Abstract

Photonic crystal nanobeam cavities are versatile platforms of interest for optical communications, optomechanics, optofluidics, cavity QED, etc. In a previous work [Appl. Phys. Lett. 96, 203102 (2010)], we proposed a deterministic method to achieve ultrahigh Q cavities. This follow-up work provides systematic analysis and verifications of the deterministic design recipe and further extends the discussion to air-mode cavities. We demonstrate designs of dielectric-mode and air-mode cavities with Q > 109, as well as dielectric-mode nanobeam cavities with both ultrahigh-Q (> 107) and ultrahigh on-resonance transmissions (T > 95%).

© 2011 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. Quality factor is defined as Q=ω0Energy storedPower loss, and mode volume is defined as V = ∫ dVε|E|2/[ε|E|2]max.
  2. K. J. Vahala, “Optical microcavities,” Nature 424, 839–846 (2003).
    [CrossRef] [PubMed]
  3. J. L. O’Brien, A. Furusawa, and J. Vuckovic, “Photonic quantum technologies,” Nat. Photonics 3, 687–695 (2009).
    [CrossRef]
  4. J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photonics 4, 535–544 (2010).
    [CrossRef]
  5. M. Eichenfield, J. Chan, R. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462, 78–82 (2009).
    [CrossRef] [PubMed]
  6. D. Van Thourhout and J. Roels, “Optomechanical device actuation through the optical gradient force,” Nat. Photonics 4, 211–217 (2010).
    [CrossRef]
  7. D. G. Grier, “A revolution in optical manipulationm,” Nature 424, 21–27 (2003).
    [CrossRef]
  8. D. Psaltis, S. R. Quake, and C. Yang, “Developing optofluidic technology through the fusion of microfluidics and optics,” Nature 442, 381–386 (2006).
    [CrossRef] [PubMed]
  9. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
    [CrossRef] [PubMed]
  10. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486 (1987).
    [CrossRef] [PubMed]
  11. J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
    [CrossRef]
  12. O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
    [CrossRef] [PubMed]
  13. J. Ctyroky, “Photonic bandgap structures in planar waveguides,” J. Opt. Soc. Am. A 18, 435–441 (2001).
    [CrossRef]
  14. M. R. Watts, S. G. Johnson, H. A. Haus, and J. D. Joannopoulos, “Electromagnetic cavity with arbitrary Q and small modal volume without a complete photonic bandgap,” Opt. Lett. 27, 1785–1787 (2002).
    [CrossRef]
  15. J. M. Geremia, J. Williams, and H. Mabuchi, “Inverse-problem approach to designing photonic crystals for cavity QED experiments,” Phys. Rev. E 66, 066606 (2002).
    [CrossRef]
  16. M. Burger, S. J Osher, and E. Yablonovitch, “Inverse problem techniques for the design of photonic crystals,” IEICE Trans. Electron. E87C, 258–265 (2004).
  17. 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]
  18. B. S. Song, S. Noda, T. Asano, and Y. Akahane, “Ultra-high-Q photonic double-heterostructure nanocavity,” Nat. Mater. 4, 207–210 (2005).
    [CrossRef]
  19. S. Tomljenovic-Hanic, C. M. de Sterke, and M. J. Steel, “Design of high-Q cavities in photonic crystal slab heterostructures by air-holes infiltration,” Opt. Express 14, 12451–12456 (2006).
    [CrossRef] [PubMed]
  20. E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88, 041112 (2006).
    [CrossRef]
  21. 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] [PubMed]
  22. Y. Tanaka, T. Asano, and S. Noda, “Design of photonic crystal nanocavity with Q-factor of ∼109,” J. Lightwave Technol. 26, 1532 (2008).
    [CrossRef]
  23. M. Notomi, E. Kuramochi, and H. Taniyama, “Ultrahigh-Q nanocavity with 1D Photonic Gap,” Opt. Express,  16, 11095 (2008).
    [CrossRef] [PubMed]
  24. P. Velha, E. Picard, T. Charvolin, E. Hadji, J. C. Rodier, P. Lalanne, and E. Peyrage, “Ultra-high Q/V Fabry-Perot microcavity on SOI substrate,” Opt. Express 15, 16090–16096 (2007).
    [CrossRef] [PubMed]
  25. S. Reitzenstein, C. Hofmann, A. Gorbunov, M Strauß, S. H. Kwon, C. Schneider, A. Loffler, S. Hofling, M. Kamp, and A. Forchel, “AlAs/GaAs micropillar cavities with quality factors exceeding 150000,” Appl. Phys. Lett. 90, 251109 (2007).
    [CrossRef]
  26. A. R. Md Zain, N. P. Johnson, M. Sorel, and R. M. De La Rue, “Ultra high quality factor one dimensional photonic crystal/photonic wire microcavities in silicon-on-insulator (SOI),” Opt. Express 16, 12084 (2008).
    [CrossRef]
  27. Y. Zhang and M. Loncar, “Ultra-high quality factor optical resonators based on semiconductor nanowires.” Opt. Express 16, 17400–17409 (2008).
    [CrossRef] [PubMed]
  28. M. W. McCutcheon and M. Loncar, “Design of a silicon nitride photonic crystal nanocavity with a Quality factor of one million for coupling to a diamond nanocrystal,” Opt. Express 16, 19136–19145 (2008).
    [CrossRef]
  29. L. D. Haret, T. Tanabe, E. Kuramochi, and M. Notomi, “Extremely low power optical bistability in silicon demonstrated using 1D photonic crystal nanocavity,” Opt. Express 17, 21008–21117 (2009).
    [CrossRef]
  30. J. Chan, M. Eichenfield, R. Camacho, and O. Painter, “Optical and mechanical design of a “zipper” photonic crystal optomechanical cavity”, Opt. Express 17, 3802–3817 (2009).
    [CrossRef] [PubMed]
  31. 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]
  32. Q. Quan, P. B. Deotare, and M. Loncar, “Photonic crystal nanobeam cavity strongly coupled to the feeding waveguide,” Appl. Phys. Lett. 96, 203102 (2010).
    [CrossRef]
  33. E. Kuraamochi, H. Taniyama, T. Tanabe, K. Kawasaki, Y-G. Roh, and M. Notomi, “Ultrahigh-Q one-dimensional photonic crystal nanocavities with modulated mode-gap barriers on SiO2 claddings and on air claddings,” Opt. Express 18, 15859–15869 (2010).
    [CrossRef]
  34. Q. Quan, I. B. Burgess, S. K. Y. Tang, D. L. Floyd, and M. Loncar, “High-Q/V photonic crystal nanobeam cavities in an ultra-low index-contrast polymeric optofluidic platform,” arXiv:1108.2669 (2010).
  35. J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, “Optimization of the Q factor in photonic crystal microcavities,” IEEE J. Quantum Electron. 38, 850–856 (2002).
    [CrossRef]
  36. K. Srinivasan and O. Painter, “Momentum space design of high-Q photonic crystal optical cavities,” Opt. Express 10, 670–684 (2002).
    [PubMed]
  37. D. Englund, I. Fushman, and J. Vuckovic, “General recipe for designing photonic crystal cavities,” Opt. Express 13, 5961–5975 (2005).
    [CrossRef] [PubMed]
  38. M. Palamaru and P. Lalanne, “Photonic crystal waveguides: Out-of-plane losses and adiabatic modal conversion,” Appl. Phys. Lett. 78, 1466–1468 (2001).
    [CrossRef]
  39. P. Lalanne, S. Mias, and J. P. Hugonin, “Two physical mechanisms for boosting the quality factor to cavity volume ratio of photonic crystal microcavities,” Opt. Express 12, 458–467 (2004).
    [CrossRef] [PubMed]
  40. K. Sakoda, Optical Properties of Photonic Crystals, 2nd Ed. (Springer, 2005).
  41. J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd Ed. (Cambridge University Press, 2007).
  42. S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisbergs, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E 65, 066611 (2002).
    [CrossRef]
  43. J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, “Optimization of three-dimensional micropost microcavities for cavity quantum electrodynamics,” Phys. Rev. E 65, 016608 (2001).
  44. B. H. Ahn, J. H. Kang, M. K. Kim, J. H. Song, B. Min, K. S. Kim, and Y. H. Lee, “One-dimensional parabolic-beam photonic crystal laser,” Opt. Express 18, 5654–5660 (2010).
    [CrossRef] [PubMed]
  45. D. W. Vernooy, A. Furusawa, N. P. Georgiades, V. S. Ilchenko, and H. J. Kimble, “Cavity QED with high-Q whispering gallery modes,” Phys. Rev. A 57, R2293–R2296 (1998).
    [CrossRef]
  46. D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421, 925–928 (2003).
    [CrossRef] [PubMed]
  47. M. Soltani, S. Yegnanarayanan, and A. Adibi, “Ultra-high Q planar silicon microdisk resonators for chip-scale silicon photonics,” Opt. Express 15, 4694–4704 (2007).
    [CrossRef] [PubMed]

