Abstract

We theoretically analyze plasmonic gap-mode nanocavities covered by a thick cladding layer at telecommunication wavelengths. In the presence of high-index cladding materials such as semiconductors, the first-order hybrid gap mode becomes more promising for lasing than the fundamental one. Still, the significant mirror loss remains the main challenge to lasing. Using silver coatings within a decent thickness range at two end facets, we show that the reflectivity is substantially enhanced above 95 %. At a coating thickness of 50 nm and cavity length of 1.51 μm, the quality factor is about 150, and the threshold gain is lower than 1500 cm−1.

© 2013 Optical Society of America

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  1. J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nature Mater. 9, 193–204 (2010).
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  7. M. T. Hill, Y. S. Oei, B. Smalbrugge, Y. Zhu, T. de Vries, P. J. van Veldhoven, F. W. M. van Otten, T. J. Eijkemans, J. P. Turkiewicz, H. de Waardt, E. J. Geluk, S. H. Kwon, Y. H. Lee, R. Nötzel, and M. K. Smit, “Lasing in metallic-coated nanocavities,” Nat. Photonics 1, 589–594 (2007).
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    [Crossref] [PubMed]
  9. M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
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  10. R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461, 629–632 (2009).
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  11. C. Y. Lu, S. W. Chang, S. L. Chuang, T. D. Germann, and D. Bimberg, “Metal-cavity surface-emitting microlaser at room temperature,” Appl. Phys. Lett. 96, 251101 (2010).
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    [Crossref]
  22. P. J. Cheng, C. Y. Weng, S. W. Chang, T. R. Lin, and C. H. Tien, “Cladding effect on hybrid plasmonic nanowire cavity at telecommunication wavelengths,” IEEE J. Sel. Top. Quantum Electron. 19, 4800306 (2013).
    [Crossref]
  23. J. Grandidier, G. C. des Francs, S. Massenot, A. Bouhelier, L. Markey, J.-C. Weeber, C. Finot, and A. Dereux, “Gain-assisted propagation in a plasmonic waveguide at telecom wavelength,” Nano Lett. 9, 2935–2939 (2009).
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  24. D. Dai, Y. Shi, S. He, L. Wosinski, and L. Thylen, “Gain enhancement in a hybrid plasmonic nano-waveguide with a low-index or high-index gain medium,” Opt. Express 19, 12925–12936 (2011).
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  27. D. P. Arnold, F. Cros, I. Zana, D. R. Veazie, and M. G. Allen, “Electroplated metal microstructures embedded in fusion-bonded silicon: conductors and magnetic materials,” J. Microelectromech. Syst. 13, 791–798 (2004).
    [Crossref]
  28. S. W. Chang, T. R. Lin, and S. L. Chuang, “Theory of plasmonic Fabry-Perot nanolasers,” Opt. Express 18, 15039–15053 (2010).
    [Crossref] [PubMed]
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  33. T. R. Lin, S. W. Chang, S. L. Chuang, Z. Zhang, and P. J. Schuck, “Coating effect on optical resonance of plasmonic nanobowtie antenna,” Appl. Phys. Lett. 97, 063106 (2010).
    [Crossref]
  34. T. D. Visser, H. Blok, B. Demeulenaere, and D. Lenstra, “Confinement factors and gain in optical amplifiers,” IEEE J. Quantum Electron. 33, 1763–1766 (1997).
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  39. A. Mock, “First principles derivation of microcavity semiconductor laser threshold condition and its application to FDTD active cavity modeling,” J. Opt. Soc. Am. B 27, 2262–2272 (2010).
    [Crossref]

2013 (2)

R. M. Ma, R. F. Oulton, V. J. Sorger, and X. Zhang, “Plasmon lasers: coherent light source at molecular scales,” Laser & Photon. Rev. 7, 1–21 (2013).

