Abstract

We investigate the effect of the electron wave function producing permittivity (epsilon) near zero in sub-nanometer gaps and at surfaces. The field enhancement is calculated for gaps and nanoparticles, as well as the absorption from nanoparticles. Our modified quantum corrected model shows reduced absorption for nanoparticles due to “cloaking” of the epsilon near zero region, which has lower loss than the bulk region. We demonstrate that a modified quantum corrected model finite-difference time-domain simulation of metal slits with sub-nanometer gaps are in good agreement with the analytic expression for the quantum corrected plasmonic resonance wavelength as a function of gap size coming from Re{ε} = 0.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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    [Crossref]
  4. T. V. Teperik, P. Nordlander, J. Aizpurua, and A. G. Borisov, “Robust Subnanometric Plasmon Ruler by Rescaling of the Nonlocal Optical Response,” Phys. Rev. Lett. 110(26), 263901 (2013).
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  5. B. de Nijs, F. Benz, S. J. Barrow, D. O. Sigle, R. Chikkaraddy, A. Palma, C. Carnegie, M. Kamp, R. Sundararaman, P. Narang, O. A. Scherman, and J. J. Baumberg, “Plasmonic tunnel junctions for single-molecule redox chemistry,” Nat. Commun. 8(1), 994 (2017).
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
  29. T. Lee, W. Wang, and M. A. Reed, “Mechanism of Electron Conduction in Self-Assembled Alkanethiol Monolayer Devices,” Ann. N. Y. Acad. Sci. 1006(1), 21–35 (2003).
    [Crossref] [PubMed]
  30. S. F. Tan, L. Wu, J. K. W. Yang, P. Bai, M. Bosman, and C. A. Nijhuis, “Quantum plasmon resonances controlled by molecular tunnel junctions,” Science 343(6178), 1496–1499 (2014).
    [Crossref] [PubMed]
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    [Crossref]
  36. G. R. Parkins, W. E. Lawrence, and R. W. Christy, “Intraband optical conductivity σ (ω, T) of Cu, Ag, and Au: Contribution from electron-electron scattering,” Phys. Rev. B 23, 6408–6416 (1981).
    [Crossref]
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    [Crossref] [PubMed]
  38. S. Lal, N. K. Grady, J. Kundu, C. S. Levin, J. B. Lassiter, and N. J. Halas, “Tailoring plasmonic substrates for surface enhanced spectroscopies,” Chem. Soc. Rev. 37(5), 898–911 (2008).
    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  44. X. Chen, H.-R. Park, M. Pelton, X. Piao, N. C. Lindquist, H. Im, Y. J. Kim, J. S. Ahn, K. J. Ahn, N. Park, D.-S. Kim, and S.-H. Oh, “Atomic layer lithography of wafer-scale nanogap arrays for extreme confinement of electromagnetic waves,” Nat. Commun. 4(1), 2361 (2013).
    [Crossref] [PubMed]
  45. D. Yoo, N.-C. Nguyen, L. Martin-Moreno, D. A. Mohr, S. Carretero-Palacios, J. Shaver, J. Peraire, T. W. Ebbesen, and S.-H. Oh, “High-Throughput Fabrication of Resonant Metamaterials with Ultrasmall Coaxial Apertures via Atomic Layer Lithography,” Nano Lett. 16(3), 2040–2046 (2016).
    [Crossref] [PubMed]
  46. X. Chen, C. Ciracì, D. R. Smith, and S.-H. Oh, “Nanogap-Enhanced Infrared Spectroscopy with Template-Stripped Wafer-Scale Arrays of Buried Plasmonic Cavities,” Nano Lett. 15(1), 107–113 (2015).
    [Crossref] [PubMed]
  47. J. S. Ahn, T. Kang, D. K. Singh, Y.-M. Bahk, H. Lee, S. B. Choi, and D.-S. Kim, “Optical field enhancement of nanometer-sized gaps at near-infrared frequencies,” Opt. Express 23(4), 4897–4907 (2015).
    [Crossref] [PubMed]

2018 (4)

