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

1. Introduction

The ultimate limits of plasmonic enhancement have been considered in terms of non-local effects and quantum tunneling. The non-local effects caused by the Thomas-Fermi pressure term have been theorized to reduce the plasmonic shift in small gaps (and also the local field enhancement) [1]; however, two experimental works have found that local models are sufficient in this regime [2,3]. Time-dependent density functional theory simulations have shown that the electron spill-out with screening actually produces an effectively smaller gap, and so the plasmon shift is opposite to that predicted by the non-local model [4].

Separate from the non-local effects, tunneling has been postulated to reduce the gap plasmon enhancement for very small gaps by shunting out the gap. Linear spectra [5], third harmonic generation [6] and surface-enhanced Raman spectroscopy (SERS) [7] have shown an abrupt transition at the onset of tunneling. A quantum corrected model (QCM) was proposed to describe this effect [8,9]. Initially, the QCM modified the scattering rate in the Drude model, however, this was revised to modify the plasma frequency [6,10]. The physical basis for this revised model is that the carrier density is reduced away from the metal as the electron wave function decays.

A recent work has shown that including this model in gap plasmons results in increased absorption [11], which bares similarity to experimental reports [12–14]. This comes as a result of the localization of the field in the epsilon near zero (ENZ) region of gaps. ENZ has been studied in detail for field enhancement properties, as well as “supercoupling” [15] and large nonlinear responses [16–19]. Previously, it has been shown in experiment that ENZ materials can enhance the local field and thereby increase SERS significantly [20,21].

In this work, we consider the impact of the quantum plasmonic ENZ in metal nanostructures. We treat field enhancement and the resultant absorption from nanoparticles that arise due to ENZ regions within the QCM model. Surprisingly, our calculations show that the absorption density decreases due to “cloaking” in the ENZ region. These results are similar to “ENZ cloaking”, which has been reported previously [22–25]. On the other hand, the enhanced losses were observed in small metal nanoparticles and have been attributed to “surface scattering” [26,27]. We find an analytic expression for the quantum corrected plasmonic resonance wavelength as a function of gap size, which agrees with the maximum field enhancement in a QCM finite-difference time-domain simulation. These results are applicable for finding regimes of enhanced Raman from small gap structures—the optimal sizes for different wavelengths are produced in this work.

2. Quantum Corrected Model Revisited

For modeling a sub-nanometer metal gap filled with a self-assembled monolayer (SAM) and for nanoparticles, we used the QCM, which considers an effective conductive material to mimic the electron tunneling in the gap region [8,9] or the electron spill-out in the region around the nanoparticle. Using an effective Drude model, the permittivity in the QCM region is:

ε=εωg2ω(ω+iγg).
where ε is the background permittivity, ωg and γg are plasma frequency and damping parameter (collision frequency), of this effective material. γg can be estimated as equal to the damping frequency of the metal, γp.

In the past, we have considered that ωg can be modified to be [6,10]:

ωg(x)=ωpT(x).
where ωp is the plasmon frequency of the metal and T(x) is the electron tunneling probability at distance x from the center of the gap. Here, instead of T(x), we use the probability of finding electron, which is the square of the normalized electron wave function, |ψ(x)|2. As a result, the revised formula for the permittivity inside the gap region may be written as a following:
ε=εωp2|ψ(x)|2ω(ω+iγg).
For finding background permittivity, we use the background permittivity of the material adjacent to the metal. In particular, spill-out of bound electrons is not considered because their wave functions decay much faster. Finally, it should be mention that ψ(x) depends on k which is given as:
k=2me*φB2.
where m*e is the effective mass of electrons in the metal and φB is the barrier height. In vacuum, the barrier height is equal to the work function [28]. When the gap is filled with a dielectric like SAM, we use the barrier height between the metal and the dielectric inside the gap instead of using the work function of the metal [29,30].