P. J. Cheng, C. Y. Weng, S. W. Chang, T. R. Lin, and C. H. Tien, “Cladding effect on hybrid plasmonic nanowire cavity at telecommunication wavelengths,” IEEE J. Sel. Top. Quantum Electron. 19, 4800306 (2013).
[Crossref]

2012 (2)

S. Zhang and H. Xu, “Optimizing substrate-mediated plasmon coupling toward high-performance plasmonic nanowire waveguides,” ACS Nano 6, 8128–8135 (2012).
[Crossref] [PubMed]

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

2011 (8)

C. Y. Lu, S. W. Chang, S. L. Chuang, T. D. Germann, U. W. Pohl, and D. Bimberg, “Low thermal impedance of substrate-free metal cavity surface-emitting microlasers,” IEEE Photon. Technol. Lett. 23, 1031–1033 (2011).
[Crossref]

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

C. Y. Wu, C. T. Kuo, C. Y. Wang, C. L. He, M. H. Lin, H. Ahn, and S. Gwo, “Plasmonic green nanolaser based on a metal-oxide-semiconductor structure,” Nano Lett. 11, 4256–4260 (2011).
[Crossref] [PubMed]

R. A. Flynn, C. S. Kim, I. Vurgaftman, M. Kim, J. R. Meyer, A. J. Mak̈inen, K. Bussmann, L. Cheng, F. S. Choa, and J. P. Long, “A room-temperature semiconductor spaser operating near 1.5 μm,” Opt. Express 19, 8954–8961 (2011).
[Crossref] [PubMed]

D. Dai, Y. Shi, S. He, L. Wosinski, and L. Thylen, “Gain enhancement in a hybrid plasmonic nano-waveguide with a low-index or high-index gain medium,” Opt. Express 19, 12925–12936 (2011).
[Crossref] [PubMed]

C. Y. Lu and S. L. Chuang, “A surface-emitting 3D metal-nanocavity laser: proposal and theory,” Opt. Express 19, 13225–13244 (2011).
[Crossref] [PubMed]

M. J. H. Marell, B. Smalbrugge, E. J. Geluk, P. J. van Veldhoven, B. Barcones, B. Koopmans, R. Nötzel, M. K. Smit, and M. T. Hill, “Plasmonic distributed feedback lasers at telecommunications wavelengths,” Opt. Express 19, 15109–15118 (2011).
[Crossref] [PubMed]

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

2010 (9)

S. W. Chang, T. R. Lin, and S. L. Chuang, “Theory of plasmonic Fabry-Perot nanolasers,” Opt. Express 18, 15039–15053 (2010).
[Crossref] [PubMed]

A. Mock, “First principles derivation of microcavity semiconductor laser threshold condition and its application to FDTD active cavity modeling,” J. Opt. Soc. Am. B 27, 2262–2272 (2010).
[Crossref]

T. R. Lin, S. W. Chang, S. L. Chuang, Z. Zhang, and P. J. Schuck, “Coating effect on optical resonance of plasmonic nanobowtie antenna,” Appl. Phys. Lett. 97, 063106 (2010).
[Crossref]

S. M. George, “Atomic layer deposition: an overview,” Chem. Rev. 110, 111–131 (2010).
[Crossref]

C. Y. Lu, S. W. Chang, S. L. Chuang, T. D. Germann, and D. Bimberg, “Metal-cavity surface-emitting microlaser at room temperature,” Appl. Phys. Lett. 96, 251101 (2010).
[Crossref]

S. H. Kwon, J. H. Kang, C. Seassal, S. K. Kim, P. Regreny, Y. H. Lee, C. M. Lieber, and H. G. Park, “Subwavelength plasmonic lasing from a semiconductor nanodisk with silver nanopan cavity,” Nano Lett. 10, 3679–3683 (2010).
[Crossref] [PubMed]

K. J. Russell and E. L. Hu, “Gap-mode plasmonic nanocavity,” Appl. Phys. Lett. 97, 163115 (2010).
[Crossref]

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nature Mater. 9, 193–204 (2010).
[Crossref]

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

2009 (5)

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
[Crossref] [PubMed]

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

J. Grandidier, G. C. des Francs, S. Massenot, A. Bouhelier, L. Markey, J.-C. Weeber, C. Finot, and A. Dereux, “Gain-assisted propagation in a plasmonic waveguide at telecom wavelength,” Nano Lett. 9, 2935–2939 (2009).
[Crossref] [PubMed]

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

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

2008 (3)

C. Manolatou and F. Rana, “Subwavelength nanopatch cavities for semiconductor plasmon lasers,” IEEE J. Quantum Electron. 44, 435–447 (2008).
[Crossref]