M. Z. Alam, S. A. Schulz, J. Upham, I. De Leon, and R. W. Boyd, “Large optical nonlinearity of nanoantennas coupled to an epsilon-near-zero material,” Nat. Photonics 12(2), 79–83 (2018).
[Crossref]

D. Doyle, N. Charipar, C. Argyropoulos, S. A. Trammell, R. Nita, J. Naciri, A. Pique, J. B. Herzog, and J. Fontana, “Tunable subnanometer gap plasmonic metasurfaces,” ACS Photonics 5(3), 1012–1018 (2018).
[Crossref]

E. J. H. Skjølstrup, T. Søndergaard, and T. G. Pedersen, “Quantum spill-out in few-nanometer metal gaps: Effect on gap plasmons and reflectance from ultrasharp groove arrays,” Phys. Rev. B 97(11), 115429 (2018).
[Crossref]

N. Kim, S. In, D. Lee, J. Rhie, J. Jeong, D.-S. Kim, and N. Park, “Colossal Terahertz Field Enhancement Using Split-Ring Resonators with a Sub-10 nm Gap,” ACS Photonics 5(2), 278–283 (2018).
[Crossref]

2017 (5)

E. J. H. Skjølstrup and T. Søndergaard, “Optics of multiple ultrasharp grooves in metal,” J. Opt. Soc. Am. B 34(3), 673–680 (2017).
[Crossref]

G. Hajisalem, M. S. Nezami, and R. Gordon, “Switchable Metal-Insulator Phase Transition Metamaterials,” Nano Lett. 17(5), 2940–2944 (2017).
[Crossref] [PubMed]

Y.-M. Bahk, S. Han, J. Rhie, J. Park, H. Jeon, N. Park, and D.-S. Kim, “Ultimate terahertz field enhancement of single nanoslits,” Phys. Rev. B 95(7), 075424 (2017).
[Crossref]

B. de Nijs, F. Benz, S. J. Barrow, D. O. Sigle, R. Chikkaraddy, A. Palma, C. Carnegie, M. Kamp, R. Sundararaman, P. Narang, O. A. Scherman, and J. J. Baumberg, “Plasmonic tunnel junctions for single-molecule redox chemistry,” Nat. Commun. 8(1), 994 (2017).
[Crossref] [PubMed]

I. Liberal and N. Engheta, “Near-zero refractive index photonics,” Nat. Photonics 11(3), 149–158 (2017).
[Crossref]

2016 (7)

L. Caspani, R. P. M. Kaipurath, M. Clerici, M. Ferrera, T. Roger, J. Kim, N. Kinsey, M. Pietrzyk, A. Di Falco, V. M. Shalaev, A. Boltasseva, and D. Faccio, “Enhanced Nonlinear Refractive Index in ε-Near-Zero Materials,” Phys. Rev. Lett. 116(23), 233901 (2016).
[Crossref] [PubMed]

M. Z. Alam, I. De Leon, and R. W. Boyd, “Large optical nonlinearity of indium tin oxide in its epsilon-near-zero region,” Science 352(6287), 795–797 (2016).
[Crossref] [PubMed]

S. S. Islam, M. R. I. Faruque, and M. T. Islam, “An Object-Independent ENZ Metamaterial-Based Wideband Electromagnetic Cloak,” Sci. Rep. 6(1), 33624 (2016).
[Crossref] [PubMed]

S. Han, J.-Y. Kim, T. Kang, Y.-M. Bahk, J. Rhie, B. J. Kang, Y. S. Kim, J. Park, W. T. Kim, H. Jeon, F. Rotermund, and D.-S. Kim, “Colossal Terahertz Nonlinearity in Angstrom- and Nanometer-Sized Gaps,” ACS Photonics 3(8), 1440–1445 (2016).
[Crossref]

W. Zhu, R. Esteban, A. G. Borisov, J. J. Baumberg, P. Nordlander, H. J. Lezec, J. Aizpurua, and K. B. Crozier, “Quantum mechanical effects in plasmonic structures with subnanometre gaps,” Nat. Commun. 7, 11495 (2016).
[Crossref] [PubMed]

