Abstract

We present a 2-D plasmonic crystal design with visible band-gap by combining a 2-D photonic crystal with TM band-gap and a silver surface. Simulations show that the presence of the silver surface gives rise to an expanded band-gap. A plasmonic crystal defect cavity with Q ~300 and mode volume ~1.9x10−2 (λ/n) 3 can be formed using our design. The total Q of such a cavity is determined by both the radiative loss of the dielectric component, as well as absorption loss to the metal. We provide design criteria for the optimization of the total Q to allow high radiative or extraction efficiency.

© 2014 Optical Society of America

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    [CrossRef] [PubMed]
  3. K. J. Russell, T.-L. Liu, S. Cui, E. L. Hu, “Large spontaneous emission enhancement in plasmonic nanocavities,” Nat. Photonics 6(7), 459–462 (2012).
    [CrossRef]
  4. P. Anger, P. Bharadwaj, L. Novotny, “Enhancement and quenching of single-molecule fluorescence,” Phys. Rev. Lett. 96(11), 113002 (2006).
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  5. K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, A. Scherer, “Surface-plasmon-enhanced light emitters based on InGaN quantum wells,” Nat. Mater. 3(9), 601–605 (2004).
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    [CrossRef]
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2012 (1)

K. J. Russell, T.-L. Liu, S. Cui, E. L. Hu, “Large spontaneous emission enhancement in plasmonic nanocavities,” Nat. Photonics 6(7), 459–462 (2012).
[CrossRef]

2011 (3)

X. Yang, A. Ishikawa, X. Yin, X. Zhang, “Hybrid photonic-plasmonic crystal nanocavities,” ACS Nano 5(4), 2831–2838 (2011).
[CrossRef] [PubMed]

A. C. Scofield, J. N. Shapiro, A. Lin, A. D. Williams, P. S. Wong, B. L. Liang, D. L. Huffaker, “Bottom-up photonic crystal cavities formed by patterned III-V nanopillars,” Nano Lett. 11(6), 2242–2246 (2011).
[CrossRef] [PubMed]

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

2010 (2)

2009 (1)

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461(7264), 629–632 (2009).
[CrossRef] [PubMed]

2008 (1)

L. Feng, M.-H. Lu, V. Lomakin, Y. Fainman, “Plasmonic photonic crystal with a complete band gap for surface plasmon polariton waves,” Appl. Phys. Lett. 93(23), 231105 (2008).
[CrossRef]

2007 (1)

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, A. Imamoğlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445(7130), 896–899 (2007).
[CrossRef] [PubMed]

2006 (2)

S. Kühn, U. Håkanson, L. Rogobete, V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett. 97(1), 017402 (2006).
[CrossRef] [PubMed]

P. Anger, P. Bharadwaj, L. Novotny, “Enhancement and quenching of single-molecule fluorescence,” Phys. Rev. Lett. 96(11), 113002 (2006).
[CrossRef] [PubMed]

2004 (1)

K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, A. Scherer, “Surface-plasmon-enhanced light emitters based on InGaN quantum wells,” Nat. Mater. 3(9), 601–605 (2004).
[CrossRef] [PubMed]

2003 (2)

K. J. Vahala, “Optical microcavities,” Nature 424(6950), 839–846 (2003).
[CrossRef] [PubMed]

Y. Akahane, T. Asano, B.-S. Song, S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425(6961), 944–947 (2003).
[CrossRef] [PubMed]

1999 (1)

1987 (1)

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

1983 (1)

P. Goy, J. M. Raimond, M. Gross, S. Haroche, “Observation of cavity-enhanced single-atom spontaneous emission,” Phys. Rev. Lett. 50(24), 1903–1906 (1983).
[CrossRef]

1972 (1)

P. B. Johnson, R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Akahane, Y.

Y. Akahane, T. Asano, B.-S. Song, S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425(6961), 944–947 (2003).
[CrossRef] [PubMed]

Anger, P.

P. Anger, P. Bharadwaj, L. Novotny, “Enhancement and quenching of single-molecule fluorescence,” Phys. Rev. Lett. 96(11), 113002 (2006).
[CrossRef] [PubMed]

Asano, T.

Y. Akahane, T. Asano, B.-S. Song, S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425(6961), 944–947 (2003).
[CrossRef] [PubMed]

Atatüre, M.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, A. Imamoğlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445(7130), 896–899 (2007).
[CrossRef] [PubMed]

Badolato, A.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, A. Imamoğlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445(7130), 896–899 (2007).
[CrossRef] [PubMed]

Bartal, G.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461(7264), 629–632 (2009).
[CrossRef] [PubMed]

Bharadwaj, P.