2010 (5)

J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photonics 4, 535–544 (2010).
[CrossRef]

D. Van Thourhout and J. Roels, “Optomechanical device actuation through the optical gradient force,” Nat. Photonics 4, 211–217 (2010).
[CrossRef]

Q. Quan, P. B. Deotare, and M. Loncar, “Photonic crystal nanobeam cavity strongly coupled to the feeding waveguide,” Appl. Phys. Lett. 96, 203102 (2010).
[CrossRef]

E. Kuraamochi, H. Taniyama, T. Tanabe, K. Kawasaki, Y-G. Roh, and M. Notomi, “Ultrahigh-Q one-dimensional photonic crystal nanocavities with modulated mode-gap barriers on SiO2 claddings and on air claddings,” Opt. Express 18, 15859–15869 (2010).
[CrossRef]

B. H. Ahn, J. H. Kang, M. K. Kim, J. H. Song, B. Min, K. S. Kim, and Y. H. Lee, “One-dimensional parabolic-beam photonic crystal laser,” Opt. Express 18, 5654–5660 (2010).
[CrossRef] [PubMed]

2009 (5)

L. D. Haret, T. Tanabe, E. Kuramochi, and M. Notomi, “Extremely low power optical bistability in silicon demonstrated using 1D photonic crystal nanocavity,” Opt. Express 17, 21008–21117 (2009).
[CrossRef]

J. Chan, M. Eichenfield, R. Camacho, and O. Painter, “Optical and mechanical design of a “zipper” photonic crystal optomechanical cavity”, Opt. Express 17, 3802–3817 (2009).
[CrossRef] [PubMed]

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]

M. Eichenfield, J. Chan, R. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462, 78–82 (2009).
[CrossRef] [PubMed]

J. L. O’Brien, A. Furusawa, and J. Vuckovic, “Photonic quantum technologies,” Nat. Photonics 3, 687–695 (2009).
[CrossRef]

2008 (5)

2007 (4)

2006 (3)

S. Tomljenovic-Hanic, C. M. de Sterke, and M. J. Steel, “Design of high-Q cavities in photonic crystal slab heterostructures by air-holes infiltration,” Opt. Express 14, 12451–12456 (2006).
[CrossRef] [PubMed]

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88, 041112 (2006).
[CrossRef]

D. Psaltis, S. R. Quake, and C. Yang, “Developing optofluidic technology through the fusion of microfluidics and optics,” Nature 442, 381–386 (2006).
[CrossRef] [PubMed]

2005 (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]

D. Englund, I. Fushman, and J. Vuckovic, “General recipe for designing photonic crystal cavities,” Opt. Express 13, 5961–5975 (2005).
[CrossRef] [PubMed]

2004 (2)

M. Burger, S. J Osher, and E. Yablonovitch, “Inverse problem techniques for the design of photonic crystals,” IEICE Trans. Electron. E87C, 258–265 (2004).