T. Søndergaard and S. I. Bozhevolnyi, “Optics of a single ultrasharp groove in metal,” Opt. Lett. 41(13), 2903–2906 (2016).
[Crossref] [PubMed]

D. Yoo, N.-C. Nguyen, L. Martin-Moreno, D. A. Mohr, S. Carretero-Palacios, J. Shaver, J. Peraire, T. W. Ebbesen, and S.-H. Oh, “High-Throughput Fabrication of Resonant Metamaterials with Ultrasmall Coaxial Apertures via Atomic Layer Lithography,” Nano Lett. 16(3), 2040–2046 (2016).
[Crossref] [PubMed]

2015 (5)

X. Chen, C. Ciracì, D. R. Smith, and S.-H. Oh, “Nanogap-Enhanced Infrared Spectroscopy with Template-Stripped Wafer-Scale Arrays of Buried Plasmonic Cavities,” Nano Lett. 15(1), 107–113 (2015).
[Crossref] [PubMed]

J. S. Ahn, T. Kang, D. K. Singh, Y.-M. Bahk, H. Lee, S. B. Choi, and D.-S. Kim, “Optical field enhancement of nanometer-sized gaps at near-infrared frequencies,” Opt. Express 23(4), 4897–4907 (2015).
[Crossref] [PubMed]

X. Chen, C. Ciracì, D. R. Smith, and S. H. Oh, “Nanogap-enhanced infrared spectroscopy with template-stripped wafer-scale arrays of buried plasmonic cavities,” Nano Lett. 15(1), 107–113 (2015).
[Crossref] [PubMed]

A. D. Neira, N. Olivier, M. E. Nasir, W. Dickson, G. A. Wurtz, and A. V. Zayats, “Eliminating material constraints for nonlinearity with plasmonic metamaterials,” Nat. Commun. 6(1), 7757 (2015).
[Crossref] [PubMed]

H. U. Yang, J. D’Archangel, M. L. Sundheimer, E. Tucker, G. D. Boreman, and M. B. Raschke, “Optical dielectric function of silver,” Phys. Rev. B 91(23), 235137 (2015).
[Crossref]

2014 (5)

G. Hajisalem, M. S. Nezami, and R. Gordon, “Probing the quantum tunneling limit of plasmonic enhancement by third harmonic generation,” Nano Lett. 14(11), 6651–6654 (2014).
[Crossref] [PubMed]

W. Zhu and K. B. Crozier, “Quantum mechanical limit to plasmonic enhancement as observed by surface-enhanced Raman scattering,” Nat. Commun. 5(1), 5228 (2014).
[Crossref] [PubMed]

S. F. Tan, L. Wu, J. K. W. Yang, P. Bai, M. Bosman, and C. A. Nijhuis, “Quantum plasmon resonances controlled by molecular tunnel junctions,” Science 343(6178), 1496–1499 (2014).
[Crossref] [PubMed]

G. Hajisalem, Q. Min, R. Gelfand, and R. Gordon, “Effect of surface roughness on self-assembled monolayer plasmonic ruler in nonlocal regime,” Opt. Express 22(8), 9604–9610 (2014).
[Crossref] [PubMed]

A. Stolz, J. Berthelot, M.-M. Mennemanteuil, G. Colas des Francs, L. Markey, V. Meunier, and A. Bouhelier, “Nonlinear Photon-Assisted Tunneling Transport in Optical Gap Antennas,” Nano Lett. 14(5), 2330–2338 (2014).
[Crossref] [PubMed]

2013 (3)

X. Chen, H.-R. Park, M. Pelton, X. Piao, N. C. Lindquist, H. Im, Y. J. Kim, J. S. Ahn, K. J. Ahn, N. Park, D.-S. Kim, and S.-H. Oh, “Atomic layer lithography of wafer-scale nanogap arrays for extreme confinement of electromagnetic waves,” Nat. Commun. 4(1), 2361 (2013).
[Crossref] [PubMed]

