Abstract

We propose a metal nanodisk hybrid plasmonic resonator (HPR), which consists of a metallic nanodisk on top of a dielectric slab. In contrast to the previously studied plasmonic resonator structures based on metal substrates such as the nanopatch resonator, the fabrication process of the proposed resonator is much easier because of a dielectric substrate. The performance of the proposed resonator has been theoretically investigated and compared to the previously studied structures. It has been shown that the performance of the proposed resonator is superior to that of the nanopatch resonator and comparable to that of a hybrid resonator based on a metal substrate.

© 2014 Optical Society of America

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  2. K. Nozaki, T. Baba, “Laser characteristics with ultimate-small mode volume in photonic crystal slab point-shift nanolasers,” Appl. Phys. Lett. 88(21), 211101 (2006).
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  3. B. Ellis, M. A. Mayer, G. Shambat, T. Sarmiento, J. Harris, E. E. Haller, J. Vuckovic, “Ultralow-threshold electrically pumped quantum-dot photonic-crystal nanocavity laser,” Nat. Photonics 3(1), 55–58 (2009).
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  5. D. A. Genov, R. F. Oulton, G. Bartal, X. Zhang, “Anomalous spectral scaling of light emission rates in low-dimensional metallic nanostructures,” Phys. Rev. B 83(24), 245312 (2011).
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    [CrossRef]
  7. M. K. Seo, S. H. Kwon, H. S. Ee, H. G. Park, “Full three-dimensional subwavelength high-Q surface-plasmon-polariton cavity,” Nano Lett. 9(12), 4078–4082 (2009).
    [CrossRef] [PubMed]
  8. J. H. Kang, Y. S. No, S. H. Kwon, H. G. Park, “Ultrasmall subwavelength nanorod plasmonic cavity,” Opt. Lett. 36(11), 2011–2013 (2011).
    [CrossRef] [PubMed]
  9. A. Mizrahi, V. Lomakin, B. A. Slutsky, M. P. Nezhad, L. Feng, Y. Fainman, “Low threshold gain metal coated laser nanoresonators,” Opt. Lett. 33(11), 1261–1263 (2008).
    [CrossRef] [PubMed]
  10. 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).
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    [CrossRef]
  12. 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]
  13. W. Cai, J. S. White, M. L. Brongersma, “Compact, high-speed and power-efficient electrooptic plasmonic modulators,” Nano Lett. 9(12), 4403–4411 (2009).
    [CrossRef] [PubMed]
  14. V. J. Sorger, N. D. L. Kimura, R. M. Ma, X. Zhang, “Ultra-compact silicon nanophotonic modulator with broadband response,” Nanophotonics 1(1), 17–22 (2012).
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    [CrossRef]
  17. K.-H. Su, S. Durant, J. M. Steele, Y. Xiong, C. Sun, X. Zhang, “Raman enhancement factor of a single tunable nanoplasmonic resonator,” J. Phys. Chem. B 110(9), 3964–3968 (2006).
    [CrossRef] [PubMed]
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  22. R.-M. Ma, R. F. Oulton, V. J. Sorger, G. Bartal, X. Zhang, “Room-temperature sub-diffraction-limited plasmon laser by total internal reflection,” Nat. Mater. 10(2), 110–113 (2011).
    [CrossRef] [PubMed]
  23. R.-M. Ma, X. Yin, R. F. Oulton, V. J. Sorger, X. Zhang, “Multiplexed and electrically modulated plasmon laser circuit,” Nano Lett. 12(10), 5396–5402 (2012).
    [CrossRef] [PubMed]
  24. P. B. Johnson, R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
    [CrossRef]
  25. S.-W. Chang, S. L. Chuang, “Normal modes for plasmonic nanolasers with dispersive and inhomogeneous media,” Opt. Lett. 34(1), 91–93 (2009).
    [CrossRef] [PubMed]
  26. P. Berini, “Figures of merit for surface plasmon waveguides,” Opt. Express 14(26), 13030–13042 (2006).
    [CrossRef] [PubMed]
  27. A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 1995).
  28. W. Porod, D. K. Ferry, “Modification of the virtual-crystal approximation for ternary III-V compounds,” Phys. Rev. B 27(4), 2587–2589 (1983).
    [CrossRef]
  29. J.-K. Hwang, H.-Y. Ryu, Y.-H. Lee, “Spontaneous emission rate of an electric dipole in a general microcavity,” Phys. Rev. B 60(7), 4688–4695 (1999).
    [CrossRef]

2012 (4)

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]

V. J. Sorger, N. D. L. Kimura, R. M. Ma, X. Zhang, “Ultra-compact silicon nanophotonic modulator with broadband response,” Nanophotonics 1(1), 17–22 (2012).
[CrossRef]

S.-H. Kwon, “Deep subwavelength plasmonic whispering-gallery-mode cavity,” Opt. Express 20(22), 24918–24924 (2012).
[CrossRef] [PubMed]

R.-M. Ma, X. Yin, R. F. Oulton, V. J. Sorger, X. Zhang, “Multiplexed and electrically modulated plasmon laser circuit,” Nano Lett. 12(10), 5396–5402 (2012).
[CrossRef] [PubMed]

2011 (3)

