Abstract

We propose a novel design of an all-dielectric optical antenna based on photonic-band-gap confinement. Specifically, we have engineered the photonic-crystal dipole mode to have broad spectral response (Q ~70) and well-directed vertical-radiation by introducing a plane mirror below the cavity. Considerably large local electric-field intensity enhancement ~4,500 is expected from the proposed design for a normally incident planewave. Furthermore, an analytic model developed based on coupled-mode theory predicts that the electric-field intensity enhancement can easily be over 100,000 by employing reasonably high-Q (~10,000) resonators.

© 2010 OSA

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  1. K. B. Crozier, A. Sundaramurthy, G. S. Kino, and C. F. Quate, “Optical antennas: Resonators for local field enhancement,” J. Appl. Phys. 94, 4632–4642 (2003).
    [CrossRef]
  2. P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308(5728), 1607–1609 (2005).
    [CrossRef] [PubMed]
  3. E. Cubukcu, E. A. Kort, K. B. Crozier, and F. Capasso, “Plasmonic laser antenna,” Appl. Phys. Lett. 89, 093120 (2006).
    [CrossRef]
  4. C. Sönnichsen, T. Franzl, T. Wilk, G. von Plessen, J. Feldmann, O. Wilson, and P. Mulvaney, “Drastic reduction of plasmon damping in gold nanorods,” Phys. Rev. Lett. 88(7), 077402 (2002).
    [CrossRef] [PubMed]
  5. T. Kosako, Y. Kadoya, and H. F. Hofmann, “Directional control of light by a nano-optical Yagi-Uda antenna,” Nat. Photonics 4, 312–315 (2010).
    [CrossRef]
  6. Y. Lu, G. L. Liu, J. Kim, Y. X. Mejia, and L. P. Lee, “Nanophotonic crescent moon structures with sharp edge for ultrasensitive biomolecular detection by local electromagnetic field enhancement effect,” Nano Lett. 5(1), 119–124 (2005).
    [CrossRef] [PubMed]
  7. K. Kneipp and ., “Single molecule detection using surface-enhanced Raman scattering (SERS),” Phys. Rev. Lett. 78, 1667–1670 (1997).
    [CrossRef]
  8. A. Bouhelier, M. Beversluis, A. Hartschuh, and L. Novotny, “Near-field second-harmonic generation induced by local field enhancement,” Phys. Rev. Lett. 90(1), 013903 (2003).
    [CrossRef] [PubMed]
  9. S. Kim, J. Jin, Y. J. Kim, I. Y. Park, Y. Kim, and S. W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature 453(7196), 757–760 (2008).
    [CrossRef] [PubMed]
  10. E. Prodan and P. Nordlander, “Plasmon hybridization in spherical nanoparticles,” J. Chem. Phys. 120(11), 5444–5454 (2004).
    [CrossRef] [PubMed]
  11. O. Painter, J. Vuckovic, 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]
  12. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58(20), 2059–2062 (1987).
    [CrossRef] [PubMed]
  13. 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]
  14. S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nature photon. 1, 449–458 (2007).
  15. T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, and H. Taniyama, “Trapping and delaying photons for one nanosecond in an ultrasmall high-Q photonic-crystal nanocavity,” Nat. Photonics 1, 49–52 (2007).
    [CrossRef]
  16. S.-H. Kim, S.-K. Kim, and Y.-H. Lee, “Vertical beaming of wavelength-small photonic crystal resonators,” Phys. Rev. B 73, 235117 (2006).
    [CrossRef]
  17. S. Fan, W. Suh, and J. D. Joannopoulos, “Temporal coupled-mode theory for the Fano resonance in optical resonators,” J. Opt. Soc. Am. A 20(3), 569–572 (2003).
    [CrossRef]
  18. R. E. Hamam, A. Karalis, J. D. Joannopoulos, and M. Soljacic, “Coupled-mode theory for general free-space resonant scattering of waves,” Phys. Rev. A 75, 053801 (2007).
    [CrossRef]
  19. C. A. Balanis, Antenna Theory: Analyses and Design (John Wiley and Sons, Inc., Hoboken, New Jersey, 2005).
  20. E. M. Purcell, “Spontaneous emission probabilities at radio frequencies,” Phys. Rev. 69, 681 (1946).
  21. A. Campion and P. Kambhampati, “Surface-enhanced Raman scattering,” Chem. Soc. Rev. 27, 241–250 (1998).
    [CrossRef]
  22. J. T. Robinson, C. Manolatou, L. Chen, and M. Lipson, “Ultrasmall mode volumes in dielectric optical microcavities,” Phys. Rev. Lett. 95(14), 143901 (2005).
    [CrossRef] [PubMed]
  23. M. Loncar, A. Scherer, and Y. Qiu, “Photonic crystal laser sources for chemical detection,” Appl. Phys. Lett. 82, 4648–4650 (2003).
    [CrossRef]
  24. A. Taflove, and S. C. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method (2nd ed) (Artech House, 2000).
  25. J. Aizpurua, P. Hanarp, D. S. Sutherland, M. Käll, G. W. Bryant, and F. J. García de Abajo, “Optical properties of gold nanorings,” Phys. Rev. Lett. 90(5), 057401 (2003).
    [CrossRef] [PubMed]
  26. H. Wang, D. W. Brandl, F. Le, P. Nordlander, and N. J. Halas, “Nanorice: a hybrid plasmonic nanostructure,” Nano Lett. 6(4), 827–832 (2006).
    [CrossRef] [PubMed]
  27. A. Rodriguez, M. Soljacic, J. D. Joannopoulos, and S. G. Johnson, “χ(2) and χ(3) harmonic generation at a critical power in inhomogeneous doubly resonant cavities,” Opt. Express 15(12), 7303–7318 (2007).
    [CrossRef] [PubMed]
  28. B. Tian, X. Zheng, T. J. Kempa, Y. Fang, N. Yu, G. Yu, J. Huang, and C. M. Lieber, “Coaxial silicon nanowires as solar cells and nanoelectronic power sources,” Nature 449(7164), 885–889 (2007).
    [CrossRef] [PubMed]
  29. S. G. Johnson, http://ab-initio.mit.edu/wiki/index.php/Harminv