T. V. Teperik, P. Nordlander, J. Aizpurua, and A. G. Borisov, “Robust Subnanometric Plasmon Ruler by Rescaling of the Nonlocal Optical Response,” Phys. Rev. Lett. 110(26), 263901 (2013).
[Crossref] [PubMed]

C. R. Zamecnik, A. Ahmed, C. M. Walters, R. Gordon, and G. C. Walker, “Surface-enhanced Raman spectroscopy using lipid encapsulated plasmonic nanoparticles and J-aggregates to create locally enhanced electric fields,” J. Phys. Chem. C 117(4), 1879–1886 (2013).
[Crossref]

2012 (6)

K. J. Savage, M. M. Hawkeye, R. Esteban, A. G. Borisov, J. Aizpurua, and J. J. Baumberg, “Revealing the quantum regime in tunnelling plasmonics,” Nature 491(7425), 574–577 (2012).
[Crossref] [PubMed]

R. Esteban, A. G. Borisov, P. Nordlander, and J. Aizpurua, “Bridging quantum and classical plasmonics with a quantum-corrected model,” Nat. Commun. 3(1), 825 (2012).
[Crossref] [PubMed]

R. L. Olmon, B. Slovick, T. W. Johnson, D. Shelton, S.-H. Oh, G. D. Boreman, and M. B. Raschke, “Optical dielectric function of gold,” Phys. Rev. B 86(23), 235147 (2012).
[Crossref]

C. Ciracì, R. T. Hill, J. J. Mock, Y. Urzhumov, A. I. Fernández-Domínguez, S. A. Maier, J. B. Pendry, A. Chilkoti, and D. R. Smith, “Probing the ultimate limits of plasmonic enhancement,” Science 337(6098), 1072–1074 (2012).
[Crossref] [PubMed]

T. Søndergaard, S. M. Novikov, T. Holmgaard, R. L. Eriksen, J. Beermann, Z. Han, K. Pedersen, and S. I. Bozhevolnyi, “Plasmonic black gold by adiabatic nanofocusing and absorption of light in ultra-sharp convex grooves,” Nat. Commun. 3(1), 969 (2012).
[Crossref] [PubMed]

J. Berthelot, G. Bachelier, M. Song, P. Rai, G. Colas des Francs, A. Dereux, and A. Bouhelier, “Silencing and enhancement of second-harmonic generation in optical gap antennas,” Opt. Express 20(10), 10498–10508 (2012).
[Crossref] [PubMed]

2011 (1)

N. J. Halas, S. Lal, W.-S. Chang, S. Link, and P. Nordlander, “Plasmons in Strongly Coupled Metallic Nanostructures,” Chem. Rev. 111(6), 3913–3961 (2011).
[Crossref] [PubMed]

2010 (2)

S. Hrabar, I. Krois, and A. Kiricenko, “Towards active dispersionless ENZ metamaterial for cloaking applications,” Metamaterials (Amst.) 4(2-3), 89–97 (2010).
[Crossref]

E. O. Liznev, A. V. Dorofeenko, L. Huizhe, A. P. Vinogradov, and S. Zouhdi, “Epsilon-near-zero material as a unique solution to three different approaches to cloaking,” Appl. Phys., A Mater. Sci. Process. 100(2), 321–325 (2010).
[Crossref]

2008 (1)

S. Lal, N. K. Grady, J. Kundu, C. S. Levin, J. B. Lassiter, and N. J. Halas, “Tailoring plasmonic substrates for surface enhanced spectroscopies,” Chem. Soc. Rev. 37(5), 898–911 (2008).
[Crossref] [PubMed]

2007 (1)

A. Alù, M. G. Silveirinha, A. Salandrino, and N. Engheta, “Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B 75(15), 155410 (2007).
[Crossref]

2003 (1)

T. Lee, W. Wang, and M. A. Reed, “Mechanism of Electron Conduction in Self-Assembled Alkanethiol Monolayer Devices,” Ann. N. Y. Acad. Sci. 1006(1), 21–35 (2003).
[Crossref] [PubMed]

1999 (1)