R.-M. Ma, R. F. Oulton, V. J. Sorger, G. Bartal, X. Zhang, “Room-temperature sub-diffraction-limited plasmon laser by total internal reflection,” Nat. Mater. 10(2), 110–113 (2011).
[CrossRef] [PubMed]

D. A. Genov, R. F. Oulton, G. Bartal, X. Zhang, “Anomalous spectral scaling of light emission rates in low-dimensional metallic nanostructures,” Phys. Rev. B 83(24), 245312 (2011).
[CrossRef]

J. H. Kang, Y. S. No, S. H. Kwon, H. G. Park, “Ultrasmall subwavelength nanorod plasmonic cavity,” Opt. Lett. 36(11), 2011–2013 (2011).
[CrossRef] [PubMed]

2010 (3)

J. Gao, J. F. McMilan, M. C. Wu, J. Zheng, S. Assefa, C. W. Wong, “Demonstration of an air-slot mode-gap confined photonic crystal slab nanocavity with ultrasmall mode volumes,” Appl. Phys. Lett. 96(5), 051123 (2010).
[CrossRef]

M. Kuttge, F. J. García de Abajo, A. Polman, “Ultrasmall mode volume plasmonic nanodisk resonators,” Nano Lett. 10(5), 1537–1541 (2010).
[CrossRef] [PubMed]

K. Yu, A. Lakhani, M. C. Wu, “Subwavelength metal-optic semiconductor nanopatch lasers,” Opt. Express 18(9), 8790–8799 (2010).
[CrossRef] [PubMed]

2009 (5)

S.-W. Chang, S. L. Chuang, “Normal modes for plasmonic nanolasers with dispersive and inhomogeneous media,” Opt. Lett. 34(1), 91–93 (2009).
[CrossRef] [PubMed]

M. K. Seo, S. H. Kwon, H. S. Ee, H. G. Park, “Full three-dimensional subwavelength high-Q surface-plasmon-polariton cavity,” Nano Lett. 9(12), 4078–4082 (2009).
[CrossRef] [PubMed]

B. Ellis, M. A. Mayer, G. Shambat, T. Sarmiento, J. Harris, E. E. Haller, J. Vuckovic, “Ultralow-threshold electrically pumped quantum-dot photonic-crystal nanocavity laser,” Nat. Photonics 3(1), 55–58 (2009).

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]

W. Cai, J. S. White, M. L. Brongersma, “Compact, high-speed and power-efficient electrooptic plasmonic modulators,” Nano Lett. 9(12), 4403–4411 (2009).
[CrossRef] [PubMed]

2008 (3)

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2(8), 496–500 (2008).
[CrossRef]

F. Vollmer, S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5(7), 591–596 (2008).
[CrossRef] [PubMed]

A. Mizrahi, V. Lomakin, B. A. Slutsky, M. P. Nezhad, L. Feng, Y. Fainman, “Low threshold gain metal coated laser nanoresonators,” Opt. Lett. 33(11), 1261–1263 (2008).
[CrossRef] [PubMed]

2007 (1)

M. T. Hill, Y. S. Oei, B. Smalbrugge, Y. Zhu, T. D. Vries, P. J. V. Veldhoven, F. W. M. V. Otten, T. J. Eijkemans, J. P. Turkiewicz, H. D. Waardt, E. J. Geluk, S. H. Kwon, Y. H. Lee, R. Notzel, M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1(10), 589–594 (2007).
[CrossRef]

2006 (5)

K. Nozaki, T. Baba, “Laser characteristics with ultimate-small mode volume in photonic crystal slab point-shift nanolasers,” Appl. Phys. Lett. 88(21), 211101 (2006).
[CrossRef]

T. J. Kippenberg, J. Kalkman, A. Polman, K. J. Vahala, “Demonstration of an erbium-doped microdisk laser on a silicon chip,” Phys. Rev. A 74(5), 051802 (2006).
[CrossRef]

K.-H. Su, S. Durant, J. M. Steele, Y. Xiong, C. Sun, X. Zhang, “Raman enhancement factor of a single tunable nanoplasmonic resonator,” J. Phys. Chem. B 110(9), 3964–3968 (2006).
[CrossRef] [PubMed]

K. H. Su, Q. H. Wei, X. Zhang, “Tunable and augmented plasmon resonances of Au/SiO2/Au nanodisks,” Appl. Phys. Lett. 88(6), 063118 (2006).
[CrossRef]

P. Berini, “Figures of merit for surface plasmon waveguides,” Opt. Express 14(26), 13030–13042 (2006).
[CrossRef] [PubMed]

1999 (1)

J.-K. Hwang, H.-Y. Ryu, Y.-H. Lee, “Spontaneous emission rate of an electric dipole in a general microcavity,” Phys. Rev. B 60(7), 4688–4695 (1999).
[CrossRef]

1983 (1)

W. Porod, D. K. Ferry, “Modification of the virtual-crystal approximation for ternary III-V compounds,” Phys. Rev. B 27(4), 2587–2589 (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]

1946 (1)

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

Arnold, S.

F. Vollmer, S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5(7), 591–596 (2008).
[CrossRef] [PubMed]

Assefa, S.

J. Gao, J. F. McMilan, M. C. Wu, J. Zheng, S. Assefa, C. W. Wong, “Demonstration of an air-slot mode-gap confined photonic crystal slab nanocavity with ultrasmall mode volumes,” Appl. Phys. Lett. 96(5), 051123 (2010).
[CrossRef]

Baba, T.