2010 (1)

T. Kosako, Y. Kadoya, and H. F. Hofmann, “Directional control of light by a nano-optical Yagi-Uda antenna,” Nat. Photonics 4, 312–315 (2010).
[CrossRef]

2008 (1)

S. Kim, J. Jin, Y. J. Kim, I. Y. Park, Y. Kim, and S. W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature 453(7196), 757–760 (2008).
[CrossRef] [PubMed]

2007 (5)

S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nature photon. 1, 449–458 (2007).

T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, and H. Taniyama, “Trapping and delaying photons for one nanosecond in an ultrasmall high-Q photonic-crystal nanocavity,” Nat. Photonics 1, 49–52 (2007).
[CrossRef]

R. E. Hamam, A. Karalis, J. D. Joannopoulos, and M. Soljacic, “Coupled-mode theory for general free-space resonant scattering of waves,” Phys. Rev. A 75, 053801 (2007).
[CrossRef]

A. Rodriguez, M. Soljacic, J. D. Joannopoulos, and S. G. Johnson, “χ(2) and χ(3) harmonic generation at a critical power in inhomogeneous doubly resonant cavities,” Opt. Express 15(12), 7303–7318 (2007).
[CrossRef] [PubMed]

B. Tian, X. Zheng, T. J. Kempa, Y. Fang, N. Yu, G. Yu, J. Huang, and C. M. Lieber, “Coaxial silicon nanowires as solar cells and nanoelectronic power sources,” Nature 449(7164), 885–889 (2007).
[CrossRef] [PubMed]

2006 (3)

H. Wang, D. W. Brandl, F. Le, P. Nordlander, and N. J. Halas, “Nanorice: a hybrid plasmonic nanostructure,” Nano Lett. 6(4), 827–832 (2006).
[CrossRef] [PubMed]

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

E. Cubukcu, E. A. Kort, K. B. Crozier, and F. Capasso, “Plasmonic laser antenna,” Appl. Phys. Lett. 89, 093120 (2006).
[CrossRef]

2005 (3)

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308(5728), 1607–1609 (2005).
[CrossRef] [PubMed]

Y. Lu, G. L. Liu, J. Kim, Y. X. Mejia, and L. P. Lee, “Nanophotonic crescent moon structures with sharp edge for ultrasensitive biomolecular detection by local electromagnetic field enhancement effect,” Nano Lett. 5(1), 119–124 (2005).
[CrossRef] [PubMed]

J. T. Robinson, C. Manolatou, L. Chen, and M. Lipson, “Ultrasmall mode volumes in dielectric optical microcavities,” Phys. Rev. Lett. 95(14), 143901 (2005).
[CrossRef] [PubMed]

2004 (1)

E. Prodan and P. Nordlander, “Plasmon hybridization in spherical nanoparticles,” J. Chem. Phys. 120(11), 5444–5454 (2004).
[CrossRef] [PubMed]

2003 (6)

K. B. Crozier, A. Sundaramurthy, G. S. Kino, and C. F. Quate, “Optical antennas: Resonators for local field enhancement,” J. Appl. Phys. 94, 4632–4642 (2003).
[CrossRef]

A. Bouhelier, M. Beversluis, A. Hartschuh, and L. Novotny, “Near-field second-harmonic generation induced by local field enhancement,” Phys. Rev. Lett. 90(1), 013903 (2003).
[CrossRef] [PubMed]

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

S. Fan, W. Suh, and J. D. Joannopoulos, “Temporal coupled-mode theory for the Fano resonance in optical resonators,” J. Opt. Soc. Am. A 20(3), 569–572 (2003).
[CrossRef]

M. Loncar, A. Scherer, and Y. Qiu, “Photonic crystal laser sources for chemical detection,” Appl. Phys. Lett. 82, 4648–4650 (2003).
[CrossRef]

J. Aizpurua, P. Hanarp, D. S. Sutherland, M. Käll, G. W. Bryant, and F. J. García de Abajo, “Optical properties of gold nanorings,” Phys. Rev. Lett. 90(5), 057401 (2003).
[CrossRef] [PubMed]

2002 (1)

C. Sönnichsen, T. Franzl, T. Wilk, G. von Plessen, J. Feldmann, O. Wilson, and P. Mulvaney, “Drastic reduction of plasmon damping in gold nanorods,” Phys. Rev. Lett. 88(7), 077402 (2002).
[CrossRef] [PubMed]

1999 (1)

1998 (1)

A. Campion and P. Kambhampati, “Surface-enhanced Raman scattering,” Chem. Soc. Rev. 27, 241–250 (1998).
[CrossRef]

1997 (1)

K. Kneipp and ., “Single molecule detection using surface-enhanced Raman scattering (SERS),” Phys. Rev. Lett. 78, 1667–1670 (1997).
[CrossRef]

1987 (1)

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58(20), 2059–2062 (1987).
[CrossRef] [PubMed]

1946 (1)

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

Aizpurua, J.