G. Compagnini, C. Galati, and S. Pignataro, “Distance dependence of surface enhanced Raman scattering probed by alkanethiol self-assembled monolayers,” Phys. Chem. Chem. Phys. 1(9), 2351–2353 (1999).
[Crossref]

1985 (1)

1982 (1)

A. Wokaun, J. P. Gordon, and P. F. Liao, “Radiation Damping in Surface-Enhanced Raman Scattering,” Phys. Rev. Lett. 48(14), 957–960 (1982).
[Crossref]

1981 (1)

G. R. Parkins, W. E. Lawrence, and R. W. Christy, “Intraband optical conductivity σ (ω, T) of Cu, Ag, and Au: Contribution from electron-electron scattering,” Phys. Rev. B 23, 6408–6416 (1981).
[Crossref]

1975 (1)

A. W. Dweydari and C. H. B. Mee, “Work function measurements on (100) and (110) surfaces of silver,” Phys. Status Solidi 27(1), 223–230 (1975).
[Crossref]

1969 (1)

U. Kreibig and C. Fragstein, “The limitation of electron mean free path in small silver particles,” Z. Phys. 224(4), 307–323 (1969).
[Crossref]

Ahmed, A.

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E. J. H. Skjølstrup, T. Søndergaard, and T. G. Pedersen, “Quantum spill-out in few-nanometer metal gaps: Effect on gap plasmons and reflectance from ultrasharp groove arrays,” Phys. Rev. B 97(11), 115429 (2018).
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ACS Photonics (3)

D. Doyle, N. Charipar, C. Argyropoulos, S. A. Trammell, R. Nita, J. Naciri, A. Pique, J. B. Herzog, and J. Fontana, “Tunable subnanometer gap plasmonic metasurfaces,” ACS Photonics 5(3), 1012–1018 (2018).
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S. Han, J.-Y. Kim, T. Kang, Y.-M. Bahk, J. Rhie, B. J. Kang, Y. S. Kim, J. Park, W. T. Kim, H. Jeon, F. Rotermund, and D.-S. Kim, “Colossal Terahertz Nonlinearity in Angstrom- and Nanometer-Sized Gaps,” ACS Photonics 3(8), 1440–1445 (2016).
[Crossref]

N. Kim, S. In, D. Lee, J. Rhie, J. Jeong, D.-S. Kim, and N. Park, “Colossal Terahertz Field Enhancement Using Split-Ring Resonators with a Sub-10 nm Gap,” ACS Photonics 5(2), 278–283 (2018).
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Ann. N. Y. Acad. Sci. (1)

T. Lee, W. Wang, and M. A. Reed, “Mechanism of Electron Conduction in Self-Assembled Alkanethiol Monolayer Devices,” Ann. N. Y. Acad. Sci. 1006(1), 21–35 (2003).
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Appl. Opt. (1)

Appl. Phys., A Mater. Sci. Process. (1)

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Chem. Rev. (1)

N. J. Halas, S. Lal, W.-S. Chang, S. Link, and P. Nordlander, “Plasmons in Strongly Coupled Metallic Nanostructures,” Chem. Rev. 111(6), 3913–3961 (2011).
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Chem. Soc. Rev. (1)

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

J. Phys. Chem. C (1)

C. R. Zamecnik, A. Ahmed, C. M. Walters, R. Gordon, and G. C. Walker, “Surface-enhanced Raman spectroscopy using lipid encapsulated plasmonic nanoparticles and J-aggregates to create locally enhanced electric fields,” J. Phys. Chem. C 117(4), 1879–1886 (2013).
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Nano Lett. (6)

X. Chen, C. Ciracì, D. R. Smith, and S. H. Oh, “Nanogap-enhanced infrared spectroscopy with template-stripped wafer-scale arrays of buried plasmonic cavities,” Nano Lett. 15(1), 107–113 (2015).
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G. Hajisalem, M. S. Nezami, and R. Gordon, “Probing the quantum tunneling limit of plasmonic enhancement by third harmonic generation,” Nano Lett. 14(11), 6651–6654 (2014).
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G. Hajisalem, M. S. Nezami, and R. Gordon, “Switchable Metal-Insulator Phase Transition Metamaterials,” Nano Lett. 17(5), 2940–2944 (2017).
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D. Yoo, N.-C. Nguyen, L. Martin-Moreno, D. A. Mohr, S. Carretero-Palacios, J. Shaver, J. Peraire, T. W. Ebbesen, and S.-H. Oh, “High-Throughput Fabrication of Resonant Metamaterials with Ultrasmall Coaxial Apertures via Atomic Layer Lithography,” Nano Lett. 16(3), 2040–2046 (2016).
[Crossref] [PubMed]