K. Nozaki, T. Baba, “Laser characteristics with ultimate-small mode volume in photonic crystal slab point-shift nanolasers,” Appl. Phys. Lett. 88(21), 211101 (2006).
[CrossRef]

Bartal, G.

D. A. Genov, R. F. Oulton, G. Bartal, X. Zhang, “Anomalous spectral scaling of light emission rates in low-dimensional metallic nanostructures,” Phys. Rev. B 83(24), 245312 (2011).
[CrossRef]

R.-M. Ma, R. F. Oulton, V. J. Sorger, G. Bartal, X. Zhang, “Room-temperature sub-diffraction-limited plasmon laser by total internal reflection,” Nat. Mater. 10(2), 110–113 (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]

Berini, P.

Brongersma, M. L.

W. Cai, J. S. White, M. L. Brongersma, “Compact, high-speed and power-efficient electrooptic plasmonic modulators,” Nano Lett. 9(12), 4403–4411 (2009).
[CrossRef] [PubMed]

Cai, W.

W. Cai, J. S. White, M. L. Brongersma, “Compact, high-speed and power-efficient electrooptic plasmonic modulators,” Nano Lett. 9(12), 4403–4411 (2009).
[CrossRef] [PubMed]

Chang, S.-W.

Christy, R. W.

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

Chuang, S. L.

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]

Durant, S.

K.-H. Su, S. Durant, J. M. Steele, Y. Xiong, C. Sun, X. Zhang, “Raman enhancement factor of a single tunable nanoplasmonic resonator,” J. Phys. Chem. B 110(9), 3964–3968 (2006).
[CrossRef] [PubMed]

Ee, H. S.

M. K. Seo, S. H. Kwon, H. S. Ee, H. G. Park, “Full three-dimensional subwavelength high-Q surface-plasmon-polariton cavity,” Nano Lett. 9(12), 4078–4082 (2009).
[CrossRef] [PubMed]

Eijkemans, T. J.

M. T. Hill, Y. S. Oei, B. Smalbrugge, Y. Zhu, T. D. Vries, P. J. V. Veldhoven, F. W. M. V. Otten, T. J. Eijkemans, J. P. Turkiewicz, H. D. Waardt, E. J. Geluk, S. H. Kwon, Y. H. Lee, R. Notzel, M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1(10), 589–594 (2007).
[CrossRef]

Ellis, B.

B. Ellis, M. A. Mayer, G. Shambat, T. Sarmiento, J. Harris, E. E. Haller, J. Vuckovic, “Ultralow-threshold electrically pumped quantum-dot photonic-crystal nanocavity laser,” Nat. Photonics 3(1), 55–58 (2009).

Fainman, Y.

Feng, L.

Ferry, D. K.

W. Porod, D. K. Ferry, “Modification of the virtual-crystal approximation for ternary III-V compounds,” Phys. Rev. B 27(4), 2587–2589 (1983).
[CrossRef]

Gao, J.

J. Gao, J. F. McMilan, M. C. Wu, J. Zheng, S. Assefa, C. W. Wong, “Demonstration of an air-slot mode-gap confined photonic crystal slab nanocavity with ultrasmall mode volumes,” Appl. Phys. Lett. 96(5), 051123 (2010).
[CrossRef]

García de Abajo, F. J.

M. Kuttge, F. J. García de Abajo, A. Polman, “Ultrasmall mode volume plasmonic nanodisk resonators,” Nano Lett. 10(5), 1537–1541 (2010).
[CrossRef] [PubMed]

Geluk, E. J.

M. T. Hill, Y. S. Oei, B. Smalbrugge, Y. Zhu, T. D. Vries, P. J. V. Veldhoven, F. W. M. V. Otten, T. J. Eijkemans, J. P. Turkiewicz, H. D. Waardt, E. J. Geluk, S. H. Kwon, Y. H. Lee, R. Notzel, M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1(10), 589–594 (2007).
[CrossRef]

Genov, D. A.

D. A. Genov, R. F. Oulton, G. Bartal, X. Zhang, “Anomalous spectral scaling of light emission rates in low-dimensional metallic nanostructures,” Phys. Rev. B 83(24), 245312 (2011).
[CrossRef]

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2(8), 496–500 (2008).
[CrossRef]

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]

Haller, E. E.

B. Ellis, M. A. Mayer, G. Shambat, T. Sarmiento, J. Harris, E. E. Haller, J. Vuckovic, “Ultralow-threshold electrically pumped quantum-dot photonic-crystal nanocavity laser,” Nat. Photonics 3(1), 55–58 (2009).

Harris, J.

B. Ellis, M. A. Mayer, G. Shambat, T. Sarmiento, J. Harris, E. E. Haller, J. Vuckovic, “Ultralow-threshold electrically pumped quantum-dot photonic-crystal nanocavity laser,” Nat. Photonics 3(1), 55–58 (2009).

Hill, M. T.

M. T. Hill, Y. S. Oei, B. Smalbrugge, Y. Zhu, T. D. Vries, P. J. V. Veldhoven, F. W. M. V. Otten, T. J. Eijkemans, J. P. Turkiewicz, H. D. Waardt, E. J. Geluk, S. H. Kwon, Y. H. Lee, R. Notzel, M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1(10), 589–594 (2007).
[CrossRef]

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]

Hwang, J.-K.

