Abstract

We study the quality factor variation of three-dimensional Metal-Insulator-Metal nanoresonators when their volume is shrunk from the diffraction limit (λ/2n)3 down to a deep subwavelength scale (λ/50)3. In addition to rigorous fully-vectorial calculations, we provide a semi-analytical expression of the quality factor Q obtained with a Fabry-Perot model. The latter quantitatively predicts the absorption and radiation losses of the nanoresonator and provides an in-depth understanding of the mode lifetime that cannot be obtained with brute-force computations. In particular, it highlights the impact of slow-wave effects on the Q-factor as the size of the resonator is decreased. The Fabry-Perot model also evidences that, unexpectedly, wave retardation effects are present in metallic nanoparticles, even for deep subwavelength dimensions in the quasi-static regime.

© 2012 OSA

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    [CrossRef]
  42. Because of symmetry reasons, anti-symmetric higher-order modes do not impact the reflectivity of the symmetric fundamental mode.
  43. Unusual Fabry-Perot resonances with m = 0 may exist in subwavelength metallic structures, see E. Feigenbaum and M. Orenstein, “Ultrasmall volume plasmons, yet with complete retardation effects”, Phys. Rev. Lett.101, 163902 (2008). For this situation to occur, the positive propagation phase has to be fully compensated by a negative reflection phase. Such a resonance does not exist in the MIM resonators under study since ϕr ≈ 0.
    [CrossRef] [PubMed]
  44. The assumption Lp ≪ L is valid, since for large waveguide cross-sections (w = 100 nm and td = 100 nm) Lp ≈ 5 nm ≪ L ≈ 100 nm and for small cross-sections (w = 40 nm and td < 25 nm) Lp < 1 nm ≪ L ≈ 30 nm.
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  46. S. B. Hasan, R. Filter, A. Ahmed, R. Vogelgesang, R. Gordon, C. Rockstuhl, and F. Lederer, “Relating localized nanoparticle resonances to an associated antenna problem,” Phys. Rev. B84, 195405 (2011).
    [CrossRef]
  47. G. Della Valle, T. Søndergaard, and S. I. Bozhevolnyi, “High-Q plasmonic resonators based on metal split nanocylinders,” Phys. Rev. B80, 235405 (2009).
    [CrossRef]

2011 (10)

N. Liu, M. L. Tang, M. Hentschel, H. Giessen, and A. P. Alivisatos, “Nanoantenna-enhanced gas sensing in a single tailored nanofocus,” Nature Mater.10, 631–636 (2011).
[CrossRef]

A. Cattoni, P. Ghenuche, A. M. Haghiri-Gosnet, D. Decanini, J. Chen, J.-L. Pelouard, and S. Collin, “λ3/1000 plasmonic nanocavities for biosensing fabricated by soft uv nanoimprint lithography,” Nano Lett.11, 3557–3563 (2011).
[CrossRef] [PubMed]

J. T. Choy, B. J. M. Hausmann, T. M. Babinec, I. Bulu, M. Khan, P. Maletinsky, A. Yacoby, and M. Loncar, “Enhanced single-photon emission from a diamond-silver aperture,” Nat. Photonics5, 738–743 (2011).
[CrossRef]

C. M. Soukoulis and M. Wegener, “Past achievements and future challenges in the development of three-dimensional photonic metamaterials,” Nat. Photonics5, 523–530 (2011).

J. Yang, C. Sauvan, H. T. Liu, and P. Lalanne, “Theory of fishnet negative-index optical metamaterials,” Phys. Rev. Lett.107, 043903 (2011).
[CrossRef] [PubMed]

C. Wu, B. Neuner, G. Shvets, J. John, A. Milder, B. Zollars, and S. Savoy, “Large-area wide-angle spectrally selective plasmonic absorber,” Phys. Rev. B84, 075102 (2011).
[CrossRef]

C. Koechlin, P. Bouchon, F. Pardo, J. Jaeck, X. Lafosse, J.-L. Pelouard, and R. Haidar, “Total routing and absorption of photons in dual color plasmonic antennas,” Appl. Phys. Lett.99, 241104 (2011).
[CrossRef]

C. Rockstuhl, C. Menzel, S. Mühlig, J. Petschulat, C. Helgert, C. Etrich, A. Chipouline, T. Pertsch, and F. Lederer, “Scattering properties of meta-atoms,” Phys. Rev. B83, 245119 (2011).
[CrossRef]

