London) 461, 629–632 (2009).
[CrossRef]

Opt. Commun. (1)

J. P. Dowling, M. O. Scully, and F. DeMartini, “Radiation pattern of a classical dipole in a cavity,” Opt. Commun. 82, 415–419 (1991).
[CrossRef]

Opt. Express (11)

M. T. Hill, M. Marell, E. S. P. Leong, B. Smalbrugge, Y. Zhu, M. Sun, P. J. van Veldhoven, E. J. Geluk, F. Karouta, Y.-S. Oei, R. Nötzel, C.-Z. Ning, and M. K. Smit, “Lasing in metal-insulator-metal sub-wavelength plasmonic waveguides,” Opt. Express 17, 11107–11112 (2009).
[CrossRef]

J. Huang, S.-H. Kim, and A. Scherer, “Design of a surface-emitting, subwavelength metal-clad disk laser in the visible spectrum,” Opt. Express 18, 19581–19591 (2010).
[CrossRef]

K. Nozaki, S. Kita, and T. Baba, “Room temperature continuous wave operation and controlled spontaneous emission in ultrasmall photonic crystal nanolaser,” Opt. Express 15, 7506–7514 (2007).
[CrossRef]

T. Okumura, M. Kurokawa, M. Shirao, D. Kondo, H. Ito, N. Nishiyama, T. Maruyama, and S. Arai, “Lateral current injection GaInAsP/InP laser on semi-insulating substrate for membrane-based photonic circuits,” Opt. Express 17, 12564–12570 (2009).
[CrossRef]

M. Toishi, D. Englund, A. Faraon, and J. Vučković, “High-brightness single photon source from a quantum dot in a directional-emission nanocavity,” Opt. Express 17, 14618–14626 (2009).
[CrossRef]

H.-J. Chang, S.-H. Kim, Y.-H. Lee, E. P. Kartalov, and A. Scherer, “A photonic-crystal optical antenna for extremely large local-field enhancement,” Opt. Express 18, 24163–24177 (2010).
[CrossRef]

A. M. Lakhani, M. ki Kim, E. K. Lau, and M. C. Wu, “Plasmonic crystal defect nanolaser,” Opt. Express 19, 18237–18245 (2011).
[CrossRef]

I. Friedler, C. Sauvan, J. P. Hugonin, P. Lalanne, J. Claudon, and J. M. Gérard, “Solid-state single photon sources: the nanowire antenna,” Opt. Express 17, 2095–2110 (2009).
[CrossRef]

W.-D. Li, F. Ding, J. Hu, and S. Y. Chou, “Three-dimensional cavity nanoantenna coupled plasmonic nanodots for ultrahigh and uniform surface-enhanced Raman scattering over large area,” Opt. Express 19, 3925–3936 (2011).
[CrossRef]

J.-H. Kang, M.-K. Seo, S.-K. Kim, S.-H. Kim, M.-K. Kim, H.-G. Park, K.-S. Kim, and Y.-H. Lee, “Polarized vertical beaming of an engineered hexapole mode laser,” Opt. Express 17, 6074–6081 (2009).
[CrossRef]

A. Tandaechanurat, S. Iwamoto, M. Nomura, N. Kumagai, and Y. Arakawa, “Increase of Q-factor in photonic crystal H1-defect nanocavities after closing of photonic bandgap with optimal slab thickness,” Opt. Express 16, 448–455 (2008).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. (1)

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

Phys. Rev. B (6)

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

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65, 235112 (2002).
[CrossRef]

T. Ochiai and K. Sakoda, “Dispersion relation and optical transmittance of a hexagonal photonic crystal slab,” Phys. Rev. B 63, 125107 (2001).
[CrossRef]

M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: refractionlike behavior in the vicinity of the photonic band gap,” Phys. Rev. B 62, 10696–10705 (2000).
[CrossRef]

Phys. Rev. Lett. (4)

D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimulated emission of radiation: quantum generation of coherent surface plasmons in nanosystems,” Phys. Rev. Lett. 90, 027402 (2003).
[CrossRef]

M. I. Stockman, “Nanofocusing of optical energy in tapered plasmonic waveguides,” Phys. Rev. Lett. 93, 137404 (2004).
[CrossRef]

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

S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987).
[CrossRef]

Rep. Prog. Phys. (1)

J. M. Pitarke, V. M. Silkin, E. V. Chulkov, and P. M. Echenique, “Theory of surface plasmons and surface-plasmon polaritions,” Rep. Prog. Phys. 70, 1–87 (2007).
[CrossRef]

Science (4)

S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full three-dimensional photonic bandgap crystals at near-infrared wavelengths,” Science 289, 604–606 (2000).
[CrossRef]

H. Yokoyama, “Physics and device applications of optical microcavities,” Science 256, 66–70 (1992).
[CrossRef]

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

Other (8)

S.-H. Kim, Y.-H. Lee, J. Huang, and A. Scherer, “Unidirectional vertical emission from photonic crystal nanolasers,” in Proceedings of 11th International IEEE Conference on Transparent Optical Networks (IEEE, 2009), pp. 1–4.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed.(Princeton University, 2008).