J.-K. Hwang, H.-Y. Ryu, Y.-H. Lee, “Spontaneous emission rate of an electric dipole in a general microcavity,” Phys. Rev. B 60(7), 4688–4695 (1999).
[CrossRef]

Johnson, P. B.

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

Kalkman, J.

T. J. Kippenberg, J. Kalkman, A. Polman, K. J. Vahala, “Demonstration of an erbium-doped microdisk laser on a silicon chip,” Phys. Rev. A 74(5), 051802 (2006).
[CrossRef]

Kang, J. H.

Kimura, N. D. L.

V. J. Sorger, N. D. L. Kimura, R. M. Ma, X. Zhang, “Ultra-compact silicon nanophotonic modulator with broadband response,” Nanophotonics 1(1), 17–22 (2012).
[CrossRef]

Kippenberg, T. J.

T. J. Kippenberg, J. Kalkman, A. Polman, K. J. Vahala, “Demonstration of an erbium-doped microdisk laser on a silicon chip,” Phys. Rev. A 74(5), 051802 (2006).
[CrossRef]

Kuttge, M.

M. Kuttge, F. J. García de Abajo, A. Polman, “Ultrasmall mode volume plasmonic nanodisk resonators,” Nano Lett. 10(5), 1537–1541 (2010).
[CrossRef] [PubMed]

Kwon, S. H.

J. H. Kang, Y. S. No, S. H. Kwon, H. G. Park, “Ultrasmall subwavelength nanorod plasmonic cavity,” Opt. Lett. 36(11), 2011–2013 (2011).
[CrossRef] [PubMed]

M. K. Seo, S. H. Kwon, H. S. Ee, H. G. Park, “Full three-dimensional subwavelength high-Q surface-plasmon-polariton cavity,” Nano Lett. 9(12), 4078–4082 (2009).
[CrossRef] [PubMed]

M. T. Hill, Y. S. Oei, B. Smalbrugge, Y. Zhu, T. D. Vries, P. J. V. Veldhoven, F. W. M. V. Otten, T. J. Eijkemans, J. P. Turkiewicz, H. D. Waardt, E. J. Geluk, S. H. Kwon, Y. H. Lee, R. Notzel, M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1(10), 589–594 (2007).
[CrossRef]

Kwon, S.-H.

Lakhani, A.

Lee, Y. H.

M. T. Hill, Y. S. Oei, B. Smalbrugge, Y. Zhu, T. D. Vries, P. J. V. Veldhoven, F. W. M. V. Otten, T. J. Eijkemans, J. P. Turkiewicz, H. D. Waardt, E. J. Geluk, S. H. Kwon, Y. H. Lee, R. Notzel, M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1(10), 589–594 (2007).
[CrossRef]

Lee, Y.-H.

J.-K. Hwang, H.-Y. Ryu, Y.-H. Lee, “Spontaneous emission rate of an electric dipole in a general microcavity,” Phys. Rev. B 60(7), 4688–4695 (1999).
[CrossRef]

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.

Ma, R. M.

V. J. Sorger, N. D. L. Kimura, R. M. Ma, X. Zhang, “Ultra-compact silicon nanophotonic modulator with broadband response,” Nanophotonics 1(1), 17–22 (2012).
[CrossRef]

Ma, R.-M.

R.-M. Ma, X. Yin, R. F. Oulton, V. J. Sorger, X. Zhang, “Multiplexed and electrically modulated plasmon laser circuit,” Nano Lett. 12(10), 5396–5402 (2012).
[CrossRef] [PubMed]

R.-M. Ma, R. F. Oulton, V. J. Sorger, G. Bartal, X. Zhang, “Room-temperature sub-diffraction-limited plasmon laser by total internal reflection,” Nat. Mater. 10(2), 110–113 (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]

Mayer, M. A.

B. Ellis, M. A. Mayer, G. Shambat, T. Sarmiento, J. Harris, E. E. Haller, J. Vuckovic, “Ultralow-threshold electrically pumped quantum-dot photonic-crystal nanocavity laser,” Nat. Photonics 3(1), 55–58 (2009).

McMilan, J. F.

J. Gao, J. F. McMilan, M. C. Wu, J. Zheng, S. Assefa, C. W. Wong, “Demonstration of an air-slot mode-gap confined photonic crystal slab nanocavity with ultrasmall mode volumes,” Appl. Phys. Lett. 96(5), 051123 (2010).
[CrossRef]

Mizrahi, A.

Nezhad, M. P.

No, Y. S.

Notzel, R.

M. T. Hill, Y. S. Oei, B. Smalbrugge, Y. Zhu, T. D. Vries, P. J. V. Veldhoven, F. W. M. V. Otten, T. J. Eijkemans, J. P. Turkiewicz, H. D. Waardt, E. J. Geluk, S. H. Kwon, Y. H. Lee, R. Notzel, M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1(10), 589–594 (2007).
[CrossRef]

Nozaki, K.

K. Nozaki, T. Baba, “Laser characteristics with ultimate-small mode volume in photonic crystal slab point-shift nanolasers,” Appl. Phys. Lett. 88(21), 211101 (2006).
[CrossRef]

Oei, Y. S.