P. Anger, P. Bharadwaj, L. Novotny, “Enhancement and quenching of single-molecule fluorescence,” Phys. Rev. Lett. 96(11), 113002 (2006).
[CrossRef] [PubMed]

Bozhevolnyi, S. I.

D. K. Gramotnev, S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4(2), 83–91 (2010).
[CrossRef]

Christy, R. W.

P. B. Johnson, R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Cui, S.

K. J. Russell, T.-L. Liu, S. Cui, E. L. Hu, “Large spontaneous emission enhancement in plasmonic nanocavities,” Nat. Photonics 6(7), 459–462 (2012).
[CrossRef]

Dai, L.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461(7264), 629–632 (2009).
[CrossRef] [PubMed]

Enoch, S.

Fainman, Y.

L. Feng, M.-H. Lu, V. Lomakin, Y. Fainman, “Plasmonic photonic crystal with a complete band gap for surface plasmon polariton waves,” Appl. Phys. Lett. 93(23), 231105 (2008).
[CrossRef]

Fält, S.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, A. Imamoğlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445(7130), 896–899 (2007).
[CrossRef] [PubMed]

Feng, L.

L. Feng, M.-H. Lu, V. Lomakin, Y. Fainman, “Plasmonic photonic crystal with a complete band gap for surface plasmon polariton waves,” Appl. Phys. Lett. 93(23), 231105 (2008).
[CrossRef]

Gayral, B.

Gerace, D.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, A. Imamoğlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445(7130), 896–899 (2007).
[CrossRef] [PubMed]

Gerard, J.-M.

Gladden, C.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461(7264), 629–632 (2009).
[CrossRef] [PubMed]

González, M. U.

Goy, P.

P. Goy, J. M. Raimond, M. Gross, S. Haroche, “Observation of cavity-enhanced single-atom spontaneous emission,” Phys. Rev. Lett. 50(24), 1903–1906 (1983).
[CrossRef]

Gramotnev, D. K.

D. K. Gramotnev, S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4(2), 83–91 (2010).
[CrossRef]

Gross, M.

P. Goy, J. M. Raimond, M. Gross, S. Haroche, “Observation of cavity-enhanced single-atom spontaneous emission,” Phys. Rev. Lett. 50(24), 1903–1906 (1983).
[CrossRef]

Gulde, S.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, A. Imamoğlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445(7130), 896–899 (2007).
[CrossRef] [PubMed]

Håkanson, U.

S. Kühn, U. Håkanson, L. Rogobete, V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett. 97(1), 017402 (2006).
[CrossRef] [PubMed]

Haroche, S.

P. Goy, J. M. Raimond, M. Gross, S. Haroche, “Observation of cavity-enhanced single-atom spontaneous emission,” Phys. Rev. Lett. 50(24), 1903–1906 (1983).
[CrossRef]

Hennessy, K.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, A. Imamoğlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445(7130), 896–899 (2007).
[CrossRef] [PubMed]

Hu, E. L.

K. J. Russell, T.-L. Liu, S. Cui, E. L. Hu, “Large spontaneous emission enhancement in plasmonic nanocavities,” Nat. Photonics 6(7), 459–462 (2012).
[CrossRef]

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, A. Imamoğlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445(7130), 896–899 (2007).
[CrossRef] [PubMed]

Huffaker, D. L.

A. C. Scofield, J. N. Shapiro, A. Lin, A. D. Williams, P. S. Wong, B. L. Liang, D. L. Huffaker, “Bottom-up photonic crystal cavities formed by patterned III-V nanopillars,” Nano Lett. 11(6), 2242–2246 (2011).
[CrossRef] [PubMed]

Imamoglu, A.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, A. Imamoğlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445(7130), 896–899 (2007).
[CrossRef] [PubMed]

Ishikawa, A.

X. Yang, A. Ishikawa, X. Yin, X. Zhang, “Hybrid photonic-plasmonic crystal nanocavities,” ACS Nano 5(4), 2831–2838 (2011).
[CrossRef] [PubMed]

Johnson, P. B.

P. B. Johnson, R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Kim, M.-K.

Kühn, S.

S. Kühn, U. Håkanson, L. Rogobete, V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett. 97(1), 017402 (2006).
[CrossRef] [PubMed]

Lakhani, A. M.

Lau, E. K.

Liang, B. L.

A. C. Scofield, J. N. Shapiro, A. Lin, A. D. Williams, P. S. Wong, B. L. Liang, D. L. Huffaker, “Bottom-up photonic crystal cavities formed by patterned III-V nanopillars,” Nano Lett. 11(6), 2242–2246 (2011).
[CrossRef] [PubMed]

Lin, A.

A. C. Scofield, J. N. Shapiro, A. Lin, A. D. Williams, P. S. Wong, B. L. Liang, D. L. Huffaker, “Bottom-up photonic crystal cavities formed by patterned III-V nanopillars,” Nano Lett. 11(6), 2242–2246 (2011).
[CrossRef] [PubMed]

Liu, T.-L.