T. H. Taminiau, F. D. Stefani, and N. F. van Hulst, “Optical nanorod antennas modeled as cavities for dipolar emitters: evolution of sub- and super-radiant modes,” Nano Lett.11, 1020–1024 (2011).
[CrossRef] [PubMed]

S. B. Hasan, R. Filter, A. Ahmed, R. Vogelgesang, R. Gordon, C. Rockstuhl, and F. Lederer, “Relating localized nanoparticle resonances to an associated antenna problem,” Phys. Rev. B84, 195405 (2011).
[CrossRef]

2010 (5)

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett.10, 2342–2348 (2010).
[CrossRef] [PubMed]

J. Hao, J. Wang, X. Liu, W. J. Padilla, L. Zhou, and M. Qiu, “High performance optical absorber based on a plasmonic metamaterial,” Appl. Phys. Lett.96, 251104 (2010).
[CrossRef]

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

M. P. Nezhad, A. Simic, O. Bondarenko, B. Slutsky, A. Mizrahi, L. Feng, V. Lomakin, and Y. Fainman, “Room-temperature subwavelength metallo-dielectric lasers,” Nat. Photonics4, 395–399 (2010).
[CrossRef]

H. A. Atwater and A. Polman, “Plasmonic for improved photovoltaic devices,” Nature Mater.9, 205–213 (2010).
[CrossRef]

2009 (3)

J. Le Perchec, Y. Desieres, and R. Espiau de Lamaestre, “Plasmon-based photosensors comprising a very thin semiconducting region,” Appl. Phys. Lett.94, 181104 (2009).
[CrossRef]

J. Dorfmuller, R. Vogelgesang, R. T. Weitz, C. Rockstuhl, C. Etrich, T. Pertsch, F. Lederer, and K. Kern, “Fabry-perot resonances in one-dimensional plasmonic nanostructures,” Nano Lett.9, 2372–2377 (2009).
[CrossRef] [PubMed]

G. Della Valle, T. Søndergaard, and S. I. Bozhevolnyi, “High-Q plasmonic resonators based on metal split nanocylinders,” Phys. Rev. B80, 235405 (2009).
[CrossRef]

2008 (6)

Unusual Fabry-Perot resonances with m = 0 may exist in subwavelength metallic structures, see E. Feigenbaum and M. Orenstein, “Ultrasmall volume plasmons, yet with complete retardation effects”, Phys. Rev. Lett.101, 163902 (2008). For this situation to occur, the positive propagation phase has to be fully compensated by a negative reflection phase. Such a resonance does not exist in the MIM resonators under study since ϕr ≈ 0.
[CrossRef] [PubMed]

E. S. Barnard, J. S. White, A. Chandran, and M. L. Brongersma, “Spectral properties of plasmonic resonator antennas,” Opt. Express16, 16529–16537 (2008).
[CrossRef] [PubMed]

P. Lalanne, C. Sauvan, and J.-P. Hugonin, “Photon confinement in photonic crystal nanocavities,” Laser and Photon. Rev.2, 514–526 (2008).
[CrossRef]

L. C. Lindquist, W. A. Luhman, S. H. Oh, and R. J. Holmes, “Plasmonic nanocavity arrays for enhanced efficiency in organic photovoltaic cells,” Appl. Phys. Lett.93, 123308 (2008).
[CrossRef]

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. van Duyne, “Biosensing with plasmonic nanosensors,” Nature Mater.7, 442–453 (2008).
[CrossRef]

A. Mary, S. G. Rodrigo, F. J. Garcia-Vidal, and L. Martin-Moreno, “Theory of negative-refractive-index response of double-fishnet structures,” Phys. Rev. Lett.101, 103902 (2008).
[CrossRef] [PubMed]

2007 (6)

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics1, 41–48 (2007).
[CrossRef]

Y. Kurokawa and H. T. Miyazaki, “Metal-insulator-metal plasmon nanocavities: analysis of optical properties,” Phys. Rev. B75, 035411 (2007).
[CrossRef]

S. I. Bozhevolnyi and T. Søndergaard, “General properties of slow-plasmon resonant nanostructures: nano-antennas and resonators,” Opt. Express15, 10869–10877 (2007).
[CrossRef] [PubMed]

J. Jung, T. Søndergaard, and S. I. Bozhevolnyi, “Gap plasmon-polariton nanoresonators: scattering enhancement and launching of surface plasmon polaritons,” Phys. Rev. B79, 035401 (2007).
[CrossRef]