M. T. Hill, Y. S. Oei, B. Smalbrugge, Y. Zhu, T. D. Vries, P. J. V. Veldhoven, F. W. M. V. Otten, T. J. Eijkemans, J. P. Turkiewicz, H. D. Waardt, E. J. Geluk, S. H. Kwon, Y. H. Lee, R. Notzel, M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1(10), 589–594 (2007).
[CrossRef]

Otten, F. W. M. V.

M. T. Hill, Y. S. Oei, B. Smalbrugge, Y. Zhu, T. D. Vries, P. J. V. Veldhoven, F. W. M. V. Otten, T. J. Eijkemans, J. P. Turkiewicz, H. D. Waardt, E. J. Geluk, S. H. Kwon, Y. H. Lee, R. Notzel, M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1(10), 589–594 (2007).
[CrossRef]

Oulton, R. F.

R.-M. Ma, X. Yin, R. F. Oulton, V. J. Sorger, X. Zhang, “Multiplexed and electrically modulated plasmon laser circuit,” Nano Lett. 12(10), 5396–5402 (2012).
[CrossRef] [PubMed]

R.-M. Ma, R. F. Oulton, V. J. Sorger, G. Bartal, X. Zhang, “Room-temperature sub-diffraction-limited plasmon laser by total internal reflection,” Nat. Mater. 10(2), 110–113 (2011).
[CrossRef] [PubMed]

D. A. Genov, R. F. Oulton, G. Bartal, X. Zhang, “Anomalous spectral scaling of light emission rates in low-dimensional metallic nanostructures,” Phys. Rev. B 83(24), 245312 (2011).
[CrossRef]

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]

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2(8), 496–500 (2008).
[CrossRef]

Park, H. G.

J. H. Kang, Y. S. No, S. H. Kwon, H. G. Park, “Ultrasmall subwavelength nanorod plasmonic cavity,” Opt. Lett. 36(11), 2011–2013 (2011).
[CrossRef] [PubMed]

M. K. Seo, S. H. Kwon, H. S. Ee, H. G. Park, “Full three-dimensional subwavelength high-Q surface-plasmon-polariton cavity,” Nano Lett. 9(12), 4078–4082 (2009).
[CrossRef] [PubMed]

Pile, D. F. P.

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2(8), 496–500 (2008).
[CrossRef]

Polman, A.

M. Kuttge, F. J. García de Abajo, A. Polman, “Ultrasmall mode volume plasmonic nanodisk resonators,” Nano Lett. 10(5), 1537–1541 (2010).
[CrossRef] [PubMed]

T. J. Kippenberg, J. Kalkman, A. Polman, K. J. Vahala, “Demonstration of an erbium-doped microdisk laser on a silicon chip,” Phys. Rev. A 74(5), 051802 (2006).
[CrossRef]

Porod, W.

W. Porod, D. K. Ferry, “Modification of the virtual-crystal approximation for ternary III-V compounds,” Phys. Rev. B 27(4), 2587–2589 (1983).
[CrossRef]

Purcell, E. M.

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

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]

Ryu, H.-Y.

J.-K. Hwang, H.-Y. Ryu, Y.-H. Lee, “Spontaneous emission rate of an electric dipole in a general microcavity,” Phys. Rev. B 60(7), 4688–4695 (1999).
[CrossRef]

Sarmiento, T.

B. Ellis, M. A. Mayer, G. Shambat, T. Sarmiento, J. Harris, E. E. Haller, J. Vuckovic, “Ultralow-threshold electrically pumped quantum-dot photonic-crystal nanocavity laser,” Nat. Photonics 3(1), 55–58 (2009).

Seo, M. K.

M. K. Seo, S. H. Kwon, H. S. Ee, H. G. Park, “Full three-dimensional subwavelength high-Q surface-plasmon-polariton cavity,” Nano Lett. 9(12), 4078–4082 (2009).
[CrossRef] [PubMed]

Shambat, G.

B. Ellis, M. A. Mayer, G. Shambat, T. Sarmiento, J. Harris, E. E. Haller, J. Vuckovic, “Ultralow-threshold electrically pumped quantum-dot photonic-crystal nanocavity laser,” Nat. Photonics 3(1), 55–58 (2009).

Slutsky, B. A.

Smalbrugge, B.

M. T. Hill, Y. S. Oei, B. Smalbrugge, Y. Zhu, T. D. Vries, P. J. V. Veldhoven, F. W. M. V. Otten, T. J. Eijkemans, J. P. Turkiewicz, H. D. Waardt, E. J. Geluk, S. H. Kwon, Y. H. Lee, R. Notzel, M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1(10), 589–594 (2007).
[CrossRef]

Smit, M. K.

M. T. Hill, Y. S. Oei, B. Smalbrugge, Y. Zhu, T. D. Vries, P. J. V. Veldhoven, F. W. M. V. Otten, T. J. Eijkemans, J. P. Turkiewicz, H. D. Waardt, E. J. Geluk, S. H. Kwon, Y. H. Lee, R. Notzel, M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1(10), 589–594 (2007).
[CrossRef]

Sorger, V. J.