3. Nanoparticle Calculations

Silver nanoparticles were calculated using a quasi-static model in MATLAB. The 0.5 nm region outside of the nanoparticle consisted of 106 layers of Drude model materials. Drude parameters for silver (ωp, Ag = 8.9eV/ћ = 1.35215 × 1016 rad/s and γp, Ag = 1/(17 fs) = 5.88235 × 1013 rad/s) were taken from Ref [31]. We chose the background permittivity of ε = 1. The work function of silver, which is the barrier height here, is 4.5 eV [32]. The background permittivity was assumed to terminate at the edge of the silver region—the rationale for this is that the deeply bound electrons will spill out much less, and so their influence is negligible.

For electron spill-out around a nanoparticle, the approximate dependence of the wave function is given by:

ψ(r)=ek(rr0).
where r0 is the radius of the nanoparticle. This gives an ENZ region for the nanoparticles where Re{ε} = 0. As a result, the field will be concentrated in this region, which is expected to have significant impact on the scattering results. A quasi-static model is used to solve for the field around the nanoparticle, matching the constant and dipole fields in each region with sub-picometer steps to ensure convergence.

Figure 1 shows the localization of the electric field around the region where Re{ε} = 0. The field is normalized to the incident plane wave value showing an intensity enhancement of 20 million for silver in a very narrow region. The imaginary part of the permittivity at this position is reduced from the value inside the metal due to the reduced electron density in the spill-out region. Therefore, the overall losses actually go down within this model.

 figure: 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].

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Figure 2 shows the absorption density given by:

1V12Im{ε(r)}|E(r,θ)|2r2sinθdrdθdϕ.
where V is the volume of nanoparticle, E is the electric field, r, θ, and ϕ are spherical coordinates. The values are normalized to the absorption density of the classical model in the quasi-static regime for the same incident field. It is a surprising result that the absorption density actually decreases due to cloaking from the ENZ region. This is contrary to the recent report on QCM absorption in grooves [11]. In that work, the absorption in the taper is enhanced by the quantum corrected formulation; however, for the spherical geometry considered here, the absorption is reduced. Further investigation is required to explore this effect since we have assumed that the scattering is the same as the bulk value. In other works, it has been shown that surface scattering values can be higher than the bulk [26,27].

 figure: 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.

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It is also interesting to note that the ENZ region gives a very thin slice of extremely enhanced field. This may create larger interactions with molecules confined at the surface, for example, to increase their Raman cross section. Studies on Raman of self-assembled monolayer (SAM) have typically followed the expected quasi-static near-field dependence; however, one work showed an elevated signal with respect to theory for the molecular vibration closest to the surface [33]. This warrants further experimental investigation to determine if the field localization (and gradient of field) is playing a role in this regime.

4. Gap Calculations

We simulated the metal sub-nanometer gap in 2D using the finite-difference time-domain (FDTD) numerical software, Lumerical Solutions Inc., release 2017b, version 8.18.1365. A single Drude model material was used to model two gold rectangles (70 nm × 80 nm) with the background permittivity of 1 and using the plasma and collision frequencies of gold (ωp, Au = 1.3713 × 1016 rad/s and γp, Au = 4.05 × 1013 rad/s) from Ref [34]. and the effective mass of electrons in gold (m*e, Au ≃ 1.1 me) from Refs [35,36]. Different gap sizes in the range of 0.2 to 1 nm were simulated. In the classical electromagnetic model (CEM), the SAM was assumed to have a refractive index of 1.5.

In quantum corrected model (QCM), the gap region was modeled with layers of Drude model materials, each with thickness equal to the size of the mesh and permittivity calculated from Eqs. (3) with the background permittivity of ε = 2.25. The barrier height between the metal and SAM inside the gap was considered as φB = 1.5 eV [29,30]. We chose uniform mesh type with staircase mesh refinement. The mesh size was set to 0.00625 nm in x direction and 0.2 nm in y direction. The FDTD simulation region had the length of 24 nm in x direction (from −12 nm to 12 nm, with x = 0 in the center of gap) and the length of 25 nm in y direction (from 5 nm distance from gold surface to 20 nm inside the gold and gap regions). However, our monitor geometry was 2 nm × 13 nm. We used a y-polarized plane wave source with wavelength range from 500 to 1200 nm, located 4 nm away from the gold surface. The monitor collected the data for 100 wavelength points. Furthermore, we set time stability factor to 0.99 and auto shutoff to 1 × 10−5.