E. A. Hinds, Cavity Quantum Electrodynamics (Academic, 1994).

S.-H. Kim, M.-K. Seo, J.-Y. Kim, and Y.-H. Lee, “Effects of a bottom substrate on emission properties of a photonic crystal nanolaser,” in Proceedings of IEEE 19th International Conference on Indium Phosphide & Related Materials (IEEE, 2007), pp. 480–483.

C. Kittel, Introduction to Solid State Physics, 8th ed. (Wiley, 2005).

M. Staffaroni, J. Conway, S. Vedantam, J. Tang, and E. Yablonovitch, “Circuit analysis in metal-optics,” http://arxiv.org/abs/1006.3126 .

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1998).

S.-H. Kim, J. Huang, and A. Scherer, “A photonic crystal nanocavity laser in an optically very thick slab,” http://arxiv.org/abs/1111.4272 .

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Figures (10)

Fig. 1.
Fig. 1.

Evolution of PhC nanolaser: from VCSEL to hybrid metal-PhC laser.

Fig. 2.
Fig. 2.

(a) A PhC nanocavity is suspended in air above a flat mirror (a bottom reflector). The radiative decay rate (γ) of the nanocavity mode can be tuned as a function of the air-gap size. (b) The design of the PhC nanocavity. Here, two air-holes facing each other are enlarged by Rp=0.05a. Other parameters are as follows: the slab thickness (T)=0.9a, the modified hole radius (Rm)=0.25a, and the background hole radius (R)=0.25a. The lattice constant of the PhC is denoted as “a” throughout this paper. (c) Electric-field intensity distribution (|E|2) of the deformed hexapole mode detected in the middle of the slab (z=0). (d) Normalized decay rates (γ/γ0) of the deformed hexapole mode as a function of the air-gap size. Perfect electric conductor (PEC), gold, and a dielectric of the same refractive index of 3.4 as the slab material are considered as a bottom reflector. In the case of a gold mirror, we assume emission wavelength to be 1.3μm with a=450nm. Drude model parameters are as follows: ϵ=10.48, ωp=1.38×1016rad/s, and γm=1.18×1014rad/s. (e) The resonance frequency also changes as we vary the air-gap size.

Fig. 3.
Fig. 3.

(a) Vertical emission enhancement factor (W) obtained by the planewave interference model. Both the air-gap size and the slab thickness are varied, and the results of varying slab thicknesses were shown as multiple curves as a function of the air-gap. We have assumed the effective refractive index of the slab (neff) to be 2.6, which will result in r0=(neff1)/(neff+1)0.44. (b) A schematic of the model for the PhC nanocavity suspending over a bottom reflector. The perforated slab is replaced with a uniform dielectric slab with neff, and the underlying mirror is assumed to be PEC.

Fig. 4.
Fig. 4.

FDTD simulated far-field emission profiles from the deformed hexapole mode shown in Fig. 2. Far-field patterns detected over the hemispherical surface are transformed into the 2D plane by using a simple mapping defined by x=θcosϕ and y=θsinϕ. Numbers represent the air-gap size normalized to the emission wavelength of the reference cavity () in the absence of the mirror.

Fig. 5.
Fig. 5.

(a) The far-field emission profiles shown in Fig. 4 are normalized by the reference far-field pattern ( in Fig. 4), where white regions denote values >6.33. (b) We extract θ=0 components from the normalized far-field patterns and plot them together with the theoretical curves obtained by the planewave interference model.

Fig. 6.
Fig. 6.

(a) A PhC nanocavity is brought into contact with the underlying metal substrate. We assume realistic optical constants of gold at RT, which is implemented using the single-pole Drude model in FDTD. (b) FDTD simulated electric-field intensity profiles (|E|2) of the dipole mode when the slab thickness is 606 nm. Other structural parameters are as follows: Rm=0.25a, R=0.25a, Rp=0.05a, and a=315nm. (c) Optical properties of the dipole mode. Quality factor (Q), effective mode volume (V), and Purcell factor (Fp) derived from Q and V are plotted as a function of the slab thickness. Here, slightly different lattice constants (a) have been used for different slab thicknesses to keep the emission wavelength a constant at 1.3μm. (d) The total electromagnetic energy contained in the cavity dissipates into two independent loss channels, one in the form of propagating radiation in air, and the other in the form of absorption in metal. Here, radiation efficiency refers to the fraction of total dissipation into the radiation.