K. J. Russell, T.-L. Liu, S. Cui, E. L. Hu, “Large spontaneous emission enhancement in plasmonic nanocavities,” Nat. Photonics 6(7), 459–462 (2012).
[CrossRef]

Lomakin, V.

L. Feng, M.-H. Lu, V. Lomakin, Y. Fainman, “Plasmonic photonic crystal with a complete band gap for surface plasmon polariton waves,” Appl. Phys. Lett. 93(23), 231105 (2008).
[CrossRef]

Lu, M.-H.

L. Feng, M.-H. Lu, V. Lomakin, Y. Fainman, “Plasmonic photonic crystal with a complete band gap for surface plasmon polariton waves,” Appl. Phys. Lett. 93(23), 231105 (2008).
[CrossRef]

Ma, R.-M.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461(7264), 629–632 (2009).
[CrossRef] [PubMed]

Mukai, T.

K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, A. Scherer, “Surface-plasmon-enhanced light emitters based on InGaN quantum wells,” Nat. Mater. 3(9), 601–605 (2004).
[CrossRef] [PubMed]

Narukawa, Y.

K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, A. Scherer, “Surface-plasmon-enhanced light emitters based on InGaN quantum wells,” Nat. Mater. 3(9), 601–605 (2004).
[CrossRef] [PubMed]

Niki, I.

K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, A. Scherer, “Surface-plasmon-enhanced light emitters based on InGaN quantum wells,” Nat. Mater. 3(9), 601–605 (2004).
[CrossRef] [PubMed]

Noda, S.

Y. Akahane, T. Asano, B.-S. Song, S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425(6961), 944–947 (2003).
[CrossRef] [PubMed]

Novotny, L.

P. Anger, P. Bharadwaj, L. Novotny, “Enhancement and quenching of single-molecule fluorescence,” Phys. Rev. Lett. 96(11), 113002 (2006).
[CrossRef] [PubMed]

Okamoto, K.

K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, A. Scherer, “Surface-plasmon-enhanced light emitters based on InGaN quantum wells,” Nat. Mater. 3(9), 601–605 (2004).
[CrossRef] [PubMed]

Oulton, R. F.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461(7264), 629–632 (2009).
[CrossRef] [PubMed]

Quidant, R.

Raimond, J. M.

P. Goy, J. M. Raimond, M. Gross, S. Haroche, “Observation of cavity-enhanced single-atom spontaneous emission,” Phys. Rev. Lett. 50(24), 1903–1906 (1983).
[CrossRef]

Randhawa, S.

Renger, J.

Rogobete, L.

S. Kühn, U. Håkanson, L. Rogobete, V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett. 97(1), 017402 (2006).
[CrossRef] [PubMed]

Russell, K. J.

K. J. Russell, T.-L. Liu, S. Cui, E. L. Hu, “Large spontaneous emission enhancement in plasmonic nanocavities,” Nat. Photonics 6(7), 459–462 (2012).
[CrossRef]

Sandoghdar, V.

S. Kühn, U. Håkanson, L. Rogobete, V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett. 97(1), 017402 (2006).
[CrossRef] [PubMed]

Scherer, A.

K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, A. Scherer, “Surface-plasmon-enhanced light emitters based on InGaN quantum wells,” Nat. Mater. 3(9), 601–605 (2004).
[CrossRef] [PubMed]

Scofield, A. C.

A. C. Scofield, J. N. Shapiro, A. Lin, A. D. Williams, P. S. Wong, B. L. Liang, D. L. Huffaker, “Bottom-up photonic crystal cavities formed by patterned III-V nanopillars,” Nano Lett. 11(6), 2242–2246 (2011).
[CrossRef] [PubMed]

Shapiro, J. N.

A. C. Scofield, J. N. Shapiro, A. Lin, A. D. Williams, P. S. Wong, B. L. Liang, D. L. Huffaker, “Bottom-up photonic crystal cavities formed by patterned III-V nanopillars,” Nano Lett. 11(6), 2242–2246 (2011).
[CrossRef] [PubMed]

Shvartser, A.

K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, A. Scherer, “Surface-plasmon-enhanced light emitters based on InGaN quantum wells,” Nat. Mater. 3(9), 601–605 (2004).
[CrossRef] [PubMed]

Song, B.-S.

Y. Akahane, T. Asano, B.-S. Song, S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425(6961), 944–947 (2003).
[CrossRef] [PubMed]

Sorger, V. J.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461(7264), 629–632 (2009).
[CrossRef] [PubMed]

Vahala, K. J.