V. J. Sorger, N. D. L. Kimura, R. M. Ma, X. Zhang, “Ultra-compact silicon nanophotonic modulator with broadband response,” Nanophotonics 1(1), 17–22 (2012).
[CrossRef]

R.-M. Ma, X. Yin, R. F. Oulton, V. J. Sorger, X. Zhang, “Multiplexed and electrically modulated plasmon laser circuit,” Nano Lett. 12(10), 5396–5402 (2012).
[CrossRef] [PubMed]

R.-M. Ma, R. F. Oulton, V. J. Sorger, G. Bartal, X. Zhang, “Room-temperature sub-diffraction-limited plasmon laser by total internal reflection,” Nat. Mater. 10(2), 110–113 (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]

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2(8), 496–500 (2008).
[CrossRef]

Steele, J. M.

K.-H. Su, S. Durant, J. M. Steele, Y. Xiong, C. Sun, X. Zhang, “Raman enhancement factor of a single tunable nanoplasmonic resonator,” J. Phys. Chem. B 110(9), 3964–3968 (2006).
[CrossRef] [PubMed]

Su, K. H.

K. H. Su, Q. H. Wei, X. Zhang, “Tunable and augmented plasmon resonances of Au/SiO2/Au nanodisks,” Appl. Phys. Lett. 88(6), 063118 (2006).
[CrossRef]

Su, K.-H.

K.-H. Su, S. Durant, J. M. Steele, Y. Xiong, C. Sun, X. Zhang, “Raman enhancement factor of a single tunable nanoplasmonic resonator,” J. Phys. Chem. B 110(9), 3964–3968 (2006).
[CrossRef] [PubMed]

Sun, C.

K.-H. Su, S. Durant, J. M. Steele, Y. Xiong, C. Sun, X. Zhang, “Raman enhancement factor of a single tunable nanoplasmonic resonator,” J. Phys. Chem. B 110(9), 3964–3968 (2006).
[CrossRef] [PubMed]

Turkiewicz, J. P.

M. T. Hill, Y. S. Oei, B. Smalbrugge, Y. Zhu, T. D. Vries, P. J. V. Veldhoven, F. W. M. V. Otten, T. J. Eijkemans, J. P. Turkiewicz, H. D. Waardt, E. J. Geluk, S. H. Kwon, Y. H. Lee, R. Notzel, M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1(10), 589–594 (2007).
[CrossRef]

Vahala, K. J.

T. J. Kippenberg, J. Kalkman, A. Polman, K. J. Vahala, “Demonstration of an erbium-doped microdisk laser on a silicon chip,” Phys. Rev. A 74(5), 051802 (2006).
[CrossRef]

Veldhoven, P. J. V.

M. T. Hill, Y. S. Oei, B. Smalbrugge, Y. Zhu, T. D. Vries, P. J. V. Veldhoven, F. W. M. V. Otten, T. J. Eijkemans, J. P. Turkiewicz, H. D. Waardt, E. J. Geluk, S. H. Kwon, Y. H. Lee, R. Notzel, M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1(10), 589–594 (2007).
[CrossRef]

Vollmer, F.

F. Vollmer, S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5(7), 591–596 (2008).
[CrossRef] [PubMed]

Vries, T. D.

M. T. Hill, Y. S. Oei, B. Smalbrugge, Y. Zhu, T. D. Vries, P. J. V. Veldhoven, F. W. M. V. Otten, T. J. Eijkemans, J. P. Turkiewicz, H. D. Waardt, E. J. Geluk, S. H. Kwon, Y. H. Lee, R. Notzel, M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1(10), 589–594 (2007).
[CrossRef]

Vuckovic, J.

B. Ellis, M. A. Mayer, G. Shambat, T. Sarmiento, J. Harris, E. E. Haller, J. Vuckovic, “Ultralow-threshold electrically pumped quantum-dot photonic-crystal nanocavity laser,” Nat. Photonics 3(1), 55–58 (2009).

Waardt, H. D.

M. T. Hill, Y. S. Oei, B. Smalbrugge, Y. Zhu, T. D. Vries, P. J. V. Veldhoven, F. W. M. V. Otten, T. J. Eijkemans, J. P. Turkiewicz, H. D. Waardt, E. J. Geluk, S. H. Kwon, Y. H. Lee, R. Notzel, M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1(10), 589–594 (2007).
[CrossRef]

Wei, Q. H.

K. H. Su, Q. H. Wei, X. Zhang, “Tunable and augmented plasmon resonances of Au/SiO2/Au nanodisks,” Appl. Phys. Lett. 88(6), 063118 (2006).
[CrossRef]

White, J. S.

W. Cai, J. S. White, M. L. Brongersma, “Compact, high-speed and power-efficient electrooptic plasmonic modulators,” Nano Lett. 9(12), 4403–4411 (2009).
[CrossRef] [PubMed]

Wong, C. W.

J. Gao, J. F. McMilan, M. C. Wu, J. Zheng, S. Assefa, C. W. Wong, “Demonstration of an air-slot mode-gap confined photonic crystal slab nanocavity with ultrasmall mode volumes,” Appl. Phys. Lett. 96(5), 051123 (2010).
[CrossRef]

Wu, M. C.

J. Gao, J. F. McMilan, M. C. Wu, J. Zheng, S. Assefa, C. W. Wong, “Demonstration of an air-slot mode-gap confined photonic crystal slab nanocavity with ultrasmall mode volumes,” Appl. Phys. Lett. 96(5), 051123 (2010).
[CrossRef]

K. Yu, A. Lakhani, M. C. Wu, “Subwavelength metal-optic semiconductor nanopatch lasers,” Opt. Express 18(9), 8790–8799 (2010).
[CrossRef] [PubMed]

Xiong, Y.