L. Novotny, “Effective wavelength scaling for optical antennas,” Phys. Rev. Lett.98, 266802 (2007).
[CrossRef] [PubMed]

M. Besbes, J.-P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, B. Guizal, and D. V. Labeke, “Numerical analysis of a slit-groove diffraction problem,” J. Europ. Opt. Soc. Rap. Public.2, 07022 (2007).
[CrossRef]

2006 (4)

F. Wang and Y. R. Shen, “General properties of local plasmons in metal nanostructures,” Phys. Rev. Lett.97, 206806 (2006).
[CrossRef] [PubMed]

F. Garwe, C. Rockstuhl, C. Etrich, U. Hübner, U. Bauerschäfer, F. Setzpfandt, M. Augustin, T. Pertsch, A. Tünnermann, and F. Lederer, “Evaluation of gold nanowire pairs as a potential negative index material,” Appl. Phys. B84, 139–148 (2006).
[CrossRef]

H. T. Miyazaki and Y. Kurokawa, “Squeezing visible light waves into a 3-nm-thick and 55-nm-long plasmon cavity,” Phys. Rev. Lett.96, 097401 (2006).
[CrossRef] [PubMed]

G. Leveque and O. J. F. Martin, “Tunable composite nanoparticle for plasmonics,” Opt. Lett.31, 2750–2752 (2006).
[CrossRef] [PubMed]

2005 (5)

G. Dolling, C. Enkrich, M. Wegener, J. F. Zhou, C. M. Soukoulis, and S. Linden, “Cut-wire pairs and plate pairs as magnetic atoms for optical metamaterials,” Opt. Lett.30, 3198–3200 (2005).
[CrossRef] [PubMed]

V. M. Shalaev, W. Cai, U. K. Chettiar, H. K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett.30, 3356–3358 (2005).
[CrossRef]

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett.95, 137404 (2005).
[CrossRef] [PubMed]

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett.95, 257403 (2005).
[CrossRef] [PubMed]

C. Sauvan, P. Lalanne, and J.-P. Hugonin, “Slow-wave effect and mode-profile matching in photonic crystal microcavities,” Phys. Rev. B71, 165118 (2005).
[CrossRef]

2001 (1)

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6, 4370 (1972).
[CrossRef]

1969 (1)

E. N. Economou, “Surface plasmons in thin films,” Phys. Rev.182, 539–554 (1969).
[CrossRef]

1805 (1)

I. S. Maksymov, M. Besbes, J.-P. Hugonin, J. Yang, A. Beveratos, I. Sagnes, I. Robert-Philip, and P. Lalanne, “Metal-coated nanocylinder cavity for broadband nonclassical light emission,” Phys. Rev. Lett.105, 180502 (2010).

Ahmed, A.

S. B. Hasan, R. Filter, A. Ahmed, R. Vogelgesang, R. Gordon, C. Rockstuhl, and F. Lederer, “Relating localized nanoparticle resonances to an associated antenna problem,” Phys. Rev. B84, 195405 (2011).
[CrossRef]

Alivisatos, A. P.

N. Liu, M. L. Tang, M. Hentschel, H. Giessen, and A. P. Alivisatos, “Nanoantenna-enhanced gas sensing in a single tailored nanofocus,” Nature Mater.10, 631–636 (2011).
[CrossRef]

Anker, J. N.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. van Duyne, “Biosensing with plasmonic nanosensors,” Nature Mater.7, 442–453 (2008).
[CrossRef]

Atwater, H. A.

H. A. Atwater and A. Polman, “Plasmonic for improved photovoltaic devices,” Nature Mater.9, 205–213 (2010).
[CrossRef]

Augustin, M.

F. Garwe, C. Rockstuhl, C. Etrich, U. Hübner, U. Bauerschäfer, F. Setzpfandt, M. Augustin, T. Pertsch, A. Tünnermann, and F. Lederer, “Evaluation of gold nanowire pairs as a potential negative index material,” Appl. Phys. B84, 139–148 (2006).
[CrossRef]

Aussenegg, F. R.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett.95, 257403 (2005).
[CrossRef] [PubMed]

Babinec, T. M.

J. T. Choy, B. J. M. Hausmann, T. M. Babinec, I. Bulu, M. Khan, P. Maletinsky, A. Yacoby, and M. Loncar, “Enhanced single-photon emission from a diamond-silver aperture,” Nat. Photonics5, 738–743 (2011).
[CrossRef]

Baida, F. I.