R. G. Beausoleil, P. J. Kuekes, G. S. Snider, S. Y. Wang, and R. S. Williams, “Nanoelectronic and nanophotonic interconnect,” Proc. IEEE 96, 230–247 (2008).
[Crossref]

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

2007 (2)

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

Y. Nakayama, P. J. Pauzauskie, A. Radenovic, R. M. Onorato, R. J. Saykally, J. Liphardt, and P. Yang, “Tunable nanowire nonlinear optical probe,” Nature 447, 1098–1101 (2007).
[Crossref] [PubMed]

2004 (2)

A. V. Maslov and C. Z. Ning, “Modal gain in a semiconductor nanowire laser with anisotropic bandstructure,” IEEE. J. Quantum Electron. 40, 1389–1397 (2004).
[Crossref]

D. P. Arnold, F. Cros, I. Zana, D. R. Veazie, and M. G. Allen, “Electroplated metal microstructures embedded in fusion-bonded silicon: conductors and magnetic materials,” J. Microelectromech. Syst. 13, 791–798 (2004).
[Crossref]

2003 (1)

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

1997 (1)

T. D. Visser, H. Blok, B. Demeulenaere, and D. Lenstra, “Confinement factors and gain in optical amplifiers,” IEEE J. Quantum Electron. 33, 1763–1766 (1997).
[Crossref]

1992 (1)

M. Ozeki, “Atomic layer epitaxy of III–V compounds using metalorganic and hydride sources,” Mater. Sci. Rep. 8, 97–146 (1992).
[Crossref]

1972 (1)

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

Ahn, H.

C. Y. Wu, C. T. Kuo, C. Y. Wang, C. L. He, M. H. Lin, H. Ahn, and S. Gwo, “Plasmonic green nanolaser based on a metal-oxide-semiconductor structure,” Nano Lett. 11, 4256–4260 (2011).
[Crossref] [PubMed]

Allen, M. G.

D. P. Arnold, F. Cros, I. Zana, D. R. Veazie, and M. G. Allen, “Electroplated metal microstructures embedded in fusion-bonded silicon: conductors and magnetic materials,” J. Microelectromech. Syst. 13, 791–798 (2004).
[Crossref]

Arnold, D. P.

D. P. Arnold, F. Cros, I. Zana, D. R. Veazie, and M. G. Allen, “Electroplated metal microstructures embedded in fusion-bonded silicon: conductors and magnetic materials,” J. Microelectromech. Syst. 13, 791–798 (2004).
[Crossref]

Bakker, R.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
[Crossref] [PubMed]

Barcones, B.

Barnard, E. S.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nature Mater. 9, 193–204 (2010).
[Crossref]

Bartal, G.

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

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

Beausoleil, R. G.

R. G. Beausoleil, P. J. Kuekes, G. S. Snider, S. Y. Wang, and R. S. Williams, “Nanoelectronic and nanophotonic interconnect,” Proc. IEEE 96, 230–247 (2008).
[Crossref]

Belgrave, A. M.

M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
[Crossref] [PubMed]

Bimberg, D.

C. Y. Lu, S. W. Chang, S. L. Chuang, T. D. Germann, U. W. Pohl, and D. Bimberg, “Low thermal impedance of substrate-free metal cavity surface-emitting microlasers,” IEEE Photon. Technol. Lett. 23, 1031–1033 (2011).
[Crossref]

C. Y. Lu, S. W. Chang, S. L. Chuang, T. D. Germann, and D. Bimberg, “Metal-cavity surface-emitting microlaser at room temperature,” Appl. Phys. Lett. 96, 251101 (2010).
[Crossref]

Blok, H.

T. D. Visser, H. Blok, B. Demeulenaere, and D. Lenstra, “Confinement factors and gain in optical amplifiers,” IEEE J. Quantum Electron. 33, 1763–1766 (1997).
[Crossref]

Bouhelier, A.

J. Grandidier, G. C. des Francs, S. Massenot, A. Bouhelier, L. Markey, J.-C. Weeber, C. Finot, and A. Dereux, “Gain-assisted propagation in a plasmonic waveguide at telecom wavelength,” Nano Lett. 9, 2935–2939 (2009).
[Crossref] [PubMed]

Brongersma, M. L.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nature Mater. 9, 193–204 (2010).
[Crossref]

Bussmann, K.