K.-H. Su, S. Durant, J. M. Steele, Y. Xiong, C. Sun, X. Zhang, “Raman enhancement factor of a single tunable nanoplasmonic resonator,” J. Phys. Chem. B 110(9), 3964–3968 (2006).
[CrossRef] [PubMed]

Yin, X.

R.-M. Ma, X. Yin, R. F. Oulton, V. J. Sorger, X. Zhang, “Multiplexed and electrically modulated plasmon laser circuit,” Nano Lett. 12(10), 5396–5402 (2012).
[CrossRef] [PubMed]

Yu, K.

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.

V. J. Sorger, N. D. L. Kimura, R. M. Ma, X. Zhang, “Ultra-compact silicon nanophotonic modulator with broadband response,” Nanophotonics 1(1), 17–22 (2012).
[CrossRef]

R.-M. Ma, X. Yin, R. F. Oulton, V. J. Sorger, X. Zhang, “Multiplexed and electrically modulated plasmon laser circuit,” Nano Lett. 12(10), 5396–5402 (2012).
[CrossRef] [PubMed]

R.-M. Ma, R. F. Oulton, V. J. Sorger, G. Bartal, X. Zhang, “Room-temperature sub-diffraction-limited plasmon laser by total internal reflection,” Nat. Mater. 10(2), 110–113 (2011).
[CrossRef] [PubMed]

D. A. Genov, R. F. Oulton, G. Bartal, X. Zhang, “Anomalous spectral scaling of light emission rates in low-dimensional metallic nanostructures,” Phys. Rev. B 83(24), 245312 (2011).
[CrossRef]

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]

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2(8), 496–500 (2008).
[CrossRef]

K. H. Su, Q. H. Wei, X. Zhang, “Tunable and augmented plasmon resonances of Au/SiO2/Au nanodisks,” Appl. Phys. Lett. 88(6), 063118 (2006).
[CrossRef]

K.-H. Su, S. Durant, J. M. Steele, Y. Xiong, C. Sun, X. Zhang, “Raman enhancement factor of a single tunable nanoplasmonic resonator,” J. Phys. Chem. B 110(9), 3964–3968 (2006).
[CrossRef] [PubMed]

Zheng, J.

J. Gao, J. F. McMilan, M. C. Wu, J. Zheng, S. Assefa, C. W. Wong, “Demonstration of an air-slot mode-gap confined photonic crystal slab nanocavity with ultrasmall mode volumes,” Appl. Phys. Lett. 96(5), 051123 (2010).
[CrossRef]

Zhu, Y.

M. T. Hill, Y. S. Oei, B. Smalbrugge, Y. Zhu, T. D. Vries, P. J. V. Veldhoven, F. W. M. V. Otten, T. J. Eijkemans, J. P. Turkiewicz, H. D. Waardt, E. J. Geluk, S. H. Kwon, Y. H. Lee, R. Notzel, M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1(10), 589–594 (2007).
[CrossRef]

Appl. Phys. Lett. (3)

J. Gao, J. F. McMilan, M. C. Wu, J. Zheng, S. Assefa, C. W. Wong, “Demonstration of an air-slot mode-gap confined photonic crystal slab nanocavity with ultrasmall mode volumes,” Appl. Phys. Lett. 96(5), 051123 (2010).
[CrossRef]

K. Nozaki, T. Baba, “Laser characteristics with ultimate-small mode volume in photonic crystal slab point-shift nanolasers,” Appl. Phys. Lett. 88(21), 211101 (2006).
[CrossRef]

K. H. Su, Q. H. Wei, X. Zhang, “Tunable and augmented plasmon resonances of Au/SiO2/Au nanodisks,” Appl. Phys. Lett. 88(6), 063118 (2006).
[CrossRef]

J. Phys. Chem. B (1)

K.-H. Su, S. Durant, J. M. Steele, Y. Xiong, C. Sun, X. Zhang, “Raman enhancement factor of a single tunable nanoplasmonic resonator,” J. Phys. Chem. B 110(9), 3964–3968 (2006).
[CrossRef] [PubMed]

Nano Lett. (4)

R.-M. Ma, X. Yin, R. F. Oulton, V. J. Sorger, X. Zhang, “Multiplexed and electrically modulated plasmon laser circuit,” Nano Lett. 12(10), 5396–5402 (2012).
[CrossRef] [PubMed]

M. Kuttge, F. J. García de Abajo, A. Polman, “Ultrasmall mode volume plasmonic nanodisk resonators,” Nano Lett. 10(5), 1537–1541 (2010).
[CrossRef] [PubMed]

W. Cai, J. S. White, M. L. Brongersma, “Compact, high-speed and power-efficient electrooptic plasmonic modulators,” Nano Lett. 9(12), 4403–4411 (2009).
[CrossRef] [PubMed]

M. K. Seo, S. H. Kwon, H. S. Ee, H. G. Park, “Full three-dimensional subwavelength high-Q surface-plasmon-polariton cavity,” Nano Lett. 9(12), 4078–4082 (2009).
[CrossRef] [PubMed]

Nanophotonics (1)

V. J. Sorger, N. D. L. Kimura, R. M. Ma, X. Zhang, “Ultra-compact silicon nanophotonic modulator with broadband response,” Nanophotonics 1(1), 17–22 (2012).
[CrossRef]