J. Aizpurua, P. Hanarp, D. S. Sutherland, M. Käll, G. W. Bryant, and F. J. García de Abajo, “Optical properties of gold nanorings,” Phys. Rev. Lett. 90(5), 057401 (2003).
[CrossRef] [PubMed]

Asano, T.

S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nature photon. 1, 449–458 (2007).

Beversluis, M.

A. Bouhelier, M. Beversluis, A. Hartschuh, and L. Novotny, “Near-field second-harmonic generation induced by local field enhancement,” Phys. Rev. Lett. 90(1), 013903 (2003).
[CrossRef] [PubMed]

Bouhelier, A.

A. Bouhelier, M. Beversluis, A. Hartschuh, and L. Novotny, “Near-field second-harmonic generation induced by local field enhancement,” Phys. Rev. Lett. 90(1), 013903 (2003).
[CrossRef] [PubMed]

Brandl, D. W.

H. Wang, D. W. Brandl, F. Le, P. Nordlander, and N. J. Halas, “Nanorice: a hybrid plasmonic nanostructure,” Nano Lett. 6(4), 827–832 (2006).
[CrossRef] [PubMed]

Bryant, G. W.

J. Aizpurua, P. Hanarp, D. S. Sutherland, M. Käll, G. W. Bryant, and F. J. García de Abajo, “Optical properties of gold nanorings,” Phys. Rev. Lett. 90(5), 057401 (2003).
[CrossRef] [PubMed]

Campion, A.

A. Campion and P. Kambhampati, “Surface-enhanced Raman scattering,” Chem. Soc. Rev. 27, 241–250 (1998).
[CrossRef]

Capasso, F.

E. Cubukcu, E. A. Kort, K. B. Crozier, and F. Capasso, “Plasmonic laser antenna,” Appl. Phys. Lett. 89, 093120 (2006).
[CrossRef]

Chen, L.

J. T. Robinson, C. Manolatou, L. Chen, and M. Lipson, “Ultrasmall mode volumes in dielectric optical microcavities,” Phys. Rev. Lett. 95(14), 143901 (2005).
[CrossRef] [PubMed]

Crozier, K. B.

E. Cubukcu, E. A. Kort, K. B. Crozier, and F. Capasso, “Plasmonic laser antenna,” Appl. Phys. Lett. 89, 093120 (2006).
[CrossRef]

K. B. Crozier, A. Sundaramurthy, G. S. Kino, and C. F. Quate, “Optical antennas: Resonators for local field enhancement,” J. Appl. Phys. 94, 4632–4642 (2003).
[CrossRef]

Cubukcu, E.

E. Cubukcu, E. A. Kort, K. B. Crozier, and F. Capasso, “Plasmonic laser antenna,” Appl. Phys. Lett. 89, 093120 (2006).
[CrossRef]

Eisler, H.-J.

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308(5728), 1607–1609 (2005).
[CrossRef] [PubMed]

Fan, S.

Fang, Y.

B. Tian, X. Zheng, T. J. Kempa, Y. Fang, N. Yu, G. Yu, J. Huang, and C. M. Lieber, “Coaxial silicon nanowires as solar cells and nanoelectronic power sources,” Nature 449(7164), 885–889 (2007).
[CrossRef] [PubMed]

Feldmann, J.

C. Sönnichsen, T. Franzl, T. Wilk, G. von Plessen, J. Feldmann, O. Wilson, and P. Mulvaney, “Drastic reduction of plasmon damping in gold nanorods,” Phys. Rev. Lett. 88(7), 077402 (2002).
[CrossRef] [PubMed]

Franzl, T.

C. Sönnichsen, T. Franzl, T. Wilk, G. von Plessen, J. Feldmann, O. Wilson, and P. Mulvaney, “Drastic reduction of plasmon damping in gold nanorods,” Phys. Rev. Lett. 88(7), 077402 (2002).
[CrossRef] [PubMed]

Fujita, M.

S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nature photon. 1, 449–458 (2007).

García de Abajo, F. J.

J. Aizpurua, P. Hanarp, D. S. Sutherland, M. Käll, G. W. Bryant, and F. J. García de Abajo, “Optical properties of gold nanorings,” Phys. Rev. Lett. 90(5), 057401 (2003).
[CrossRef] [PubMed]

Halas, N. J.

H. Wang, D. W. Brandl, F. Le, P. Nordlander, and N. J. Halas, “Nanorice: a hybrid plasmonic nanostructure,” Nano Lett. 6(4), 827–832 (2006).
[CrossRef] [PubMed]

Hamam, R. E.

R. E. Hamam, A. Karalis, J. D. Joannopoulos, and M. Soljacic, “Coupled-mode theory for general free-space resonant scattering of waves,” Phys. Rev. A 75, 053801 (2007).
[CrossRef]

Hanarp, P.

J. Aizpurua, P. Hanarp, D. S. Sutherland, M. Käll, G. W. Bryant, and F. J. García de Abajo, “Optical properties of gold nanorings,” Phys. Rev. Lett. 90(5), 057401 (2003).
[CrossRef] [PubMed]

Hartschuh, A.

A. Bouhelier, M. Beversluis, A. Hartschuh, and L. Novotny, “Near-field second-harmonic generation induced by local field enhancement,” Phys. Rev. Lett. 90(1), 013903 (2003).
[CrossRef] [PubMed]

Hecht, B.