Cai, W.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nature Mater. 9, 193–204 (2010).
[Crossref]

Chang, S. W.

P. J. Cheng, C. Y. Weng, S. W. Chang, T. R. Lin, and C. H. Tien, “Cladding effect on hybrid plasmonic nanowire cavity at telecommunication wavelengths,” IEEE J. Sel. Top. Quantum Electron. 19, 4800306 (2013).
[Crossref]

C. Y. Lu, S. W. Chang, S. L. Chuang, T. D. Germann, U. W. Pohl, and D. Bimberg, “Low thermal impedance of substrate-free metal cavity surface-emitting microlasers,” IEEE Photon. Technol. Lett. 23, 1031–1033 (2011).
[Crossref]

T. R. Lin, S. W. Chang, S. L. Chuang, Z. Zhang, and P. J. Schuck, “Coating effect on optical resonance of plasmonic nanobowtie antenna,” Appl. Phys. Lett. 97, 063106 (2010).
[Crossref]

C. Y. Lu, S. W. Chang, S. L. Chuang, T. D. Germann, and D. Bimberg, “Metal-cavity surface-emitting microlaser at room temperature,” Appl. Phys. Lett. 96, 251101 (2010).
[Crossref]

S. W. Chang, T. R. Lin, and S. L. Chuang, “Theory of plasmonic Fabry-Perot nanolasers,” Opt. Express 18, 15039–15053 (2010).
[Crossref] [PubMed]

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

Cheng, L.

Cheng, P. J.

P. J. Cheng, C. Y. Weng, S. W. Chang, T. R. Lin, and C. H. Tien, “Cladding effect on hybrid plasmonic nanowire cavity at telecommunication wavelengths,” IEEE J. Sel. Top. Quantum Electron. 19, 4800306 (2013).
[Crossref]

Choa, F. S.

Christy, R. W.

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

Chuang, S. L.

C. Y. Lu, S. W. Chang, S. L. Chuang, T. D. Germann, U. W. Pohl, and D. Bimberg, “Low thermal impedance of substrate-free metal cavity surface-emitting microlasers,” IEEE Photon. Technol. Lett. 23, 1031–1033 (2011).
[Crossref]

C. Y. Lu and S. L. Chuang, “A surface-emitting 3D metal-nanocavity laser: proposal and theory,” Opt. Express 19, 13225–13244 (2011).
[Crossref] [PubMed]

S. W. Chang, T. R. Lin, and S. L. Chuang, “Theory of plasmonic Fabry-Perot nanolasers,” Opt. Express 18, 15039–15053 (2010).
[Crossref] [PubMed]

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S. H. Kwon, J. H. Kang, C. Seassal, S. K. Kim, P. Regreny, Y. H. Lee, C. M. Lieber, and H. G. Park, “Subwavelength plasmonic lasing from a semiconductor nanodisk with silver nanopan cavity,” Nano Lett. 10, 3679–3683 (2010).
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R. M. Ma, R. F. Oulton, V. J. Sorger, and X. Zhang, “Plasmon lasers: coherent light source at molecular scales,” Laser & Photon. Rev. 7, 1–21 (2013).

R. M. Ma, R. F. Oulton, V. J. Sorger, G. Bartal, and X. Zhang, “Room-temperature sub-diffraction-limited plasmon laser by total internal reflection,” Nature Mater. 10, 110–113 (2011).
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Marell, M. J. H.

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R. M. Ma, R. F. Oulton, V. J. Sorger, and X. Zhang, “Plasmon lasers: coherent light source at molecular scales,” Laser & Photon. Rev. 7, 1–21 (2013).