M. Besbes, J.-P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, B. Guizal, and D. V. Labeke, “Numerical analysis of a slit-groove diffraction problem,” J. Europ. Opt. Soc. Rap. Public.2, 07022 (2007).
[CrossRef]

Barnard, E. S.

Bauerschäfer, U.

F. Garwe, C. Rockstuhl, C. Etrich, U. Hübner, U. Bauerschäfer, F. Setzpfandt, M. Augustin, T. Pertsch, A. Tünnermann, and F. Lederer, “Evaluation of gold nanowire pairs as a potential negative index material,” Appl. Phys. B84, 139–148 (2006).
[CrossRef]

Besbes, M.

M. Besbes, J.-P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, B. Guizal, and D. V. Labeke, “Numerical analysis of a slit-groove diffraction problem,” J. Europ. Opt. Soc. Rap. Public.2, 07022 (2007).
[CrossRef]

I. S. Maksymov, M. Besbes, J.-P. Hugonin, J. Yang, A. Beveratos, I. Sagnes, I. Robert-Philip, and P. Lalanne, “Metal-coated nanocylinder cavity for broadband nonclassical light emission,” Phys. Rev. Lett.105, 180502 (2010).

Beveratos, A.

I. S. Maksymov, M. Besbes, J.-P. Hugonin, J. Yang, A. Beveratos, I. Sagnes, I. Robert-Philip, and P. Lalanne, “Metal-coated nanocylinder cavity for broadband nonclassical light emission,” Phys. Rev. Lett.105, 180502 (2010).

Bienstman, P.

M. Besbes, J.-P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, B. Guizal, and D. V. Labeke, “Numerical analysis of a slit-groove diffraction problem,” J. Europ. Opt. Soc. Rap. Public.2, 07022 (2007).
[CrossRef]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Bondarenko, O.

M. P. Nezhad, A. Simic, O. Bondarenko, B. Slutsky, A. Mizrahi, L. Feng, V. Lomakin, and Y. Fainman, “Room-temperature subwavelength metallo-dielectric lasers,” Nat. Photonics4, 395–399 (2010).
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Chen, J.

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Chipouline, A.

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J. T. Choy, B. J. M. Hausmann, T. M. Babinec, I. Bulu, M. Khan, P. Maletinsky, A. Yacoby, and M. Loncar, “Enhanced single-photon emission from a diamond-silver aperture,” Nat. Photonics5, 738–743 (2011).
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H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett.95, 257403 (2005).
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J. Dorfmuller, R. Vogelgesang, R. T. Weitz, C. Rockstuhl, C. Etrich, T. Pertsch, F. Lederer, and K. Kern, “Fabry-perot resonances in one-dimensional plasmonic nanostructures,” Nano Lett.9, 2372–2377 (2009).
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F. Garwe, C. Rockstuhl, C. Etrich, U. Hübner, U. Bauerschäfer, F. Setzpfandt, M. Augustin, T. Pertsch, A. Tünnermann, and F. Lederer, “Evaluation of gold nanowire pairs as a potential negative index material,” Appl. Phys. B84, 139–148 (2006).
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M. P. Nezhad, A. Simic, O. Bondarenko, B. Slutsky, A. Mizrahi, L. Feng, V. Lomakin, and Y. Fainman, “Room-temperature subwavelength metallo-dielectric lasers,” Nat. Photonics4, 395–399 (2010).
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S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett.95, 137404 (2005).
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Unusual Fabry-Perot resonances with m = 0 may exist in subwavelength metallic structures, see E. Feigenbaum and M. Orenstein, “Ultrasmall volume plasmons, yet with complete retardation effects”, Phys. Rev. Lett.101, 163902 (2008). For this situation to occur, the positive propagation phase has to be fully compensated by a negative reflection phase. Such a resonance does not exist in the MIM resonators under study since ϕr ≈ 0.
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A. Cattoni, P. Ghenuche, A. M. Haghiri-Gosnet, D. Decanini, J. Chen, J.-L. Pelouard, and S. Collin, “λ3/1000 plasmonic nanocavities for biosensing fabricated by soft uv nanoimprint lithography,” Nano Lett.11, 3557–3563 (2011).
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N. Liu, M. L. Tang, M. Hentschel, H. Giessen, and A. P. Alivisatos, “Nanoantenna-enhanced gas sensing in a single tailored nanofocus,” Nature Mater.10, 631–636 (2011).
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N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett.10, 2342–2348 (2010).
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S. B. Hasan, R. Filter, A. Ahmed, R. Vogelgesang, R. Gordon, C. Rockstuhl, and F. Lederer, “Relating localized nanoparticle resonances to an associated antenna problem,” Phys. Rev. B84, 195405 (2011).
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M. Besbes, J.-P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, B. Guizal, and D. V. Labeke, “Numerical analysis of a slit-groove diffraction problem,” J. Europ. Opt. Soc. Rap. Public.2, 07022 (2007).
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M. Besbes, J.-P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, B. Guizal, and D. V. Labeke, “Numerical analysis of a slit-groove diffraction problem,” J. Europ. Opt. Soc. Rap. Public.2, 07022 (2007).
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A. Cattoni, P. Ghenuche, A. M. Haghiri-Gosnet, D. Decanini, J. Chen, J.-L. Pelouard, and S. Collin, “λ3/1000 plasmonic nanocavities for biosensing fabricated by soft uv nanoimprint lithography,” Nano Lett.11, 3557–3563 (2011).
[CrossRef] [PubMed]