Nat. Mater. (1)

R.-M. Ma, R. F. Oulton, V. J. Sorger, G. Bartal, X. Zhang, “Room-temperature sub-diffraction-limited plasmon laser by total internal reflection,” Nat. Mater. 10(2), 110–113 (2011).
[CrossRef] [PubMed]

Nat. Methods (1)

F. Vollmer, S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5(7), 591–596 (2008).
[CrossRef] [PubMed]

Nat. Photonics (4)

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]

R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2(8), 496–500 (2008).
[CrossRef]

B. Ellis, M. A. Mayer, G. Shambat, T. Sarmiento, J. Harris, E. E. Haller, J. Vuckovic, “Ultralow-threshold electrically pumped quantum-dot photonic-crystal nanocavity laser,” Nat. Photonics 3(1), 55–58 (2009).

M. T. Hill, Y. S. Oei, B. Smalbrugge, Y. Zhu, T. D. Vries, P. J. V. Veldhoven, F. W. M. V. Otten, T. J. Eijkemans, J. P. Turkiewicz, H. D. Waardt, E. J. Geluk, S. H. Kwon, Y. H. Lee, R. Notzel, M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1(10), 589–594 (2007).
[CrossRef]

Nature (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]

Opt. Express (3)

Opt. Lett. (3)

Phys. Rev. (1)

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

Phys. Rev. A (1)

T. J. Kippenberg, J. Kalkman, A. Polman, K. J. Vahala, “Demonstration of an erbium-doped microdisk laser on a silicon chip,” Phys. Rev. A 74(5), 051802 (2006).
[CrossRef]

Phys. Rev. B (4)

D. A. Genov, R. F. Oulton, G. Bartal, X. Zhang, “Anomalous spectral scaling of light emission rates in low-dimensional metallic nanostructures,” Phys. Rev. B 83(24), 245312 (2011).
[CrossRef]

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

W. Porod, D. K. Ferry, “Modification of the virtual-crystal approximation for ternary III-V compounds,” Phys. Rev. B 27(4), 2587–2589 (1983).
[CrossRef]

J.-K. Hwang, H.-Y. Ryu, Y.-H. Lee, “Spontaneous emission rate of an electric dipole in a general microcavity,” Phys. Rev. B 60(7), 4688–4695 (1999).
[CrossRef]

Other (1)

A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 1995).

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Figures (7)

Fig. 1
Fig. 1

Schematics of the nanodisk-based plasmonic resonators. (a) Nanopatch resonator. Most of energy is confined in the InGaAs region. (b) Metal substrate HPR. (c) Dielectric substrate HPR. Most of energy is confined in the thin SiO2 layer in (b) and (c).

Fig. 2
Fig. 2

Normalized Ez profiles of the (a) InP- and (b) Air-based HPWs. The insets show the schematics of each 1D waveguide. The geometrical parameters are given by tM = 200 nm, tLow = 5 nm, and tHigh = 300 nm, and InP and Air are considered to be semi-infinite.

Fig. 3
Fig. 3

Properties of the 1D InP- and Air-based HPWs. (a) Normalized mode size, (b) propagation length, and (c) FOM as a function of tLow. (d) Normalized mode size, (e) propagation length, and (f) FOM as a function of tHigh. InP and Air indicate the InP- and Air-based HPWs, respectively, and the same color indicates the same geometrical parameter.

Fig. 4
Fig. 4

Calculated spectra for (a) the dielectric and (b) the metal substrate HPRs of tLow = 2 nm, tHigh = 300 nm, R = 400 nm, and tM = 200 nm. The insets show schematics of the resonators and resonant mode profiles (Ez component) in the horizontal and the vertical directions. The azimuthal number of each resonant mode is indicated.

Fig. 5
Fig. 5

Geometrical parameter dependence of the resonant mode properties of the HPRs. (a) Quality factor (Q, black curve) and mode volume (Vm, green curve), and (b) Q/Vm as a function of tLow. (c) Q and Vm, and (d) Q/Vm as a function of tHigh. tM is fixed to 200 nm for all cases. Only the resonant mode of N = 7 is considered. The solid and the dashed lines represent the properties of the dielectric and the metal substrate HPRs, respectively.

Fig. 6
Fig. 6

Comparison of the three nanodisk-based plasmonic resonators. tHigh and tLow in the HPRs are fixed to 300 nm and 5 nm, respectively. tHigh in the nanopatch resonator is fixed to 120 nm, in which the mode volume of the nanopatch resonator is similar to that of the dielectric substrate HPR. tM is fixed to 200 nm for all cases. For the HPRs, the modes of resonant wavelengths closest to 950 nm are chosen for each R.

Fig. 7
Fig. 7

Purcell enhancement factor (Fp) as a function of wavelength for the dielectric and metal substrate HPRs of R = 250 nm.

Equations (4)

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

ε A g = ε ω p 2 ω ( ω + i γ ) ,
A m = W ( ω , z ) d z max [ W ( ω , z ) ] ,
W ( ω , z ) = 1 2 [ d ( ω ε R ) d ω ε o | E ( ω , z ) | 2 + μ o | H ( ω , z ) | 2 ] ,
V m = W ( x , y , z ) d x d y d z max [ W ( x , y , z ) ] ,

Metrics