P. Lalanne, S. Mias, and J. P. Hugonin, “Two physical mechanisms for boosting the quality factor to cavity volume ratio of photonic crystal microcavities,” Opt. Express 12, 458–467 (2004).
[CrossRef] [PubMed]

2003 (4)

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421, 925–928 (2003).
[CrossRef] [PubMed]

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]

D. G. Grier, “A revolution in optical manipulationm,” Nature 424, 21–27 (2003).
[CrossRef]

K. J. Vahala, “Optical microcavities,” Nature 424, 839–846 (2003).
[CrossRef] [PubMed]

2002 (5)

M. R. Watts, S. G. Johnson, H. A. Haus, and J. D. Joannopoulos, “Electromagnetic cavity with arbitrary Q and small modal volume without a complete photonic bandgap,” Opt. Lett. 27, 1785–1787 (2002).
[CrossRef]

J. M. Geremia, J. Williams, and H. Mabuchi, “Inverse-problem approach to designing photonic crystals for cavity QED experiments,” Phys. Rev. E 66, 066606 (2002).
[CrossRef]

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, “Optimization of the Q factor in photonic crystal microcavities,” IEEE J. Quantum Electron. 38, 850–856 (2002).
[CrossRef]

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

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisbergs, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E 65, 066611 (2002).
[CrossRef]

2001 (3)

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, “Optimization of three-dimensional micropost microcavities for cavity quantum electrodynamics,” Phys. Rev. E 65, 016608 (2001).

M. Palamaru and P. Lalanne, “Photonic crystal waveguides: Out-of-plane losses and adiabatic modal conversion,” Appl. Phys. Lett. 78, 1466–1468 (2001).
[CrossRef]

J. Ctyroky, “Photonic bandgap structures in planar waveguides,” J. Opt. Soc. Am. A 18, 435–441 (2001).
[CrossRef]

1999 (1)

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

1998 (1)

D. W. Vernooy, A. Furusawa, N. P. Georgiades, V. S. Ilchenko, and H. J. Kimble, “Cavity QED with high-Q whispering gallery modes,” Phys. Rev. A 57, R2293–R2296 (1998).
[CrossRef]

1997 (1)

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
[CrossRef]

1987 (2)

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

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

Adibi, A.

Ahn, B. H.

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]

Armani, D. K.

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421, 925–928 (2003).
[CrossRef] [PubMed]

Asano, T.

Y. Tanaka, T. Asano, and S. Noda, “Design of photonic crystal nanocavity with Q-factor of ∼109,” J. Lightwave Technol. 26, 1532 (2008).
[CrossRef]

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.

Burger, M.

M. Burger, S. J Osher, and E. Yablonovitch, “Inverse problem techniques for the design of photonic crystals,” IEICE Trans. Electron. E87C, 258–265 (2004).

Burgess, I. B.

Q. Quan, I. B. Burgess, S. K. Y. Tang, D. L. Floyd, and M. Loncar, “High-Q/V photonic crystal nanobeam cavities in an ultra-low index-contrast polymeric optofluidic platform,” arXiv:1108.2669 (2010).

Camacho, R.

Chan, J.

Charvolin, T.

Ctyroky, J.

Dapkus, P. D.

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

De La Rue, R. M.

de Sterke, C. M.

Deotare, P. B.

Q. Quan, P. B. Deotare, and M. Loncar, “Photonic crystal nanobeam cavity strongly coupled to the feeding waveguide,” Appl. Phys. Lett. 96, 203102 (2010).
[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]

Eichenfield, M.

Englund, D.

Fan, S.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
[CrossRef]

Ferrera, J.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
[CrossRef]

Fink, Y.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisbergs, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E 65, 066611 (2002).
[CrossRef]

Floyd, D. L.

Q. Quan, I. B. Burgess, S. K. Y. Tang, D. L. Floyd, and M. Loncar, “High-Q/V photonic crystal nanobeam cavities in an ultra-low index-contrast polymeric optofluidic platform,” arXiv:1108.2669 (2010).

Forchel, A.

S. Reitzenstein, C. Hofmann, A. Gorbunov, M Strauß, S. H. Kwon, C. Schneider, A. Loffler, S. Hofling, M. Kamp, and A. Forchel, “AlAs/GaAs micropillar cavities with quality factors exceeding 150000,” Appl. Phys. Lett. 90, 251109 (2007).
[CrossRef]

Foresi, J. S.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
[CrossRef]

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]

Freude, W.

J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photonics 4, 535–544 (2010).
[CrossRef]

Furusawa, A.

J. L. O’Brien, A. Furusawa, and J. Vuckovic, “Photonic quantum technologies,” Nat. Photonics 3, 687–695 (2009).
[CrossRef]

D. W. Vernooy, A. Furusawa, N. P. Georgiades, V. S. Ilchenko, and H. J. Kimble, “Cavity QED with high-Q whispering gallery modes,” Phys. Rev. A 57, R2293–R2296 (1998).
[CrossRef]

Fushman, I.

Georgiades, N. P.

D. W. Vernooy, A. Furusawa, N. P. Georgiades, V. S. Ilchenko, and H. J. Kimble, “Cavity QED with high-Q whispering gallery modes,” Phys. Rev. A 57, R2293–R2296 (1998).
[CrossRef]

Geremia, J. M.

J. M. Geremia, J. Williams, and H. Mabuchi, “Inverse-problem approach to designing photonic crystals for cavity QED experiments,” Phys. Rev. E 66, 066606 (2002).
[CrossRef]

Gorbunov, A.

S. Reitzenstein, C. Hofmann, A. Gorbunov, M Strauß, S. H. Kwon, C. Schneider, A. Loffler, S. Hofling, M. Kamp, and A. Forchel, “AlAs/GaAs micropillar cavities with quality factors exceeding 150000,” Appl. Phys. Lett. 90, 251109 (2007).
[CrossRef]

Grier, D. G.

D. G. Grier, “A revolution in optical manipulationm,” Nature 424, 21–27 (2003).
[CrossRef]

Hadji, E.

Haret, L. D.

L. D. Haret, T. Tanabe, E. Kuramochi, and M. Notomi, “Extremely low power optical bistability in silicon demonstrated using 1D photonic crystal nanocavity,” Opt. Express 17, 21008–21117 (2009).
[CrossRef]

Haus, H. A.