Haidar, R.

C. Koechlin, P. Bouchon, F. Pardo, J. Jaeck, X. Lafosse, J.-L. Pelouard, and R. Haidar, “Total routing and absorption of photons in dual color plasmonic antennas,” Appl. Phys. Lett.99, 241104 (2011).
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J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. van Duyne, “Biosensing with plasmonic nanosensors,” Nature Mater.7, 442–453 (2008).
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Hao, J.

J. Hao, J. Wang, X. Liu, W. J. Padilla, L. Zhou, and M. Qiu, “High performance optical absorber based on a plasmonic metamaterial,” Appl. Phys. Lett.96, 251104 (2010).
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Hasan, S. B.

S. B. Hasan, R. Filter, A. Ahmed, R. Vogelgesang, R. Gordon, C. Rockstuhl, and F. Lederer, “Relating localized nanoparticle resonances to an associated antenna problem,” Phys. Rev. B84, 195405 (2011).
[CrossRef]

Hausmann, B. J. M.

J. T. Choy, B. J. M. Hausmann, T. M. Babinec, I. Bulu, M. Khan, P. Maletinsky, A. Yacoby, and M. Loncar, “Enhanced single-photon emission from a diamond-silver aperture,” Nat. Photonics5, 738–743 (2011).
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M. Besbes, J.-P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, B. Guizal, and D. V. Labeke, “Numerical analysis of a slit-groove diffraction problem,” J. Europ. Opt. Soc. Rap. Public.2, 07022 (2007).
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C. Rockstuhl, C. Menzel, S. Mühlig, J. Petschulat, C. Helgert, C. Etrich, A. Chipouline, T. Pertsch, and F. Lederer, “Scattering properties of meta-atoms,” Phys. Rev. B83, 245119 (2011).
[CrossRef]

Hentschel, M.

N. Liu, M. L. Tang, M. Hentschel, H. Giessen, and A. P. Alivisatos, “Nanoantenna-enhanced gas sensing in a single tailored nanofocus,” Nature Mater.10, 631–636 (2011).
[CrossRef]

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett.10, 2342–2348 (2010).
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Hofer, F.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett.95, 257403 (2005).
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H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett.95, 257403 (2005).
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L. C. Lindquist, W. A. Luhman, S. H. Oh, and R. J. Holmes, “Plasmonic nanocavity arrays for enhanced efficiency in organic photovoltaic cells,” Appl. Phys. Lett.93, 123308 (2008).
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Hübner, U.

F. Garwe, C. Rockstuhl, C. Etrich, U. Hübner, U. Bauerschäfer, F. Setzpfandt, M. Augustin, T. Pertsch, A. Tünnermann, and F. Lederer, “Evaluation of gold nanowire pairs as a potential negative index material,” Appl. Phys. B84, 139–148 (2006).
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Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Hugonin, J.-P.