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308(5728), 1607–1609 (2005).
[CrossRef] [PubMed]

Hofmann, H. F.

T. Kosako, Y. Kadoya, and H. F. Hofmann, “Directional control of light by a nano-optical Yagi-Uda antenna,” Nat. Photonics 4, 312–315 (2010).
[CrossRef]

Huang, J.

B. Tian, X. Zheng, T. J. Kempa, Y. Fang, N. Yu, G. Yu, J. Huang, and C. M. Lieber, “Coaxial silicon nanowires as solar cells and nanoelectronic power sources,” Nature 449(7164), 885–889 (2007).
[CrossRef] [PubMed]

Jin, J.

S. Kim, J. Jin, Y. J. Kim, I. Y. Park, Y. Kim, and S. W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature 453(7196), 757–760 (2008).
[CrossRef] [PubMed]

Joannopoulos, J. D.

Johnson, S. G.

Kadoya, Y.

T. Kosako, Y. Kadoya, and H. F. Hofmann, “Directional control of light by a nano-optical Yagi-Uda antenna,” Nat. Photonics 4, 312–315 (2010).
[CrossRef]

Käll, M.

J. Aizpurua, P. Hanarp, D. S. Sutherland, M. Käll, G. W. Bryant, and F. J. García de Abajo, “Optical properties of gold nanorings,” Phys. Rev. Lett. 90(5), 057401 (2003).
[CrossRef] [PubMed]

Kambhampati, P.

A. Campion and P. Kambhampati, “Surface-enhanced Raman scattering,” Chem. Soc. Rev. 27, 241–250 (1998).
[CrossRef]

Karalis, A.

R. E. Hamam, A. Karalis, J. D. Joannopoulos, and M. Soljacic, “Coupled-mode theory for general free-space resonant scattering of waves,” Phys. Rev. A 75, 053801 (2007).
[CrossRef]

Kempa, T. J.

B. Tian, X. Zheng, T. J. Kempa, Y. Fang, N. Yu, G. Yu, J. Huang, and C. M. Lieber, “Coaxial silicon nanowires as solar cells and nanoelectronic power sources,” Nature 449(7164), 885–889 (2007).
[CrossRef] [PubMed]

Kim, J.

Y. Lu, G. L. Liu, J. Kim, Y. X. Mejia, and L. P. Lee, “Nanophotonic crescent moon structures with sharp edge for ultrasensitive biomolecular detection by local electromagnetic field enhancement effect,” Nano Lett. 5(1), 119–124 (2005).
[CrossRef] [PubMed]

Kim, S.

S. Kim, J. Jin, Y. J. Kim, I. Y. Park, Y. Kim, and S. W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature 453(7196), 757–760 (2008).
[CrossRef] [PubMed]

Kim, S. W.

S. Kim, J. Jin, Y. J. Kim, I. Y. Park, Y. Kim, and S. W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature 453(7196), 757–760 (2008).
[CrossRef] [PubMed]

Kim, S.-H.

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

Kim, S.-K.

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

Kim, Y.

S. Kim, J. Jin, Y. J. Kim, I. Y. Park, Y. Kim, and S. W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature 453(7196), 757–760 (2008).
[CrossRef] [PubMed]

Kim, Y. J.

S. Kim, J. Jin, Y. J. Kim, I. Y. Park, Y. Kim, and S. W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature 453(7196), 757–760 (2008).
[CrossRef] [PubMed]

Kino, G. S.

K. B. Crozier, A. Sundaramurthy, G. S. Kino, and C. F. Quate, “Optical antennas: Resonators for local field enhancement,” J. Appl. Phys. 94, 4632–4642 (2003).
[CrossRef]

Kneipp, K.

K. Kneipp and ., “Single molecule detection using surface-enhanced Raman scattering (SERS),” Phys. Rev. Lett. 78, 1667–1670 (1997).
[CrossRef]

Kort, E. A.

E. Cubukcu, E. A. Kort, K. B. Crozier, and F. Capasso, “Plasmonic laser antenna,” Appl. Phys. Lett. 89, 093120 (2006).
[CrossRef]

Kosako, T.

T. Kosako, Y. Kadoya, and H. F. Hofmann, “Directional control of light by a nano-optical Yagi-Uda antenna,” Nat. Photonics 4, 312–315 (2010).
[CrossRef]

Kuramochi, E.

T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, and H. Taniyama, “Trapping and delaying photons for one nanosecond in an ultrasmall high-Q photonic-crystal nanocavity,” Nat. Photonics 1, 49–52 (2007).
[CrossRef]

Le, F.

H. Wang, D. W. Brandl, F. Le, P. Nordlander, and N. J. Halas, “Nanorice: a hybrid plasmonic nanostructure,” Nano Lett. 6(4), 827–832 (2006).
[CrossRef] [PubMed]

Lee, L. P.

Y. Lu, G. L. Liu, J. Kim, Y. X. Mejia, and L. P. Lee, “Nanophotonic crescent moon structures with sharp edge for ultrasensitive biomolecular detection by local electromagnetic field enhancement effect,” Nano Lett. 5(1), 119–124 (2005).
[CrossRef] [PubMed]

Lee, Y.-H.

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

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

Lieber, C. M.

B. Tian, X. Zheng, T. J. Kempa, Y. Fang, N. Yu, G. Yu, J. Huang, and C. M. Lieber, “Coaxial silicon nanowires as solar cells and nanoelectronic power sources,” Nature 449(7164), 885–889 (2007).
[CrossRef] [PubMed]

Lipson, M.