Hofling, S.

S. Reitzenstein, C. Hofmann, A. Gorbunov, M Strauß, S. H. Kwon, C. Schneider, A. Loffler, S. Hofling, M. Kamp, and A. Forchel, “AlAs/GaAs micropillar cavities with quality factors exceeding 150000,” Appl. Phys. Lett. 90, 251109 (2007).
[CrossRef]

Hofmann, C.

S. Reitzenstein, C. Hofmann, A. Gorbunov, M Strauß, S. H. Kwon, C. Schneider, A. Loffler, S. Hofling, M. Kamp, and A. Forchel, “AlAs/GaAs micropillar cavities with quality factors exceeding 150000,” Appl. Phys. Lett. 90, 251109 (2007).
[CrossRef]

Hugonin, J. P.

Ibanescu, M.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisbergs, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E 65, 066611 (2002).
[CrossRef]

Ilchenko, V. S.

D. W. Vernooy, A. Furusawa, N. P. Georgiades, V. S. Ilchenko, and H. J. Kimble, “Cavity QED with high-Q whispering gallery modes,” Phys. Rev. A 57, R2293–R2296 (1998).
[CrossRef]

Ippen, E. P.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
[CrossRef]

Joannopoulos, J. D.

M. R. Watts, S. G. Johnson, H. A. Haus, and J. D. Joannopoulos, “Electromagnetic cavity with arbitrary Q and small modal volume without a complete photonic bandgap,” Opt. Lett. 27, 1785–1787 (2002).
[CrossRef]

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisbergs, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E 65, 066611 (2002).
[CrossRef]

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
[CrossRef]

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd Ed. (Cambridge University Press, 2007).

John, S.

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

Johnson, N. P.

Johnson, S. G.

M. R. Watts, S. G. Johnson, H. A. Haus, and J. D. Joannopoulos, “Electromagnetic cavity with arbitrary Q and small modal volume without a complete photonic bandgap,” Opt. Lett. 27, 1785–1787 (2002).
[CrossRef]

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisbergs, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E 65, 066611 (2002).
[CrossRef]

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd Ed. (Cambridge University Press, 2007).

Kamp, M.

S. Reitzenstein, C. Hofmann, A. Gorbunov, M Strauß, S. H. Kwon, C. Schneider, A. Loffler, S. Hofling, M. Kamp, and A. Forchel, “AlAs/GaAs micropillar cavities with quality factors exceeding 150000,” Appl. Phys. Lett. 90, 251109 (2007).
[CrossRef]

Kang, J. H.

Kawasaki, K.

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]

Kim, I.

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

Kim, K. S.

Kim, M. K.

Kimble, H. J.

D. W. Vernooy, A. Furusawa, N. P. Georgiades, V. S. Ilchenko, and H. J. Kimble, “Cavity QED with high-Q whispering gallery modes,” Phys. Rev. A 57, R2293–R2296 (1998).
[CrossRef]

Kimerling, L. C.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
[CrossRef]

Kippenberg, T. J.

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421, 925–928 (2003).
[CrossRef] [PubMed]

Kita, S.

Koos, C.

J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photonics 4, 535–544 (2010).
[CrossRef]

Kuraamochi, E.

Kuramochi, E.

L. D. Haret, T. Tanabe, E. Kuramochi, and M. Notomi, “Extremely low power optical bistability in silicon demonstrated using 1D photonic crystal nanocavity,” Opt. Express 17, 21008–21117 (2009).
[CrossRef]

M. Notomi, E. Kuramochi, and H. Taniyama, “Ultrahigh-Q nanocavity with 1D Photonic Gap,” Opt. Express,  16, 11095 (2008).
[CrossRef] [PubMed]

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88, 041112 (2006).
[CrossRef]

Kwon, S. H.

S. Reitzenstein, C. Hofmann, A. Gorbunov, M Strauß, S. H. Kwon, C. Schneider, A. Loffler, S. Hofling, M. Kamp, and A. Forchel, “AlAs/GaAs micropillar cavities with quality factors exceeding 150000,” Appl. Phys. Lett. 90, 251109 (2007).
[CrossRef]

Lalanne, P.

Lee, R. K.

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

Lee, Y. H.

Leuthold, J.

J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photonics 4, 535–544 (2010).
[CrossRef]

Loffler, A.

S. Reitzenstein, C. Hofmann, A. Gorbunov, M Strauß, S. H. Kwon, C. Schneider, A. Loffler, S. Hofling, M. Kamp, and A. Forchel, “AlAs/GaAs micropillar cavities with quality factors exceeding 150000,” Appl. Phys. Lett. 90, 251109 (2007).
[CrossRef]

Loncar, M.

Q. Quan, P. B. Deotare, and M. Loncar, “Photonic crystal nanobeam cavity strongly coupled to the feeding waveguide,” Appl. Phys. Lett. 96, 203102 (2010).
[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]

M. W. McCutcheon and M. Loncar, “Design of a silicon nitride photonic crystal nanocavity with a Quality factor of one million for coupling to a diamond nanocrystal,” Opt. Express 16, 19136–19145 (2008).
[CrossRef]

Y. Zhang and M. Loncar, “Ultra-high quality factor optical resonators based on semiconductor nanowires.” Opt. Express 16, 17400–17409 (2008).
[CrossRef] [PubMed]

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, “Optimization of the Q factor in photonic crystal microcavities,” IEEE J. Quantum Electron. 38, 850–856 (2002).
[CrossRef]

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, “Optimization of three-dimensional micropost microcavities for cavity quantum electrodynamics,” Phys. Rev. E 65, 016608 (2001).

Q. Quan, I. B. Burgess, S. K. Y. Tang, D. L. Floyd, and M. Loncar, “High-Q/V photonic crystal nanobeam cavities in an ultra-low index-contrast polymeric optofluidic platform,” arXiv:1108.2669 (2010).

Mabuchi, H.