K. J. Vahala, “Optical microcavities,” Nature 424(6950), 839–846 (2003).
[CrossRef] [PubMed]

Williams, A. D.

A. C. Scofield, J. N. Shapiro, A. Lin, A. D. Williams, P. S. Wong, B. L. Liang, D. L. Huffaker, “Bottom-up photonic crystal cavities formed by patterned III-V nanopillars,” Nano Lett. 11(6), 2242–2246 (2011).
[CrossRef] [PubMed]

Winger, M.

K. Hennessy, A. Badolato, M. Winger, D. Gerace, M. Atatüre, S. Gulde, S. Fält, E. L. Hu, A. Imamoğlu, “Quantum nature of a strongly coupled single quantum dot-cavity system,” Nature 445(7130), 896–899 (2007).
[CrossRef] [PubMed]

Wong, P. S.

A. C. Scofield, J. N. Shapiro, A. Lin, A. D. Williams, P. S. Wong, B. L. Liang, D. L. Huffaker, “Bottom-up photonic crystal cavities formed by patterned III-V nanopillars,” Nano Lett. 11(6), 2242–2246 (2011).
[CrossRef] [PubMed]

Wu, M. C.

Yablonovitch, E.

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

Yang, X.

X. Yang, A. Ishikawa, X. Yin, X. Zhang, “Hybrid photonic-plasmonic crystal nanocavities,” ACS Nano 5(4), 2831–2838 (2011).
[CrossRef] [PubMed]

Yin, X.

X. Yang, A. Ishikawa, X. Yin, X. Zhang, “Hybrid photonic-plasmonic crystal nanocavities,” ACS Nano 5(4), 2831–2838 (2011).
[CrossRef] [PubMed]

Zentgraf, T.

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461(7264), 629–632 (2009).
[CrossRef] [PubMed]

Zhang, X.

X. Yang, A. Ishikawa, X. Yin, X. Zhang, “Hybrid photonic-plasmonic crystal nanocavities,” ACS Nano 5(4), 2831–2838 (2011).
[CrossRef] [PubMed]

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461(7264), 629–632 (2009).
[CrossRef] [PubMed]

ACS Nano (1)

X. Yang, A. Ishikawa, X. Yin, X. Zhang, “Hybrid photonic-plasmonic crystal nanocavities,” ACS Nano 5(4), 2831–2838 (2011).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

L. Feng, M.-H. Lu, V. Lomakin, Y. Fainman, “Plasmonic photonic crystal with a complete band gap for surface plasmon polariton waves,” Appl. Phys. Lett. 93(23), 231105 (2008).
[CrossRef]

J. Lightwave Technol. (1)

Nano Lett. (1)

A. C. Scofield, J. N. Shapiro, A. Lin, A. D. Williams, P. S. Wong, B. L. Liang, D. L. Huffaker, “Bottom-up photonic crystal cavities formed by patterned III-V nanopillars,” Nano Lett. 11(6), 2242–2246 (2011).
[CrossRef] [PubMed]

Nat. Mater. (1)

K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, A. Scherer, “Surface-plasmon-enhanced light emitters based on InGaN quantum wells,” Nat. Mater. 3(9), 601–605 (2004).
[CrossRef] [PubMed]

Nat. Photonics (2)

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Figures (4)

Fig. 1
Fig. 1

(a) An angled and a top-down schematic view of the photonic crystal studied in this work. (b) Corresponding photonic band structure with a = 250nm and r = 70nm.

Fig. 2
Fig. 2

(a) A top-down and cross-sectional view of the plasmonic crystal studied in this work. (b) Evolution of the band structure as a silver film approaches the photonic crystal shown in Fig. 1. (c) Normalized electric field intensity distribution of three lowest energy bands near the M point when there is no metal. The color bar indicates the relative field strength, and applies for all electric field distributions in the paper. (d) Normalized electric field distribution of the same three bands when the silver layer is 10nm away from the photonic crystal.

Fig. 3
Fig. 3

(a) Top-down view of the plasmonic crystal defect cavity. (b) Simulated spectrum of the cavity with various defect sizes. (c) Normalized electric field distribution of the cavity with rd = 120nm at the peak of the two modes.

Fig. 4
Fig. 4

(a) Top-down and cross-sectional view of the simulated plasmonic crystal defect cavity. The rods outlined by the dashed lines are the ones whose radii are adjusted in the optimization process. (b) Near-field, far-field power radiation and extraction spectra of the cavity with rT = r. (c) Dependence of Q, power radiation and extraction efficiency at the peak of the lower frequency modes on rT. (d) Dependence of extraction efficiency on Q.

Equations (2)

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1 Q = 1 Q R + 1 Q A ,
Γ ext = Γ int Q Q R = Γ int Q( 1 Q 1 Q A )= Γ int ( 1 Q Q A ),

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