J. T. Robinson, C. Manolatou, L. Chen, and M. Lipson, “Ultrasmall mode volumes in dielectric optical microcavities,” Phys. Rev. Lett. 95(14), 143901 (2005).
[CrossRef] [PubMed]

Liu, G. L.

Y. Lu, G. L. Liu, J. Kim, Y. X. Mejia, and L. P. Lee, “Nanophotonic crescent moon structures with sharp edge for ultrasensitive biomolecular detection by local electromagnetic field enhancement effect,” Nano Lett. 5(1), 119–124 (2005).
[CrossRef] [PubMed]

Loncar, M.

M. Loncar, A. Scherer, and Y. Qiu, “Photonic crystal laser sources for chemical detection,” Appl. Phys. Lett. 82, 4648–4650 (2003).
[CrossRef]

Lu, Y.

Y. Lu, G. L. Liu, J. Kim, Y. X. Mejia, and L. P. Lee, “Nanophotonic crescent moon structures with sharp edge for ultrasensitive biomolecular detection by local electromagnetic field enhancement effect,” Nano Lett. 5(1), 119–124 (2005).
[CrossRef] [PubMed]

Manolatou, C.

J. T. Robinson, C. Manolatou, L. Chen, and M. Lipson, “Ultrasmall mode volumes in dielectric optical microcavities,” Phys. Rev. Lett. 95(14), 143901 (2005).
[CrossRef] [PubMed]

Martin, O. J. F.

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308(5728), 1607–1609 (2005).
[CrossRef] [PubMed]

Mejia, Y. X.

Y. Lu, G. L. Liu, J. Kim, Y. X. Mejia, and L. P. Lee, “Nanophotonic crescent moon structures with sharp edge for ultrasensitive biomolecular detection by local electromagnetic field enhancement effect,” Nano Lett. 5(1), 119–124 (2005).
[CrossRef] [PubMed]

Mühlschlegel, P.

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308(5728), 1607–1609 (2005).
[CrossRef] [PubMed]

Mulvaney, P.

C. Sönnichsen, T. Franzl, T. Wilk, G. von Plessen, J. Feldmann, O. Wilson, and P. Mulvaney, “Drastic reduction of plasmon damping in gold nanorods,” Phys. Rev. Lett. 88(7), 077402 (2002).
[CrossRef] [PubMed]

Noda, S.

S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nature photon. 1, 449–458 (2007).

Nordlander, P.

H. Wang, D. W. Brandl, F. Le, P. Nordlander, and N. J. Halas, “Nanorice: a hybrid plasmonic nanostructure,” Nano Lett. 6(4), 827–832 (2006).
[CrossRef] [PubMed]

E. Prodan and P. Nordlander, “Plasmon hybridization in spherical nanoparticles,” J. Chem. Phys. 120(11), 5444–5454 (2004).
[CrossRef] [PubMed]

Notomi, M.

T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, and H. Taniyama, “Trapping and delaying photons for one nanosecond in an ultrasmall high-Q photonic-crystal nanocavity,” Nat. Photonics 1, 49–52 (2007).
[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]

Novotny, L.

A. Bouhelier, M. Beversluis, A. Hartschuh, and L. Novotny, “Near-field second-harmonic generation induced by local field enhancement,” Phys. Rev. Lett. 90(1), 013903 (2003).
[CrossRef] [PubMed]

Painter, O.

Park, I. Y.

S. Kim, J. Jin, Y. J. Kim, I. Y. Park, Y. Kim, and S. W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature 453(7196), 757–760 (2008).
[CrossRef] [PubMed]

Pohl, D. W.

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308(5728), 1607–1609 (2005).
[CrossRef] [PubMed]

Prodan, E.

E. Prodan and P. Nordlander, “Plasmon hybridization in spherical nanoparticles,” J. Chem. Phys. 120(11), 5444–5454 (2004).
[CrossRef] [PubMed]

Purcell, E. M.

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

Qiu, Y.

M. Loncar, A. Scherer, and Y. Qiu, “Photonic crystal laser sources for chemical detection,” Appl. Phys. Lett. 82, 4648–4650 (2003).
[CrossRef]

Quate, C. F.

K. B. Crozier, A. Sundaramurthy, G. S. Kino, and C. F. Quate, “Optical antennas: Resonators for local field enhancement,” J. Appl. Phys. 94, 4632–4642 (2003).
[CrossRef]

Robinson, J. T.

J. T. Robinson, C. Manolatou, L. Chen, and M. Lipson, “Ultrasmall mode volumes in dielectric optical microcavities,” Phys. Rev. Lett. 95(14), 143901 (2005).
[CrossRef] [PubMed]

Rodriguez, A.

Ryu, H.-Y.

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

Scherer, A.

M. Loncar, A. Scherer, and Y. Qiu, “Photonic crystal laser sources for chemical detection,” Appl. Phys. Lett. 82, 4648–4650 (2003).
[CrossRef]

O. Painter, J. Vuckovic, 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]

Shinya, A.

T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, and H. Taniyama, “Trapping and delaying photons for one nanosecond in an ultrasmall high-Q photonic-crystal nanocavity,” Nat. Photonics 1, 49–52 (2007).
[CrossRef]

Soljacic, M.

R. E. Hamam, A. Karalis, J. D. Joannopoulos, and M. Soljacic, “Coupled-mode theory for general free-space resonant scattering of waves,” Phys. Rev. A 75, 053801 (2007).
[CrossRef]

A. Rodriguez, M. Soljacic, J. D. Joannopoulos, and S. G. Johnson, “χ(2) and χ(3) harmonic generation at a critical power in inhomogeneous doubly resonant cavities,” Opt. Express 15(12), 7303–7318 (2007).
[CrossRef] [PubMed]

Sönnichsen, C.