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, “Optimization of the Q factor in photonic crystal microcavities,” IEEE J. Quantum Electron. 38, 850–856 (2002).
[CrossRef]

J. M. Geremia, J. Williams, and H. Mabuchi, “Inverse-problem approach to designing photonic crystals for cavity QED experiments,” Phys. Rev. E 66, 066606 (2002).
[CrossRef]

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, “Optimization of three-dimensional micropost microcavities for cavity quantum electrodynamics,” Phys. Rev. E 65, 016608 (2001).

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]

M. W. McCutcheon and M. Loncar, “Design of a silicon nitride photonic crystal nanocavity with a Quality factor of one million for coupling to a diamond nanocrystal,” Opt. Express 16, 19136–19145 (2008).
[CrossRef]

Md Zain, A. R.

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. (Cambridge University Press, 2007).

Mias, S.

Min, B.

Mitsugi, S.

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88, 041112 (2006).
[CrossRef]

Noda, S.

Y. Tanaka, T. Asano, and S. Noda, “Design of photonic crystal nanocavity with Q-factor of ∼109,” J. Lightwave Technol. 26, 1532 (2008).
[CrossRef]

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.

E. Kuraamochi, H. Taniyama, T. Tanabe, K. Kawasaki, Y-G. Roh, and M. Notomi, “Ultrahigh-Q one-dimensional photonic crystal nanocavities with modulated mode-gap barriers on SiO2 claddings and on air claddings,” Opt. Express 18, 15859–15869 (2010).
[CrossRef]

L. D. Haret, T. Tanabe, E. Kuramochi, and M. Notomi, “Extremely low power optical bistability in silicon demonstrated using 1D photonic crystal nanocavity,” Opt. Express 17, 21008–21117 (2009).
[CrossRef]

M. Notomi, E. Kuramochi, and H. Taniyama, “Ultrahigh-Q nanocavity with 1D Photonic Gap,” Opt. Express,  16, 11095 (2008).
[CrossRef] [PubMed]

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88, 041112 (2006).
[CrossRef]

Nozaki, K.

O’Brien, J. D.

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

O’Brien, J. L.

J. L. O’Brien, A. Furusawa, and J. Vuckovic, “Photonic quantum technologies,” Nat. Photonics 3, 687–695 (2009).
[CrossRef]

Osher, S. J

M. Burger, S. J Osher, and E. Yablonovitch, “Inverse problem techniques for the design of photonic crystals,” IEICE Trans. Electron. E87C, 258–265 (2004).

Painter, O.

M. Eichenfield, J. Chan, R. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462, 78–82 (2009).
[CrossRef] [PubMed]

J. Chan, M. Eichenfield, R. Camacho, and O. Painter, “Optical and mechanical design of a “zipper” photonic crystal optomechanical cavity”, Opt. Express 17, 3802–3817 (2009).
[CrossRef] [PubMed]

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

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

Palamaru, M.

M. Palamaru and P. Lalanne, “Photonic crystal waveguides: Out-of-plane losses and adiabatic modal conversion,” Appl. Phys. Lett. 78, 1466–1468 (2001).
[CrossRef]

Peyrage, E.

Picard, E.

Psaltis, D.

D. Psaltis, S. R. Quake, and C. Yang, “Developing optofluidic technology through the fusion of microfluidics and optics,” Nature 442, 381–386 (2006).
[CrossRef] [PubMed]

Quake, S. R.

D. Psaltis, S. R. Quake, and C. Yang, “Developing optofluidic technology through the fusion of microfluidics and optics,” Nature 442, 381–386 (2006).
[CrossRef] [PubMed]

Quan, Q.

Q. Quan, P. B. Deotare, and M. Loncar, “Photonic crystal nanobeam cavity strongly coupled to the feeding waveguide,” Appl. Phys. Lett. 96, 203102 (2010).
[CrossRef]

Q. Quan, I. B. Burgess, S. K. Y. Tang, D. L. Floyd, and M. Loncar, “High-Q/V photonic crystal nanobeam cavities in an ultra-low index-contrast polymeric optofluidic platform,” arXiv:1108.2669 (2010).

Reitzenstein, S.

S. Reitzenstein, C. Hofmann, A. Gorbunov, M Strauß, S. H. Kwon, C. Schneider, A. Loffler, S. Hofling, M. Kamp, and A. Forchel, “AlAs/GaAs micropillar cavities with quality factors exceeding 150000,” Appl. Phys. Lett. 90, 251109 (2007).
[CrossRef]

Rodier, J. C.

Roels, J.

D. Van Thourhout and J. Roels, “Optomechanical device actuation through the optical gradient force,” Nat. Photonics 4, 211–217 (2010).
[CrossRef]

Roh, Y-G.

Sakoda, K.

K. Sakoda, Optical Properties of Photonic Crystals, 2nd Ed. (Springer, 2005).

Scherer, A.

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, “Optimization of the Q factor in photonic crystal microcavities,” IEEE J. Quantum Electron. 38, 850–856 (2002).
[CrossRef]

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, “Optimization of three-dimensional micropost microcavities for cavity quantum electrodynamics,” Phys. Rev. E 65, 016608 (2001).

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

Schneider, C.

S. Reitzenstein, C. Hofmann, A. Gorbunov, M Strauß, S. H. Kwon, C. Schneider, A. Loffler, S. Hofling, M. Kamp, and A. Forchel, “AlAs/GaAs micropillar cavities with quality factors exceeding 150000,” Appl. Phys. Lett. 90, 251109 (2007).
[CrossRef]

Shinya, A.

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88, 041112 (2006).
[CrossRef]

Skorobogatiy, M. A.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisbergs, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E 65, 066611 (2002).
[CrossRef]

Smith, H. I.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
[CrossRef]

Soltani, M.

Song, B. S.

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]

Song, J. H.

Sorel, M.

Spillane, S. M.

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421, 925–928 (2003).
[CrossRef] [PubMed]

Srinivasan, K.

Steel, M. J.