R. M. Ma, R. F. Oulton, V. J. Sorger, G. Bartal, and X. Zhang, “Room-temperature sub-diffraction-limited plasmon laser by total internal reflection,” Nature Mater. 10, 110–113 (2011).
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R. F. Oulton, V. J. Sorger, T. Zentgraf, R. M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461, 629–632 (2009).
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R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for sub-wavelength confinement and long-range propagation,” Nat. Photonics 2, 496–500 (2008).
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R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for sub-wavelength confinement and long-range propagation,” Nat. Photonics 2, 496–500 (2008).
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C. Y. Lu, S. W. Chang, S. L. Chuang, T. D. Germann, U. W. Pohl, and D. Bimberg, “Low thermal impedance of substrate-free metal cavity surface-emitting microlasers,” IEEE Photon. Technol. Lett. 23, 1031–1033 (2011).
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M. Lončar, A. Scherer, and Y. Qiu, “Photonic crystal laser sources for chemical detection,” Appl. Phys. Lett. 82, 4648–4650 (2003).
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Y. Nakayama, P. J. Pauzauskie, A. Radenovic, R. M. Onorato, R. J. Saykally, J. Liphardt, and P. Yang, “Tunable nanowire nonlinear optical probe,” Nature 447, 1098–1101 (2007).
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C. Manolatou and F. Rana, “Subwavelength nanopatch cavities for semiconductor plasmon lasers,” IEEE J. Quantum Electron. 44, 435–447 (2008).
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S. H. Kwon, J. H. Kang, C. Seassal, S. K. Kim, P. Regreny, Y. H. Lee, C. M. Lieber, and H. G. Park, “Subwavelength plasmonic lasing from a semiconductor nanodisk with silver nanopan cavity,” Nano Lett. 10, 3679–3683 (2010).
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K. J. Russell, T. L. Liu, S. Cui, and E. L. Hu, “Large spontaneous emission enhancement in plasmonic nanocavities,” Nat. Photonics 6, 459–462 (2012).
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K. J. Russell and E. L. Hu, “Gap-mode plasmonic nanocavity,” Appl. Phys. Lett. 97, 163115 (2010).
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Y. Nakayama, P. J. Pauzauskie, A. Radenovic, R. M. Onorato, R. J. Saykally, J. Liphardt, and P. Yang, “Tunable nanowire nonlinear optical probe,” Nature 447, 1098–1101 (2007).
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M. Lončar, A. Scherer, and Y. Qiu, “Photonic crystal laser sources for chemical detection,” Appl. Phys. Lett. 82, 4648–4650 (2003).
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T. R. Lin, S. W. Chang, S. L. Chuang, Z. Zhang, and P. J. Schuck, “Coating effect on optical resonance of plasmonic nanobowtie antenna,” Appl. Phys. Lett. 97, 063106 (2010).
[Crossref]

Schuller, J. A.

J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nature Mater. 9, 193–204 (2010).
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S. H. Kwon, J. H. Kang, C. Seassal, S. K. Kim, P. Regreny, Y. H. Lee, C. M. Lieber, and H. G. Park, “Subwavelength plasmonic lasing from a semiconductor nanodisk with silver nanopan cavity,” Nano Lett. 10, 3679–3683 (2010).
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M. A. Noginov, G. Zhu, A. M. Belgrave, R. Bakker, V. M. Shalaev, E. E. Narimanov, S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature 460, 1110–1112 (2009).
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Smalbrugge, B.

Smit, M. K.

Snider, G. S.

R. G. Beausoleil, P. J. Kuekes, G. S. Snider, S. Y. Wang, and R. S. Williams, “Nanoelectronic and nanophotonic interconnect,” Proc. IEEE 96, 230–247 (2008).
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Sorger, V. J.

R. M. Ma, R. F. Oulton, V. J. Sorger, and X. Zhang, “Plasmon lasers: coherent light source at molecular scales,” Laser & Photon. Rev. 7, 1–21 (2013).

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

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[Crossref] [PubMed]

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Nature (3)

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Nature Mater. (2)

R. M. Ma, R. F. Oulton, V. J. Sorger, G. Bartal, and X. Zhang, “Room-temperature sub-diffraction-limited plasmon laser by total internal reflection,” Nature Mater. 10, 110–113 (2011).
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R. G. Beausoleil, P. J. Kuekes, G. S. Snider, S. Y. Wang, and R. S. Williams, “Nanoelectronic and nanophotonic interconnect,” Proc. IEEE 96, 230–247 (2008).
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Rev. (1)

R. M. Ma, R. F. Oulton, V. J. Sorger, and X. Zhang, “Plasmon lasers: coherent light source at molecular scales,” Laser & Photon. Rev. 7, 1–21 (2013).