C. Sönnichsen, T. Franzl, T. Wilk, G. von Plessen, J. Feldmann, O. Wilson, and P. Mulvaney, “Drastic reduction of plasmon damping in gold nanorods,” Phys. Rev. Lett. 88(7), 077402 (2002).
[CrossRef] [PubMed]

Suh, W.

Sundaramurthy, A.

K. B. Crozier, A. Sundaramurthy, G. S. Kino, and C. F. Quate, “Optical antennas: Resonators for local field enhancement,” J. Appl. Phys. 94, 4632–4642 (2003).
[CrossRef]

Sutherland, D. S.

J. Aizpurua, P. Hanarp, D. S. Sutherland, M. Käll, G. W. Bryant, and F. J. García de Abajo, “Optical properties of gold nanorings,” Phys. Rev. Lett. 90(5), 057401 (2003).
[CrossRef] [PubMed]

Tanabe, T.

T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, and H. Taniyama, “Trapping and delaying photons for one nanosecond in an ultrasmall high-Q photonic-crystal nanocavity,” Nat. Photonics 1, 49–52 (2007).
[CrossRef]

Taniyama, H.

T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, and H. Taniyama, “Trapping and delaying photons for one nanosecond in an ultrasmall high-Q photonic-crystal nanocavity,” Nat. Photonics 1, 49–52 (2007).
[CrossRef]

Tian, B.

B. Tian, X. Zheng, T. J. Kempa, Y. Fang, N. Yu, G. Yu, J. Huang, and C. M. Lieber, “Coaxial silicon nanowires as solar cells and nanoelectronic power sources,” Nature 449(7164), 885–889 (2007).
[CrossRef] [PubMed]

von Plessen, G.

C. Sönnichsen, T. Franzl, T. Wilk, G. von Plessen, J. Feldmann, O. Wilson, and P. Mulvaney, “Drastic reduction of plasmon damping in gold nanorods,” Phys. Rev. Lett. 88(7), 077402 (2002).
[CrossRef] [PubMed]

Vuckovic, J.

Wang, H.

H. Wang, D. W. Brandl, F. Le, P. Nordlander, and N. J. Halas, “Nanorice: a hybrid plasmonic nanostructure,” Nano Lett. 6(4), 827–832 (2006).
[CrossRef] [PubMed]

Wilk, T.

C. Sönnichsen, T. Franzl, T. Wilk, G. von Plessen, J. Feldmann, O. Wilson, and P. Mulvaney, “Drastic reduction of plasmon damping in gold nanorods,” Phys. Rev. Lett. 88(7), 077402 (2002).
[CrossRef] [PubMed]

Wilson, O.

C. Sönnichsen, T. Franzl, T. Wilk, G. von Plessen, J. Feldmann, O. Wilson, and P. Mulvaney, “Drastic reduction of plasmon damping in gold nanorods,” Phys. Rev. Lett. 88(7), 077402 (2002).
[CrossRef] [PubMed]

Yablonovitch, E.

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58(20), 2059–2062 (1987).
[CrossRef] [PubMed]

Yu, G.

B. Tian, X. Zheng, T. J. Kempa, Y. Fang, N. Yu, G. Yu, J. Huang, and C. M. Lieber, “Coaxial silicon nanowires as solar cells and nanoelectronic power sources,” Nature 449(7164), 885–889 (2007).
[CrossRef] [PubMed]

Yu, N.

B. Tian, X. Zheng, T. J. Kempa, Y. Fang, N. Yu, G. Yu, J. Huang, and C. M. Lieber, “Coaxial silicon nanowires as solar cells and nanoelectronic power sources,” Nature 449(7164), 885–889 (2007).
[CrossRef] [PubMed]

Zheng, X.

B. Tian, X. Zheng, T. J. Kempa, Y. Fang, N. Yu, G. Yu, J. Huang, and C. M. Lieber, “Coaxial silicon nanowires as solar cells and nanoelectronic power sources,” Nature 449(7164), 885–889 (2007).
[CrossRef] [PubMed]

Appl. Phys. Lett. (3)

E. Cubukcu, E. A. Kort, K. B. Crozier, and F. Capasso, “Plasmonic laser antenna,” Appl. Phys. Lett. 89, 093120 (2006).
[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. Loncar, A. Scherer, and Y. Qiu, “Photonic crystal laser sources for chemical detection,” Appl. Phys. Lett. 82, 4648–4650 (2003).
[CrossRef]

Chem. Soc. Rev. (1)

A. Campion and P. Kambhampati, “Surface-enhanced Raman scattering,” Chem. Soc. Rev. 27, 241–250 (1998).
[CrossRef]

J. Appl. Phys. (1)

K. B. Crozier, A. Sundaramurthy, G. S. Kino, and C. F. Quate, “Optical antennas: Resonators for local field enhancement,” J. Appl. Phys. 94, 4632–4642 (2003).
[CrossRef]

J. Chem. Phys. (1)

E. Prodan and P. Nordlander, “Plasmon hybridization in spherical nanoparticles,” J. Chem. Phys. 120(11), 5444–5454 (2004).
[CrossRef] [PubMed]

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

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

Nano Lett. (2)