Steinmeyer, G.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
[CrossRef]

Strauß, M

S. Reitzenstein, C. Hofmann, A. Gorbunov, M Strauß, S. H. Kwon, C. Schneider, A. Loffler, S. Hofling, M. Kamp, and A. Forchel, “AlAs/GaAs micropillar cavities with quality factors exceeding 150000,” Appl. Phys. Lett. 90, 251109 (2007).
[CrossRef]

Tanabe, T.

E. Kuraamochi, H. Taniyama, T. Tanabe, K. Kawasaki, Y-G. Roh, and M. Notomi, “Ultrahigh-Q one-dimensional photonic crystal nanocavities with modulated mode-gap barriers on SiO2 claddings and on air claddings,” Opt. Express 18, 15859–15869 (2010).
[CrossRef]

L. D. Haret, T. Tanabe, E. Kuramochi, and M. Notomi, “Extremely low power optical bistability in silicon demonstrated using 1D photonic crystal nanocavity,” Opt. Express 17, 21008–21117 (2009).
[CrossRef]

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88, 041112 (2006).
[CrossRef]

Tanaka, Y.

Tang, S. K. Y.

Q. Quan, I. B. Burgess, S. K. Y. Tang, D. L. Floyd, and M. Loncar, “High-Q/V photonic crystal nanobeam cavities in an ultra-low index-contrast polymeric optofluidic platform,” arXiv:1108.2669 (2010).

Taniyama, H.

Thoen, E. R

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
[CrossRef]

Tomljenovic-Hanic, S.

Vahala, K. J.

M. Eichenfield, J. Chan, R. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462, 78–82 (2009).
[CrossRef] [PubMed]

K. J. Vahala, “Optical microcavities,” Nature 424, 839–846 (2003).
[CrossRef] [PubMed]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421, 925–928 (2003).
[CrossRef] [PubMed]

Van Thourhout, D.

D. Van Thourhout and J. Roels, “Optomechanical device actuation through the optical gradient force,” Nat. Photonics 4, 211–217 (2010).
[CrossRef]

Velha, P.

Vernooy, D. W.

D. W. Vernooy, A. Furusawa, N. P. Georgiades, V. S. Ilchenko, and H. J. Kimble, “Cavity QED with high-Q whispering gallery modes,” Phys. Rev. A 57, R2293–R2296 (1998).
[CrossRef]

Villeneuve, P. R.

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
[CrossRef]

Vuckovic, J.

J. L. O’Brien, A. Furusawa, and J. Vuckovic, “Photonic quantum technologies,” Nat. Photonics 3, 687–695 (2009).
[CrossRef]

D. Englund, I. Fushman, and J. Vuckovic, “General recipe for designing photonic crystal cavities,” Opt. Express 13, 5961–5975 (2005).
[CrossRef] [PubMed]

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, “Optimization of the Q factor in photonic crystal microcavities,” IEEE J. Quantum Electron. 38, 850–856 (2002).
[CrossRef]

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, “Optimization of three-dimensional micropost microcavities for cavity quantum electrodynamics,” Phys. Rev. E 65, 016608 (2001).

Watanabe, T.

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88, 041112 (2006).
[CrossRef]

Watts, M. R.

Weisbergs, O.

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisbergs, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E 65, 066611 (2002).
[CrossRef]

Williams, J.

J. M. Geremia, J. Williams, and H. Mabuchi, “Inverse-problem approach to designing photonic crystals for cavity QED experiments,” Phys. Rev. E 66, 066606 (2002).
[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. (Cambridge University Press, 2007).

Yablonovitch, E.

M. Burger, S. J Osher, and E. Yablonovitch, “Inverse problem techniques for the design of photonic crystals,” IEICE Trans. Electron. E87C, 258–265 (2004).

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

Yang, C.

D. Psaltis, S. R. Quake, and C. Yang, “Developing optofluidic technology through the fusion of microfluidics and optics,” Nature 442, 381–386 (2006).
[CrossRef] [PubMed]

Yariv, A.

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

Yegnanarayanan, S.

Zhang, Y.

Appl. Phys. Lett. (5)

E. Kuramochi, M. Notomi, S. Mitsugi, A. Shinya, T. Tanabe, and T. Watanabe, “Ultrahigh-Q photonic crystal nanocavities realized by the local width modulation of a line defect,” Appl. Phys. Lett. 88, 041112 (2006).
[CrossRef]

S. Reitzenstein, C. Hofmann, A. Gorbunov, M Strauß, S. H. Kwon, C. Schneider, A. Loffler, S. Hofling, M. Kamp, and A. Forchel, “AlAs/GaAs micropillar cavities with quality factors exceeding 150000,” Appl. Phys. Lett. 90, 251109 (2007).
[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]

Q. Quan, P. B. Deotare, and M. Loncar, “Photonic crystal nanobeam cavity strongly coupled to the feeding waveguide,” Appl. Phys. Lett. 96, 203102 (2010).
[CrossRef]

M. Palamaru and P. Lalanne, “Photonic crystal waveguides: Out-of-plane losses and adiabatic modal conversion,” Appl. Phys. Lett. 78, 1466–1468 (2001).
[CrossRef]

IEEE J. Quantum Electron. (1)

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, “Optimization of the Q factor in photonic crystal microcavities,” IEEE J. Quantum Electron. 38, 850–856 (2002).
[CrossRef]

IEICE Trans. Electron. (1)

M. Burger, S. J Osher, and E. Yablonovitch, “Inverse problem techniques for the design of photonic crystals,” IEICE Trans. Electron. E87C, 258–265 (2004).