A 1-D approximation to the wave function in the gap is given as:

ψ(x)=cosh(kx)cosh(kd2).
where x is the distance from the center of the gap and d is the gap size [Fig. 3]. Equation (7) was plugged into Eq. (3) in this simulation.

 figure: Fig. 3

Fig. 3 Schematic of a metal slit with gap size d.

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Figure 4 shows the simulation results of electric field intensity for different gaps in QCM and CEM conditions. Figure 5 depicts spatial distribution of electric field intensity in the gap of d = 0.5 nm for QCM FDTD simulation as an example.

 figure: 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).

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 figure: 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.

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5. Discussion

As can be seen in Fig. 4 and 5, QCM results shows enhancement of electric field in the center of gap, which is 20 times larger than CEM results. We attribute this field enhancement to the tunneling on ENZ in the gap region. The enhancement of field in gaps and its application such as surface-enhanced Raman spectroscopy (SERS) [20,21], surface-enhanced infrared absorption (SEIRA) [37,38], terahertz structures [39–41] and optical gap antenna [42,43] were realized experimentally by using either SAM [2,6,10], Al2O3 deposited by atomic layer deposition (ALD) [39–41,44–47], or graphene [39] as the spacer in the nanometer gap.

The effect of the tunneling on ENZ in gaps leads to field enhancement. For finding an analytic expression for the quantum corrected plasmonic resonance wavelength as a function of gap size, Eqs. (3) and (7) can be used. Considering Re(ε) = 0 at the center of the gap (x = 0) and knowing γp2 << ω2, the resonance frequency ωr and resonance wavelength λr as a function of gap size d are given by:

ωr2=ωp2εcosh2(kd2).
λr=2πcωpεcosh(kd2).
Figure 6 depicts the wavelength at which the maximum enhancement occurs (resonance wavelength λr), predicted by Eq. (8b) and QCM simulation, versus gap size d. As can be seen in Fig. 6, the simple expression of Eq. (8b) is in good agreement with the FDTD QCM simulation, which confirms this basic physical interpretation.

 figure: Fig. 6

Fig. 6 Comparison between quantum corrected model (QCM) simulated with FDTD and analytic expression.

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6. Conclusions

We used a modified version of QCM to investigate the quantum plasmonic epsilon near zero phenomena for nanoparticles and slits. Our calculations show that the electron spill-out will yield both cloaking and field enhancement due to the real part of the permittivity going through zero in the QCM. We found an analytic expression for the quantum corrected plasmonic resonance wavelength as a function of gap size using Re{ε} = 0. This analytic expression and QCM FDTD simulations for slits agree, and the results may be tested with future experimental works using field enhancements in slits from ALD or SAMs as probed by harmonic generation or Raman scattering.

Funding

Natural Sciences and Engineering Research Council of Canada Discovery Grant.