X. Chen, C. Ciracì, D. R. Smith, and S.-H. Oh, “Nanogap-Enhanced Infrared Spectroscopy with Template-Stripped Wafer-Scale Arrays of Buried Plasmonic Cavities,” Nano Lett. 15(1), 107–113 (2015).
[Crossref] [PubMed]

A. Stolz, J. Berthelot, M.-M. Mennemanteuil, G. Colas des Francs, L. Markey, V. Meunier, and A. Bouhelier, “Nonlinear Photon-Assisted Tunneling Transport in Optical Gap Antennas,” Nano Lett. 14(5), 2330–2338 (2014).
[Crossref] [PubMed]

Nat. Commun. (7)

X. Chen, H.-R. Park, M. Pelton, X. Piao, N. C. Lindquist, H. Im, Y. J. Kim, J. S. Ahn, K. J. Ahn, N. Park, D.-S. Kim, and S.-H. Oh, “Atomic layer lithography of wafer-scale nanogap arrays for extreme confinement of electromagnetic waves,” Nat. Commun. 4(1), 2361 (2013).
[Crossref] [PubMed]

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Figures (6)

Fig. 1
Fig. 1 The real and imaginary parts of the permittivity using the QCM with Drude parameters ωp, Ag = 8.9eV/ћ, γp, Ag = 1/(17 fs) and background permittivity of 1. r is the radial distance from the center of the nanoparticle (with radius 25 nm). The electric field intensity (normalized to the incident field intensity) is also shown, with a peak for the region where Re{ε} = 0. The ENZ region effectively localizes the field in this region and “cloaks” the nanoparticle [22–25].
Fig. 2
Fig. 2 Absorption density of sphere using the classical (bulk Drude) electromagnetic model (CEM) and quantum corrected model (QCM) accounting for spill out. R is the radius of nanoparticle. The classical model has no variation in the absorption density as a function of volume, as expected in the quasi-static regime. The quantum corrected model shows reduced absorption from smaller spheres due to “cloaking” of the ENZ region, which has lower losses than the bulk region. Increased surface scattering can produce the opposite effect to what has been observed here.
Fig. 3
Fig. 3 Schematic of a metal slit with gap size d.
Fig. 4
Fig. 4 Electric field intensity versus x axis and wavelength for 3 different gap sizes: (a) and (d) 0.5 nm, (b) and (e) 0.6 nm, (c) and (f) 0.7 nm. The QCM has been used to achieve top row results (a, b, c), whereas CEM results are depicted in the bottom row (d, e, f).
Fig. 5
Fig. 5 Spatial distribution of electric field intensity in the gap for the gap size d = 0.5 nm region at resonance wavelength (λr = 555.569 nm), found with QCM FDTD simulation. The surface of gold is located at y = −20.
Fig. 6
Fig. 6 Comparison between quantum corrected model (QCM) simulated with FDTD and analytic expression.

Equations (9)

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ε= ε ω g 2 ω(ω+i γ g ) .
ω g (x)= ω p T(x) .
ε= ε ω p 2 | ψ(x) | 2 ω(ω+i γ g ) .
k= 2 m e * φ B 2 .
ψ(r)= e k(r r 0 ) .
1 V 1 2 Im{ε(r)} | E (r,θ) | 2 r 2 sinθdrdθdϕ .
ψ(x)= cosh(kx) cosh(k d 2 ) .
ω r 2 = ω p 2 ε cos h 2 (k d 2 ) .
λ r = 2πc ω p ε cosh(k d 2 ).

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