J. Lightwave Technol. (1)

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

Nat. Mater. (1)

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

Nat. Photonics (3)

J. L. O’Brien, A. Furusawa, and J. Vuckovic, “Photonic quantum technologies,” Nat. Photonics 3, 687–695 (2009).
[CrossRef]

J. Leuthold, C. Koos, and W. Freude, “Nonlinear silicon photonics,” Nat. Photonics 4, 535–544 (2010).
[CrossRef]

D. Van Thourhout and J. Roels, “Optomechanical device actuation through the optical gradient force,” Nat. Photonics 4, 211–217 (2010).
[CrossRef]

Nature (7)

D. G. Grier, “A revolution in optical manipulationm,” Nature 424, 21–27 (2003).
[CrossRef]

D. Psaltis, S. R. Quake, and C. Yang, “Developing optofluidic technology through the fusion of microfluidics and optics,” Nature 442, 381–386 (2006).
[CrossRef] [PubMed]

M. Eichenfield, J. Chan, R. Camacho, K. J. Vahala, and O. Painter, “Optomechanical crystals,” Nature 462, 78–82 (2009).
[CrossRef] [PubMed]

K. J. Vahala, “Optical microcavities,” Nature 424, 839–846 (2003).
[CrossRef] [PubMed]

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]

J. S. Foresi, P. R. Villeneuve, J. Ferrera, E. R Thoen, G. Steinmeyer, S. Fan, J. D. Joannopoulos, L. C. Kimerling, H. I. Smith, and E. P. Ippen, “Photonic-bandgap microcavities in optical waveguides,” Nature 390, 143–145 (1997).
[CrossRef]

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Ultra-high-Q toroid microcavity on a chip,” Nature 421, 925–928 (2003).
[CrossRef] [PubMed]

Opt. Express (15)

M. Soltani, S. Yegnanarayanan, and A. Adibi, “Ultra-high Q planar silicon microdisk resonators for chip-scale silicon photonics,” Opt. Express 15, 4694–4704 (2007).
[CrossRef] [PubMed]

B. H. Ahn, J. H. Kang, M. K. Kim, J. H. Song, B. Min, K. S. Kim, and Y. H. Lee, “One-dimensional parabolic-beam photonic crystal laser,” Opt. Express 18, 5654–5660 (2010).
[CrossRef] [PubMed]

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

D. Englund, I. Fushman, and J. Vuckovic, “General recipe for designing photonic crystal cavities,” Opt. Express 13, 5961–5975 (2005).
[CrossRef] [PubMed]

S. Tomljenovic-Hanic, C. M. de Sterke, and M. J. Steel, “Design of high-Q cavities in photonic crystal slab heterostructures by air-holes infiltration,” Opt. Express 14, 12451–12456 (2006).
[CrossRef] [PubMed]

M. Notomi, E. Kuramochi, and H. Taniyama, “Ultrahigh-Q nanocavity with 1D Photonic Gap,” Opt. Express,  16, 11095 (2008).
[CrossRef] [PubMed]

P. Velha, E. Picard, T. Charvolin, E. Hadji, J. C. Rodier, P. Lalanne, and E. Peyrage, “Ultra-high Q/V Fabry-Perot microcavity on SOI substrate,” Opt. Express 15, 16090–16096 (2007).
[CrossRef] [PubMed]

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] [PubMed]

A. R. Md Zain, N. P. Johnson, M. Sorel, and R. M. De La Rue, “Ultra high quality factor one dimensional photonic crystal/photonic wire microcavities in silicon-on-insulator (SOI),” Opt. Express 16, 12084 (2008).
[CrossRef]

Y. Zhang and M. Loncar, “Ultra-high quality factor optical resonators based on semiconductor nanowires.” Opt. Express 16, 17400–17409 (2008).
[CrossRef] [PubMed]

M. W. McCutcheon and M. Loncar, “Design of a silicon nitride photonic crystal nanocavity with a Quality factor of one million for coupling to a diamond nanocrystal,” Opt. Express 16, 19136–19145 (2008).
[CrossRef]

L. D. Haret, T. Tanabe, E. Kuramochi, and M. Notomi, “Extremely low power optical bistability in silicon demonstrated using 1D photonic crystal nanocavity,” Opt. Express 17, 21008–21117 (2009).
[CrossRef]

J. Chan, M. Eichenfield, R. Camacho, and O. Painter, “Optical and mechanical design of a “zipper” photonic crystal optomechanical cavity”, Opt. Express 17, 3802–3817 (2009).
[CrossRef] [PubMed]

P. Lalanne, S. Mias, and J. P. Hugonin, “Two physical mechanisms for boosting the quality factor to cavity volume ratio of photonic crystal microcavities,” Opt. Express 12, 458–467 (2004).
[CrossRef] [PubMed]

E. Kuraamochi, H. Taniyama, T. Tanabe, K. Kawasaki, Y-G. Roh, and M. Notomi, “Ultrahigh-Q one-dimensional photonic crystal nanocavities with modulated mode-gap barriers on SiO2 claddings and on air claddings,” Opt. Express 18, 15859–15869 (2010).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (1)

D. W. Vernooy, A. Furusawa, N. P. Georgiades, V. S. Ilchenko, and H. J. Kimble, “Cavity QED with high-Q whispering gallery modes,” Phys. Rev. A 57, R2293–R2296 (1998).
[CrossRef]

Phys. Rev. E (3)

S. G. Johnson, M. Ibanescu, M. A. Skorobogatiy, O. Weisbergs, J. D. Joannopoulos, and Y. Fink, “Perturbation theory for Maxwell’s equations with shifting material boundaries,” Phys. Rev. E 65, 066611 (2002).
[CrossRef]

J. Vuckovic, M. Loncar, H. Mabuchi, and A. Scherer, “Optimization of three-dimensional micropost microcavities for cavity quantum electrodynamics,” Phys. Rev. E 65, 016608 (2001).

J. M. Geremia, J. Williams, and H. Mabuchi, “Inverse-problem approach to designing photonic crystals for cavity QED experiments,” Phys. Rev. E 66, 066606 (2002).
[CrossRef]

Phys. Rev. Lett. (2)

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

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

Science (1)

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

Other (4)

Quality factor is defined as Q=ω0Energy storedPower loss, and mode volume is defined as V = ∫ dVε|E|2/[ε|E|2]max.

Q. Quan, I. B. Burgess, S. K. Y. Tang, D. L. Floyd, and M. Loncar, “High-Q/V photonic crystal nanobeam cavities in an ultra-low index-contrast polymeric optofluidic platform,” arXiv:1108.2669 (2010).