Other (2)

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Figures (7)

Fig. 1
Fig. 1

(a) A metallic nanowire is separated from the Ag substrate by the active layer. The structure is embedded in a cladding layer. (b) The side view of the plasmonic gap-mode nanocavity. In practical calculations, the extended regions are surrounded by PMLs.

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Fig. 2
Fig. 2

Square magnitudes |E(ρ)|2 of the cross-sectional profiles for the fundamental mode at (a) nc = 2.5 (inset: nc = 1) and (b) nc = 3.5, and for the first-order mode at (c) nc = 2.5 and (d) nc = 3.5. The height h and radius r are 10 and 70 nm, respectively. At nc = 3.5, the first-order mode is better confined in the active region than the fundamental one is.

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Fig. 3
Fig. 3

(a) The waveguide confinement factor Γwg and (b) modal loss αi of the fundamental and first-order hybrid gap modes versus nc at different h = 5, 10, and 15 nm and a fixed r = 70 nm. (c) and (d) are the counterparts of (a) and (b) at a fixed h = 10 nm and different r = 70, 100, and 130 nm. Symbols “F” and “1st” indicate fundamental and first-order modes, respectively.

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Fig. 4
Fig. 4

Transparency gains gtr of the fundamental and first-order hybrid gap modes at (a) different h = 5, 10, and 15 nm and a fixed r = 70 nm, and (b) different r = 70, 100, and 130 nm and a fixed h = 10 nm. Symbols “F” and “1st” indicate fundamental and first-order modes, respectively.

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Fig. 5
Fig. 5

The reflectivity R of the first-order mode as a function of the Ag thickness t at h = 10 nm, r = 70 nm, and nc = 3.5. Without the mirror, the reflectivity is about 50 %. As t > 25 nm, the reflectivity can exceed 90 %. The inset is the standing-wave pattern |f(z)| (circle marks) and its fitting (solid line) at t = 50 nm (R = 95.7 %).

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Fig. 6
Fig. 6

The resonance lineshape calculated from 3D FEM for the mode at L = 1547 nm and t = 0 nm. The corresponding Q factor is about 26.43.

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Fig. 7
Fig. 7

(a) The side view (y–z plane), (b) front view (x–y plane), and (c) top (oblique) view (x–z plane) of the mode profile corresponding to the case of L = 1511 nm in Table 1. The field pattern is excited by a plane wave normally incident onto the Ag mirror from the free space outside the nanocavity.

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Tables (1)

Tables Icon

Table 1 The reflectivities, quality factors, and threshold gains of cavity modes corresponding to mirror thicknesses t = 0 (L = 660 and 1547 nm) and 50 nm (L = 625 and 1511 nm) at the wavelength of 1.55 μm. The cavity parameters are set as follows: h = 10 nm, r = 70 nm, and nc = 3.5.

View Table

Equations (10)

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Γ wg = n a 2 η 0 ∫ A a d ρ | E ( ρ ) | 2 ∫ A d ρ 1 2 Re [ E ( ρ ) × H * ( ρ ) ] ⋅ z ^ ,
∫ A d ρ [ E l ′ ( ρ ) × H l ( ρ ) ] ⋅ z ^ = ∫ A d ρ [ E ˜ l ′ ( ρ ) × H l ( ρ ) ] ⋅ z ^ = δ l ′ l Λ l ,
E inc ( r ) = F l E l ( ρ ) e i k z , l z ,
E r ( r ) = ∑ l ′ B l ′ E ˜ l ′ ( ρ ) e − i k z , l ′ z .
∫ A d ρ [ E tot ( r ) × H l ( ρ ) ] ⋅ z ^ ≡ f ( z ) = Λ l ( F l e i k z , l z + B l e − i k z , l z ) = C ( e i k z , l z + r m e − i k z , l z ) ,
| f ( z ) | = | C | e − 2 Im [ k z , l ] z + | r m | 2 e 2 Im [ k z , l ] z + 2 | r m | cos ( 2 Re [ k z , l ] z − θ r ) ,
1 Q FP = 1 Q abs + 1 Q mir ,
1 Q abs = v g , z α i ω r ,                       1 Q mir = v g , z α mir ω r ,                 α mir = 1 L ln ( 1 R ) ,
g th , FP = α i + α mir Γ wg ,
2 Re [ k z ] L + 2 θ r = 2 m π ,                 m ∈ ℕ ,

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