P. Lalanne, C. Sauvan, and J.-P. Hugonin, “Photon confinement in photonic crystal nanocavities,” Laser and Photon. Rev.2, 514–526 (2008).
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M. Besbes, J.-P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, B. Guizal, and D. V. Labeke, “Numerical analysis of a slit-groove diffraction problem,” J. Europ. Opt. Soc. Rap. Public.2, 07022 (2007).
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C. Sauvan, P. Lalanne, and J.-P. Hugonin, “Slow-wave effect and mode-profile matching in photonic crystal microcavities,” Phys. Rev. B71, 165118 (2005).
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E. Silberstein, P. Lalanne, J.-P. Hugonin, and Q. Cao, “On the use of grating theory in integrated optics,” J. Opt. Soc. Am. A18, 2865–2875 (2001).
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I. S. Maksymov, M. Besbes, J.-P. Hugonin, J. Yang, A. Beveratos, I. Sagnes, I. Robert-Philip, and P. Lalanne, “Metal-coated nanocylinder cavity for broadband nonclassical light emission,” Phys. Rev. Lett.105, 180502 (2010).

Jaeck, J.

C. Koechlin, P. Bouchon, F. Pardo, J. Jaeck, X. Lafosse, J.-L. Pelouard, and R. Haidar, “Total routing and absorption of photons in dual color plasmonic antennas,” Appl. Phys. Lett.99, 241104 (2011).
[CrossRef]

Janssen, O. T. A.

M. Besbes, J.-P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, B. Guizal, and D. V. Labeke, “Numerical analysis of a slit-groove diffraction problem,” J. Europ. Opt. Soc. Rap. Public.2, 07022 (2007).
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C. Wu, B. Neuner, G. Shvets, J. John, A. Milder, B. Zollars, and S. Savoy, “Large-area wide-angle spectrally selective plasmonic absorber,” Phys. Rev. B84, 075102 (2011).
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P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B6, 4370 (1972).
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J. Jung, T. Søndergaard, and S. I. Bozhevolnyi, “Gap plasmon-polariton nanoresonators: scattering enhancement and launching of surface plasmon polaritons,” Phys. Rev. B79, 035401 (2007).
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Kern, K.

J. Dorfmuller, R. Vogelgesang, R. T. Weitz, C. Rockstuhl, C. Etrich, T. Pertsch, F. Lederer, and K. Kern, “Fabry-perot resonances in one-dimensional plasmonic nanostructures,” Nano Lett.9, 2372–2377 (2009).
[CrossRef] [PubMed]

Khan, M.

J. T. Choy, B. J. M. Hausmann, T. M. Babinec, I. Bulu, M. Khan, P. Maletinsky, A. Yacoby, and M. Loncar, “Enhanced single-photon emission from a diamond-silver aperture,” Nat. Photonics5, 738–743 (2011).
[CrossRef]

Kildishev, A. V.

Koechlin, C.

C. Koechlin, P. Bouchon, F. Pardo, J. Jaeck, X. Lafosse, J.-L. Pelouard, and R. Haidar, “Total routing and absorption of photons in dual color plasmonic antennas,” Appl. Phys. Lett.99, 241104 (2011).
[CrossRef]

Kreibig, U.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett.95, 257403 (2005).
[CrossRef] [PubMed]

Krenn, J. R.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett.95, 257403 (2005).
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Y. Kurokawa and H. T. Miyazaki, “Metal-insulator-metal plasmon nanocavities: analysis of optical properties,” Phys. Rev. B75, 035411 (2007).
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H. T. Miyazaki and Y. Kurokawa, “Squeezing visible light waves into a 3-nm-thick and 55-nm-long plasmon cavity,” Phys. Rev. Lett.96, 097401 (2006).
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Kuttge, M.

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

Labeke, D. V.

M. Besbes, J.-P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, B. Guizal, and D. V. Labeke, “Numerical analysis of a slit-groove diffraction problem,” J. Europ. Opt. Soc. Rap. Public.2, 07022 (2007).
[CrossRef]

Lafosse, X.

C. Koechlin, P. Bouchon, F. Pardo, J. Jaeck, X. Lafosse, J.-L. Pelouard, and R. Haidar, “Total routing and absorption of photons in dual color plasmonic antennas,” Appl. Phys. Lett.99, 241104 (2011).
[CrossRef]

Lalanne, P.