K. Sakoda, Optical Properties of Photonic Crystals, 2nd Ed. (Springer, 2005).

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd Ed. (Cambridge University Press, 2007).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

(a) Schematic of the proposed nanobeam cavity. (b) FDTD simulation of the energy density distribution in the middle plane of the nanobeam cavity.

Fig. 2
Fig. 2

(a) Mirror strengths of each mirror segment for different tapering profiles obtained from the plane wave expansion method (‘1’ indicates the mirror segment in the center of the cavity). (b) Band diagram of the TE-like mode for f = 0.2 and f = 0.1. The green line indicates the light line. The circle indicates the target cavity resonant frequency. (c) Mirror strengths for different filling fractions, obtained using 3D band diagram simulation. (d) Mirror strengths as a function of mirror number after quadratic tapering. (e) Radiation-Q factors for nanobeam cavities with different cavity lengths between the two Gaussian mirrors, obtained using 3D FDTD simulations. (f) Resonances of the cavities that have different total number of mirror pair segments in the Gaussian mirror, and their deviations from the dielectric band-edge of the central mirror segment, obtained using both FDTD simulation and perturbation theory. (g) Hz field distribution on the surface right above the cavity, obtained from 3D FDTD simulation. The structure has dimension of a = 0.33μm, b = 0.7μm, the first 20 mirror segments (counted from the center) have fs varying from 0.2 to 0.1, followed by 10 additional mirror segments with f = 0.1. (h) Hz field distribution on the surface right above the cavity, obtained from the analytical formula H z = sin ( π a x ) exp ( σ x 2 ) exp ( ξ y 2 ) , with a = 0.33μm, σ = 0.14, ξ = 14. (i) Hz field distribution along the dashed line in (g)&(h). Length unit in (g)–(i) is μm.

Fig. 3
Fig. 3

(a) Schematic of the Gaussian nanobeam cavity, with an air hole in the symmetry plane (dashed line). (b) Energy distribution in the middle plane of the cavity obtained from 3D FDTD simulation. (c)&(d) Hz field distribution on the surface right above the cavity: (c) is obtained from 3D FDTD simulation and (d) is obtained from the analytical formula H z = cos ( π a x ) exp ( σ x 2 ) exp ( ξ y 2 ) , with a = 0.33μm, σ = 0.14, ξ = 14. (e) Hz field distribution along the dashed line in (c)&(d). Length unit: μm.

Fig. 4
Fig. 4

(a)&(b) The distribution of the spatial Fourier components of the cavity mode, obtained from 3D FDTD simulation: (a) for the H z o d d cavity and (b) for the H z e v e n cavity respectively. (c)&(d) The far field profile of the cavity mode obtained from 3D FDTD simulation: (c) for the H z o d d cavity and (d) for the H z e v e n cavity respectively. The inset cavity structure shows the orientation of the waveguide direction in (c)&(d). Dashed line indicates the symmetry plane.

Fig. 5
Fig. 5

(a) Total Q-factors (log(10) scale) and effective mode volumes (V/(λ res/n Si)3) of nanobeam cavities for different total number of mirror pair segments in the Gaussian mirror. In each case, 10 additional mirror segments with f=0.1 (maximum mirror strength) are added on both ends of the Gaussian mirror. Therefore, the total-Q of the cavity is limited by radiation-Q. A record ultra-high Q of 5.0 × 109 is achieved with a Gaussian mirror that comprises 30 mirror segments and an additional 10 mirror pairs on both ends. (b) On-resonance transmissions and total Q-factors (log(10) scale) v.s the total number of mirror pair segments in the Gaussian mirror. In this case additional mirror pairs (10 of them) are not included. A record high-T (97%) and high-Q (1.3 × 107) cavity is achieved at N = 25.

Fig. 6
Fig. 6

(a) Transmission spectrum of the cavity from FDTD simulation. (b)–(d) The Ey field distribution in the middle plain of the nanobeam cavity. Resonances and symmetries of the modes are indicated in the plot. Symmetry plane is indicated by the dashed line. Length unit in (b)–(d) is μm.

Fig. 7
Fig. 7

(a) TE band diagram for an air-mode nanobeam cavity. Hole radii r = 100nm, a = 330nm, b=1μm (red) and b=0.7μm (black). (b) Mirror strengths for different beam widths. (c) Linearization of mirror strengths after quadratic tapering the beam widths.

Fig. 8
Fig. 8

(a) Total Q-factors (log(10) scale) and effective mode volumes (V/(λ res/n Si)3) of the nanobeam cavities for different total number of mirror pair segments in the Gaussian mirror. In each case, 10 additional mirror segments with w=0.7μm are added on both ends of the Gaussian mirror, so that the total-Q of the cavity is limited by radiation-Q. A record ultra-high Q of 1.4 × 109 is achieved with a Gaussian mirror that comprises 30 mirror segments and 10 additional mirror pairs on both ends. (b) On-resonance transmissions and total Q-factors (log(10) scale) v.s the total number of mirror pair segments in the Gaussian mirror. In this case additional mirror pairs (10 of them) are not included. A record high-T (96%) and high-Q (3.0 × 106) cavity is achieved at N = 25.

Fig. 9
Fig. 9

(a) Transmission spectrum of the cavity from FDTD simulation. (b)&(c) The Ey field distribution in the middle plain of the nanobeam cavity. Resonances and symmetries of the modes are indicated in the plot. Symmetry plane is indicated by the dashed line. Length unit in (b)&(c) is μm.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

1 ε ( ρ ) = 1 ε Si + ( 1 ε air 1 ε Si ) S ( ρ )
S ( ρ ) = { 1 | ρ r j | R 0 | ρ r j | > R
1 ε ( x ) = κ 0 + κ 1 e i G x + κ 1 e i G x +
κ 0 = f ε air + 1 f ε Si
κ 1 = 2 f ( 1 ε air 1 ε Si ) J 1 ( G R ) G R
c 2 ε ( x ) 2 E x 2 = 2 E t 2
δ λ λ = δ ε | E | | | 2 δ ( ε 1 ) | D | 2 d V 2 ε | E | 2 d V

Metrics