References and links

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References

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  1. 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]
  2. 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]
  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).
    [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).
    [Crossref] [PubMed]
  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).
    [Crossref] [PubMed]
  6. 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]
  7. 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]
  8. 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]
  9. 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]
  10. G. Hajisalem, M. S. Nezami, and R. Gordon, “Switchable Metal-Insulator Phase Transition Metamaterials,” Nano Lett. 17(5), 2940–2944 (2017).
    [Crossref] [PubMed]
  11. 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]
  12. T. Søndergaard and S. I. Bozhevolnyi, “Optics of a single ultrasharp groove in metal,” Opt. Lett. 41(13), 2903–2906 (2016).
    [Crossref] [PubMed]
  13. 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]
  14. 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]
  15. I. Liberal and N. Engheta, “Near-zero refractive index photonics,” Nat. Photonics 11(3), 149–158 (2017).
    [Crossref]
  16. 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]
  17. 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]
  18. 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]
  19. 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]
  20. 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]
  21. 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]
  22. S. Hrabar, I. Krois, and A. Kiricenko, “Towards active dispersionless ENZ metamaterial for cloaking applications,” Metamaterials (Amst.) 4(2-3), 89–97 (2010).
    [Crossref]
  23. 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]
  24. 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]
  25. 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]
  26. U. Kreibig and C. Fragstein, “The limitation of electron mean free path in small silver particles,” Z. Phys. 224(4), 307–323 (1969).
    [Crossref]
  27. 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]
  28. 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]
  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]
  31. 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]
  32. 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]
  33. 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]
  34. M. A. Ordal, R. J. Bell, R. W. Alexander, L. L. Long, and M. R. Querry, “Optical properties of fourteen metals in the infrared and far infrared: Al, Co, Cu, Au, Fe, Pb, Mo, Ni, Pd, Pt, Ag, Ti, V, and W,” Appl. Opt. 24(24), 4493 (1985).
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  35. 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]
  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]
  37. 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]
  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]
  39. 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]
  40. 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]
  41. 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]
  42. 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]
  43. 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]
  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)

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]

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]

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)

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]

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]

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

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]

2016 (7)

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

2012 (6)

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]

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]

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]

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. 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]

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.

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]

Ahn, J. S.

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, 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]

Ahn, K. J.

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]

Aizpurua, J.

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. 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]

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]

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]

Alam, M. Z.

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]

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]

Alexander, R. W.

Alù, A.

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]

Argyropoulos, C.

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]

Bachelier, G.

Bahk, Y.-M.

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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]

Pendry, J. B.

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]

Peraire, J.

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]

Piao, X.

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]

Pietrzyk, M.

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]

Pignataro, S.

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]

Pique, A.

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]

Querry, M. R.

Rai, P.

Raschke, M. B.

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]

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]

Reed, M. A.

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]

Rhie, J.

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]

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).
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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]

Roger, T.

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]

Rotermund, F.

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]

Salandrino, A.

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]

Savage, K. J.

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]

Scherman, O. A.

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]

Schulz, S. A.

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]

Shalaev, V. M.

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]

Shaver, J.

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]

Shelton, D.

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]

Sigle, D. O.

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]

Silveirinha, M. G.

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]

Singh, D. K.

Skjølstrup, E. J. H.

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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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]

Slovick, B.

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]

Smith, D. R.

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]

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]

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]

Søndergaard, T.

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]

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]

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

Song, M.

Stolz, A.

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]

Sundararaman, R.

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]

Sundheimer, M. L.

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]

Tan, S. F.

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).
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Teperik, T. V.

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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Trammell, S. A.

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]

Tucker, E.

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]

Upham, J.

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]

Urzhumov, Y.

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]

Vinogradov, A. P.

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).
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Walker, G. C.

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]

Walters, C. M.

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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Wang, W.

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

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).
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Wurtz, G. A.

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]

Yang, H. U.

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]

Yang, J. K. W.

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).
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Yoo, D.

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]

Zamecnik, C. R.

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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Zayats, A. V.

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).
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Zhu, W.

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).
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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]

Zouhdi, S.

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]

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).
[Crossref]

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).
[Crossref]

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).
[Crossref] [PubMed]

Appl. Opt. (1)

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

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).
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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)

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).
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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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Metamaterials (Amst.) (1)

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

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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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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

Nat. Photonics (2)

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

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]

Nature (1)

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]

Opt. Express (3)

Opt. Lett. (1)

Phys. Chem. Chem. Phys. (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]

Phys. Rev. B (6)

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).
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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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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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