J. Yang, C. Sauvan, H. T. Liu, and P. Lalanne, “Theory of fishnet negative-index optical metamaterials,” Phys. Rev. Lett.107, 043903 (2011).
[CrossRef] [PubMed]

P. Lalanne, C. Sauvan, and J.-P. Hugonin, “Photon confinement in photonic crystal nanocavities,” Laser and Photon. Rev.2, 514–526 (2008).
[CrossRef]

M. Besbes, J.-P. Hugonin, P. Lalanne, S. van Haver, O. T. A. Janssen, A. M. Nugrowati, M. Xu, S. F. Pereira, H. P. Urbach, A. S. van de Nes, P. Bienstman, G. Granet, A. Moreau, S. Helfert, M. Sukharev, T. Seideman, F. I. Baida, B. Guizal, and D. V. Labeke, “Numerical analysis of a slit-groove diffraction problem,” J. Europ. Opt. Soc. Rap. Public.2, 07022 (2007).
[CrossRef]

C. Sauvan, P. Lalanne, and J.-P. Hugonin, “Slow-wave effect and mode-profile matching in photonic crystal microcavities,” Phys. Rev. B71, 165118 (2005).
[CrossRef]

E. Silberstein, P. Lalanne, J.-P. Hugonin, and Q. Cao, “On the use of grating theory in integrated optics,” J. Opt. Soc. Am. A18, 2865–2875 (2001).
[CrossRef]

I. S. Maksymov, M. Besbes, J.-P. Hugonin, J. Yang, A. Beveratos, I. Sagnes, I. Robert-Philip, and P. Lalanne, “Metal-coated nanocylinder cavity for broadband nonclassical light emission,” Phys. Rev. Lett.105, 180502 (2010).

Le Perchec, J.

J. Le Perchec, Y. Desieres, and R. Espiau de Lamaestre, “Plasmon-based photosensors comprising a very thin semiconducting region,” Appl. Phys. Lett.94, 181104 (2009).
[CrossRef]

Lederer, F.

C. Rockstuhl, C. Menzel, S. Mühlig, J. Petschulat, C. Helgert, C. Etrich, A. Chipouline, T. Pertsch, and F. Lederer, “Scattering properties of meta-atoms,” Phys. Rev. B83, 245119 (2011).
[CrossRef]

S. B. Hasan, R. Filter, A. Ahmed, R. Vogelgesang, R. Gordon, C. Rockstuhl, and F. Lederer, “Relating localized nanoparticle resonances to an associated antenna problem,” Phys. Rev. B84, 195405 (2011).
[CrossRef]

J. Dorfmuller, R. Vogelgesang, R. T. Weitz, C. Rockstuhl, C. Etrich, T. Pertsch, F. Lederer, and K. Kern, “Fabry-perot resonances in one-dimensional plasmonic nanostructures,” Nano Lett.9, 2372–2377 (2009).
[CrossRef] [PubMed]

F. Garwe, C. Rockstuhl, C. Etrich, U. Hübner, U. Bauerschäfer, F. Setzpfandt, M. Augustin, T. Pertsch, A. Tünnermann, and F. Lederer, “Evaluation of gold nanowire pairs as a potential negative index material,” Appl. Phys. B84, 139–148 (2006).
[CrossRef]

Leveque, G.

Linden, S.

Lindquist, L. C.

L. C. Lindquist, W. A. Luhman, S. H. Oh, and R. J. Holmes, “Plasmonic nanocavity arrays for enhanced efficiency in organic photovoltaic cells,” Appl. Phys. Lett.93, 123308 (2008).
[CrossRef]

Liu, H. T.

J. Yang, C. Sauvan, H. T. Liu, and P. Lalanne, “Theory of fishnet negative-index optical metamaterials,” Phys. Rev. Lett.107, 043903 (2011).
[CrossRef] [PubMed]

Liu, N.

N. Liu, M. L. Tang, M. Hentschel, H. Giessen, and A. P. Alivisatos, “Nanoantenna-enhanced gas sensing in a single tailored nanofocus,” Nature Mater.10, 631–636 (2011).
[CrossRef]

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, “Infrared perfect absorber and its application as plasmonic sensor,” Nano Lett.10, 2342–2348 (2010).
[CrossRef] [PubMed]

Liu, X.

J. Hao, J. Wang, X. Liu, W. J. Padilla, L. Zhou, and M. Qiu, “High performance optical absorber based on a plasmonic metamaterial,” Appl. Phys. Lett.96, 251104 (2010).
[CrossRef]

Lomakin, V.

M. P. Nezhad, A. Simic, O. Bondarenko, B. Slutsky, A. Mizrahi, L. Feng, V. Lomakin, and Y. Fainman, “Room-temperature subwavelength metallo-dielectric lasers,” Nat. Photonics4, 395–399 (2010).
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Other (4)

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Because of symmetry reasons, anti-symmetric higher-order modes do not impact the reflectivity of the symmetric fundamental mode.