Fig. 7.
Fig. 7.

Here, we assume RT gold substrate and analyze the same dipole mode shown in Fig. 6(b). (a) Far-field emission profiles by varying the slab thickness from 500 nm to 900 nm. (b) Polarization resolved far-field pattern for T=600nm. In the simulation, microscopic linear polarizers, one polarized along x direction and the other along y direction, are assumed to scan over the hemispherical surface to measure |Ex|2 and |Ey|2, respectively.

Fig. 8.
Fig. 8.

We analyze the simplest SPP mode formed at a dielectric/metal interface. (a) Theoretical dispersion relation (ωk) when ϵd=5.0 and ϵ=1.0, where we assume the Drude model for the metal, ϵm(ω)=ϵωp2/(ω2+iγmω). (b) Plasmonicity is obtained by analytic calculation (solid curve) and compared with the result obtained using FDTD (square dots).

Fig. 9.
Fig. 9.

Here, we assume an ideal gold substrate by setting its damping constant to zero. (a) Quality factor of the same dipole mode as shown in Fig. 6. Since the absorption in gold has been quenched, quality factors relate to radiation losses. Again, we tune the lattice constant (a) to approximately keep the emission wavelength at 1.3μm. (b) The degree of the plasmonic character, “plasmonicity” of the dipole mode as a function of the slab thickness.

Fig. 10.
Fig. 10.

We take an example from our previous paper, a metal-clad nanodisk [38]. The diameter of the dielectric disk is 220 nm. Here, two representative modes are analyzed, (a) one is an SPP-like surface confined mode and (b) the other is a photonic-like monopole mode. Their emission wavelengths, quality factors, and plasmonicities are obtained through FDTD simulations. All values correspond to ideal silver with zero damping.

Equations (30)

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W|1+S|2=|1+t02eiϕ(1r02e2iϕ)(r0e2iφ)r0t02e2iϕ|2.
UEM(t)=UEM(0)exp[ωQtott].
UE(t)Vd3ruE(r,t),
UM(t)Vd3ruM(r,t).
uE(r,t)ϵ02Re[d(ωϵ)dω]E(r,t)·E(r,t)T,
uM(r,t)ϵ02Re[ϵ(ω)]E(r,t)·E(r,t)T.
uE(r,t)=ϵ02{ϵ+ωp2(ω2γm2)(ω2+γm2)2}E(r,t)·E(r,t)T,
uM(r,t)=ϵ02{ϵωp2ω2+γm2}E(r,t)·E(r,t)T.
VUEM(t)max{uE(rmax,t)+uM(rmax,t)},
Fp3Qtot4π2V(λn)3,
gth=1ΓE·Qtot·2πng,aλ,
ΓE=Vad3ruE(r,t)+uM(r,t)Vd3ruE(r,t)+uM(r,t).
1Qtot=1Qrad+1Qabs.
ηrad1/Qrad1/Qtot=11/Qabs1/Qtot.
Pabs(t)Vd3rωϵ0Im[ϵm(ω)]E(r,t)·E(r,t)T.
Qabs=ωUEM(t)Pabs(t).
Qrad=ωUEM(t)Prad(t),
Prad(t)Sd2r·E(r,t)×H(r,t)T.
ukin(r,t)12meNe(r,t)v(r,t)·v(r,t)T.
ukin(r,t)=12meNee2(Neev(r,t))·(Neev(r,t))T,
=12[meNee2]J(r,t)·J(r,t)T.
ukin(r)14[meNee2]|J˜(r)|2,
=14[meNee2]|σ(ω)|2|E˜(r)|2.
σ(ω)=ϵ0ωp2γmiω,
ukin(r)=ϵ04ωp2γm2+ω2|E˜(r)|2.
ukin(r,t)=ϵ02ωp2γm2+ω2E(r,t)·E(r,t)T.
Π2×Total kinetic energyTotal EM energy=2×metald3rukin(r)Vd3r(uE(r)+uM(r))(in the limitγm0).
kx2=(ωc)ϵmϵdϵm+ϵd.
ΠSPP=01/kxdx0dzϵ0(ωpω)2Em·EmT01/kxdx0dzϵ0ϵdEd·EdT+01/kxdx0dzϵ0ϵEm·EmT,
ΠSPP=(ωpω)21ϵm21ϵd+ϵϵm2.

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