Y. Lu, G. L. Liu, J. Kim, Y. X. Mejia, and L. P. Lee, “Nanophotonic crescent moon structures with sharp edge for ultrasensitive biomolecular detection by local electromagnetic field enhancement effect,” Nano Lett. 5(1), 119–124 (2005).
[CrossRef] [PubMed]

H. Wang, D. W. Brandl, F. Le, P. Nordlander, and N. J. Halas, “Nanorice: a hybrid plasmonic nanostructure,” Nano Lett. 6(4), 827–832 (2006).
[CrossRef] [PubMed]

Nat. Photonics (2)

T. Kosako, Y. Kadoya, and H. F. Hofmann, “Directional control of light by a nano-optical Yagi-Uda antenna,” Nat. Photonics 4, 312–315 (2010).
[CrossRef]

T. Tanabe, M. Notomi, E. Kuramochi, A. Shinya, and H. Taniyama, “Trapping and delaying photons for one nanosecond in an ultrasmall high-Q photonic-crystal nanocavity,” Nat. Photonics 1, 49–52 (2007).
[CrossRef]

Nature (2)

S. Kim, J. Jin, Y. J. Kim, I. Y. Park, Y. Kim, and S. W. Kim, “High-harmonic generation by resonant plasmon field enhancement,” Nature 453(7196), 757–760 (2008).
[CrossRef] [PubMed]

B. Tian, X. Zheng, T. J. Kempa, Y. Fang, N. Yu, G. Yu, J. Huang, and C. M. Lieber, “Coaxial silicon nanowires as solar cells and nanoelectronic power sources,” Nature 449(7164), 885–889 (2007).
[CrossRef] [PubMed]

Opt. Express (1)

Phys. Rev. (1)

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

Phys. Rev. A (1)

R. E. Hamam, A. Karalis, J. D. Joannopoulos, and M. Soljacic, “Coupled-mode theory for general free-space resonant scattering of waves,” Phys. Rev. A 75, 053801 (2007).
[CrossRef]

Phys. Rev. B (1)

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

Phys. Rev. Lett. (6)

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58(20), 2059–2062 (1987).
[CrossRef] [PubMed]

K. Kneipp and ., “Single molecule detection using surface-enhanced Raman scattering (SERS),” Phys. Rev. Lett. 78, 1667–1670 (1997).
[CrossRef]

A. Bouhelier, M. Beversluis, A. Hartschuh, and L. Novotny, “Near-field second-harmonic generation induced by local field enhancement,” Phys. Rev. Lett. 90(1), 013903 (2003).
[CrossRef] [PubMed]

C. Sönnichsen, T. Franzl, T. Wilk, G. von Plessen, J. Feldmann, O. Wilson, and P. Mulvaney, “Drastic reduction of plasmon damping in gold nanorods,” Phys. Rev. Lett. 88(7), 077402 (2002).
[CrossRef] [PubMed]

J. Aizpurua, P. Hanarp, D. S. Sutherland, M. Käll, G. W. Bryant, and F. J. García de Abajo, “Optical properties of gold nanorings,” Phys. Rev. Lett. 90(5), 057401 (2003).
[CrossRef] [PubMed]

J. T. Robinson, C. Manolatou, L. Chen, and M. Lipson, “Ultrasmall mode volumes in dielectric optical microcavities,” Phys. Rev. Lett. 95(14), 143901 (2005).
[CrossRef] [PubMed]

Science (1)

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308(5728), 1607–1609 (2005).
[CrossRef] [PubMed]

Other (4)

S. Noda, M. Fujita, and T. Asano, “Spontaneous-emission control by photonic crystals and nanocavities,” Nature photon. 1, 449–458 (2007).

C. A. Balanis, Antenna Theory: Analyses and Design (John Wiley and Sons, Inc., Hoboken, New Jersey, 2005).

A. Taflove, and S. C. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method (2nd ed) (Artech House, 2000).

S. G. Johnson, http://ab-initio.mit.edu/wiki/index.php/Harminv

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Figures (8)

Fig. 1
Fig. 1

All-dielectric photonic-crystal (PhC) antenna. (a) The 2-D PhC cavity is placed at a distance of d from the reflector. The linearly-polarized planewave is being illuminated from the top. (b) A coupled-mode theory diagram describes interaction between the incident planewave and the PhC cavity. The port k is defined for an imaginary two-way waveguide in the direction of k = ( θ , ϕ ) with an angular extent defined by a differential solid angle, d Ω ( θ , ϕ ) . α represents the energy amplitude of the cavity. S+k and S-k are the power amplitudes propagating in the port k. The PhC antenna is excited only through the 'port 0' with carried power of | S+0 |2.

Fig. 2
Fig. 2

Effects of the nano-slot on local-field enhancement. The photonic-crystal (PhC) cavity is completely immersed in water ( n b g = 1.33), where the bottom reflector is excluded. (a) The left panel shows a schematic illustration of the nano-slot positioned at the center of the PhC cavity. The nano-slot has a rectangular geometry whose width is fixed to 0.05 a while its length, L, is to be varied. The right panel shows electric-field intensity ( | E | 2 ) distribution around the nano-slot. (b) Quality factor, Qtot , mode volume, Vm , and the far-field coupling factor, η ( θ = 0 ) , calculated as a function of L. (c) The electric-field intensity enhancement factors, Φ I , obtained from the coupled-mode theory (CMT) are compared with those obtained from the rigorous finite-difference time-domain (FDTD) simulation. The maximum Φ I of ~750 (~783) is obtained from CMT (FDTD) at L = 0.8 a.