The assumption Lp ≪ L is valid, since for large waveguide cross-sections (w = 100 nm and td = 100 nm) Lp ≈ 5 nm ≪ L ≈ 100 nm and for small cross-sections (w = 40 nm and td < 25 nm) Lp < 1 nm ≪ L ≈ 30 nm.

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Figures (4)

Fig. 1
Fig. 1

Magnetic resonance of a single MIM nanoresonator. (a) The nanoresonator consists of a dielectric rectangular nanoparticle (width w, length L and thickness td) sandwiched between a metal substrate and a metal layer of thickness tm. The metal is silver and the dielectric material is a semiconductor (such as GaAs) with a high refractive index of 3.5. (b) Spectrum of the intensity enhancement |E|2/|Einc|2 at the point A in (c) for a resonator (w = 40 nm, td = 20 nm and L = 70 nm) illuminated by a plane wave impinging from air at normal incidence and polarized along the z-direction. (c) Distribution of the induced current J (see the text for its definition) and of the magnetic field |Hx|2 at resonance in the (y, z) plane (x = 0). Blue and red colors correspond to negative and positive values. The induced current forms a loop, which highlights the magnetic response of MIM resonators.

Fig. 2
Fig. 2

Fundamental plasmonic mode of the MIM waveguide for λ = 950 nm. (a)–(c) Main field components |Ey|2, |Ez|2 and |Hx|2 of the mode for w = 40 nm and td = 20 nm. (d) Dependence on the dielectric thickness td of the effective index neff = Re(β)/k0, (e) of the attenuation α = 2Im(β) and (f) of the group index n g = n eff λ n eff λ. In (d)–(f), four different widths are considered, w = 40 nm (solid blue), 100 nm (dashed red), 350 nm (dashed-dotted black) and ∞ (planar waveguide, thin solid line).

Fig. 3
Fig. 3

Reflectivity at the air/MIM interface for λ = 950 nm. (a) Map of the reflectivity as a function of the width w and the dielectric thickness td. (b) Reflectivity as a function of td for w = 40 nm (solid blue), 100 nm (dashed red), 350 nm (dashed-dotted black) and ∞ (planar waveguide, thin solid line). (c) Reflectivity as a function of w for td = 20 nm (solid blue), 35 nm (dashed red) and 50 nm (dashed-dotted black). The insets show the distribution of |Hx|2 in the (x, y) plane for the first two symmetric higher-order waveguide modes for td = 50 nm. The first two drops in the reflectivity curves identified by arrows correspond to the cut-off of these modes (w = 190 nm and w = 370 nm).

Fig. 4
Fig. 4

Fabry-Perot model predictions for the resonance at λ0 = 950 nm. (a) Length of the nanoresonator predicted with Eq. (2) for w = 40 nm (solid blue), 100 nm (dashed red) and 350 nm (dashed-dotted black). (b) Quality factor predicted with Eq. (3), Q = k0ngLeff/[1 − Rexp(−αL)], for w = 40 nm (solid blue), 100 nm (dashed red) and 350 nm (dashed-dotted black). The markers represent the Q-factor values extracted from fully-vectorial calculations of intensity enhancement spectra [see Fig. 1(b)] for the same widths, w = 40 nm (blue circles), 100 nm (red squares) and 350 nm (black triangles). The horizontal arrow shows the quasi-static Q-factor Qs given by Eq. (4). (c) Quality factor predicted with the Fabry-Perot model for w = 40 nm (thick solid blue). The Q-factors predicted without radiation (R = 1 in Eq. (3), solid magenta), without absorption (α = 0 in Eq. (3), dashed-dotted black) and without slow light effect (ng = 5 in Eq. (3), dashed red) are also presented. The vertical dashed lines mark the different regimes of the Q-factor variation.

Equations (8)

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J ( r ) = i ω ε 0 [ ε ( r ) ε ref ( r ) ] E ( r ) ,
L = λ 0 2 n eff ( m ϕ r π ) ,
Q = k 0 n g L eff 1 R eff ,
Q s = ω 0 ε m ω 2 ε m .
Q = k 0 n g α .
n eff 1 D ε d λ 0 π ε m t d ,
Q FP s = ω 0 ε m ω 2 ε m ,
( k 0 n g α ) s = ω 0 ε m ω 2 ε m ,

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