Fig. 3
Fig. 3

Far-field radiation patterns. Far-field patterns are calculated by using the finite-difference time-domain method (FDTD) and the near- to far-field transformation formulae presented in ref. 11. The two far-field patterns (x,y) in the upper row are for the upper hemispherical surface ( 0 θ 90 ), where the mapping between (x,y) and (θ,ϕ) is given by x = θ cos ϕ and x = θ sin ϕ . In the two polar plots in the lower row, the dotted line (solid line) shows the radiation pattern in the x = 0 (y = 0) plane. (a, c) The photonic-crystal cavity without the bottom reflector, where the length of the nano-slot is 0.8 a. (b, d) The same photonic-cavity cavity as before but with the bottom reflector, where the gap size is d = λ / n b g .

Fig. 4
Fig. 4

Effects of the bottom reflector on local-field enhancement. The length of the nano-slot is fixed to be 0.8 a, at which Φ I has been optimized in the absence of the bottom reflector. (a) Electric-field intensity distribution in the x-z plane. The downward-propagating waves can be redirected to the top by the reflector and they can interfere with the originally upward-propagating waves. The interference condition can be determined by the gap size, d. (b) Quality factor, Qtot , mode volume, Vm , and the far-field coupling factor, η ( θ = 0 ) , calculated as a function of d. (c) The electric-field intensity enhancement factors, Φ I , obtained from the coupled-mode theory (CMT) are compared with those obtained from the rigorous finite-difference time-domain (FDTD) simulation. Φ I of ~3,437 (~4,500) is obtained from CMT (FDTD) at d = 0.9 λ / n b g ( d = 1.0 λ / n b g ).

Fig. 5
Fig. 5

(a) Structure of the low-Q dipole mode cavity. (b) Normalized frequency and Quality factor as a function of the modified hole radius, Rm . (c) Vector plot of the electric-fields. (d) Far-field radiation pattern from the mode shown in Fig. 5(c).

Fig. 6
Fig. 6

Resonant wavelength (nm) and normalized frequency (a/λ) as a function of the slot length (a), where a = 350 nm was assumed.

Fig. 7
Fig. 7

(a) FDTD simulations used to obtain the far-field coupling factor, η. (b) The rigorous FDTD simulation used to directly obtain Φ I .

Fig. 8
Fig. 8

(a) Structure of the high-Q PhC dipole mode cavity. (b,c) Electric-field intensity (|E|2) distributions (b) in the x-y plane and (c) in the x-z plane.

Tables (1)

Tables Icon

Table 1 Electric-field intensity enhancement from the high-Q dipole mode.

Equations (21)

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d α d t = i ω c α ( 1 τ t o t ) α + κ 0 S + 0 .
| α | 2 T | t = τ t o t 2 | κ 0 | 2 | S + 0 | 2 T = 1 2 c ε 0 n b g τ t o t 2 | E 0 | 2 | κ 0 | 2 A .
| α | 2 T | t = 1 2 V m ε 0 n c 2 | E l o c | 2 ,
η ( θ , ϕ ) d P d Ω ( θ , ϕ ) P t o t ,
| κ 0 | 2 A = 2 τ t o t ( λ n b g ) 2 η ( θ = 0 ) cos 2 χ .
Φ I | E l o c | 2 | E 0 | 2 = 2 π λ 3 n b g n c 2 Q t o t V m η ( θ = 0 ) cos 2 χ .
Δ Ω = ( λ / n b g ) 2 A
Δ P ( θ 0 ) P t o t = 1 / τ 0 1 / τ t o t .
| κ 0 | 2 A = 2 τ 0 ( λ n b g ) 2 1 Δ Ω cos 2 χ = 2 τ t o t ( λ n b g ) 2 Δ P ( θ 0 ) Δ Ω 1 P t o t cos 2 χ
V m = 1 2 ε 0 ε ( r ) | E ( r , t ) | 2 + 1 2 μ 0 | H ( r , t ) | 2 d 3 r max { 1 2 ε 0 ε ( r ) | E ( r , t ) | 2 + 1 2 μ 0 | H ( r , t ) | 2 } ,
V m = | α | 2 T max { ε 0 ε ( r ) | E ( r , t ) | 2 } T = | α | 2 T 1 2 ε 0 n c 2 | E l o c | 2
( 1 2 , 3 2 ) a ( 1 + R R m 2 , 0.9 3 2 ) a
( 1 2 , 3 2 ) a ( 1 + R R m 2 , 0.9 3 2 ) a
( 1 2 , 3 2 ) a ( 1 + R R m 2 , 0.9 3 2 ) a
( 1 2 , 3 2 ) a ( 1 + R R m 2 , 0.9 3 2 ) a
n s l a b 2 E x ( x = Δ / 2 ) n b g 2 E x ' ( x = Δ / 2 ) .
V m = | α | 2 T 1 2 ε 0 n s l a b 2 | E x ( x = 0 ) | 2 .
V m ' = | α | 2 T 1 2 ε 0 n b g 2 | E x ' ( x = 0 ) | 2 ( n b g n s l a b ) 2 V m .
V m ( 1 ) = ε 0 ε ( r ) | E ( r , t m ) | 2 d 3 r max { ε 0 ε ( r ) | E ( r , t m ) | 2 } ,
V m ( 2 ) = ε 0 ε ( r ) | E ( r , t ) | 2 d 3 r T max { ε 0 ε ( r ) | E ( r , t ) | 2 } T
η ( θ = 0 ) = d P d Ω | θ = 0 P t o t = ( Power radiated through  S 0 S 0 / L z 2 ) × 1 Power radiated through  S t o t

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