Abstract

The influence of film thickness and the substrate’s refractive index on the surface mode at the superstrate is an important study step surrounding their propagation mechanisms. A single sub-wavelength slit perforating a thin metallic film is among the simplest of nanostructure capable of launching surface plasmon polaritons on their surrounding surfaces when excited by an incident field. Here, the impact of the substrate and the film thickness on surface waves is investigated. When the thickness of the film is comparable to its skin depth, SPP waves from the substrate penetrate the film and emerge from the superstrate, creating a superposition of two SPP waves that leads to a beat interference envelope with well-defined loci, which are the function of both the drive frequency and the dielectric constant of the substrate/superstrate. As the film thickness is reduced to the SPP’s penetration depth, surface waves from the optically denser dielectric/metal interface would dominate, leading to volume plasmons that propagate inside the film at optical frequencies. Interference of the periodic volume charge density with the incident field over the film creates charge bundles that are periodic in space and time.

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

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References

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2017 (2)

A. Djalalian-Assl, “Dipole emission to surface plasmon-coupled enhanced transmission in diamond substrates with nitrogen vacancy center- near the surface,” Photonics 4(4), 10 (2017).
[Crossref]

S. S. Borysov, R. M. Geilhufe, and A. V. Balatsky, “Organic materials database: an open-access online database for data mining,” PLoS One 12(2), e0171501 (2017).
[Crossref] [PubMed]

2012 (3)

F. Wilczek, “Quantum time crystals,” Phys. Rev. Lett. 109(16), 160401 (2012).
[Crossref] [PubMed]

A. Shapere and F. Wilczek, “Classical time crystals,” Phys. Rev. Lett. 109(16), 160402 (2012).
[Crossref] [PubMed]

L. M. Wang, L. X. Zhang, T. Seideman, and H. Petek, “Dynamics of coupled plasmon polariton wave packets excited at a subwavelength slit in optically thin metal films,” Phys. Rev. B Condens. Matter Mater. Phys. 86(16), 165408 (2012).
[Crossref]

2010 (1)

A. Y. Nikitin, F. J. García-Vidal, and L. Martín-Moreno, “Surface electromagnetic field radiated by a subwavelength hole in a metal film,” Phys. Rev. Lett. 105(7), 073902 (2010).
[Crossref] [PubMed]

2009 (6)

W. Chen, D. C. Abeysinghe, R. L. Nelson, and Q. Zhan, “Plasmonic lens made of multiple concentric metallic rings under radially polarized illumination,” Nano Lett. 9(12), 4320–4325 (2009).
[Crossref] [PubMed]

T. J. Davis, “Surface plasmon modes in multi-layer thin-films,” Opt. Commun. 282(1), 135–140 (2009).
[Crossref]

P. Berini, “Long-range surface plasmon polaritons,” Adv. Opt. Photonics 1(3), 484–588 (2009).
[Crossref]

R. Ortuño, C. Garcia-Meca, F. J. Rodriguez-Fortuno, J. Marti, and A. Martinez, “Role of surface plasmon polaritons on optical transmission through double layer metallic hole arrays,” Phys. Rev. B Condens. Matter Mater. Phys. 79(7), 075425 (2009).
[Crossref]

K. Y. Han, K. I. Willig, E. Rittweger, F. Jelezko, C. Eggeling, and S. W. Hell, “Three-dimensional stimulated emission depletion microscopy of nitrogen-vacancy centers in diamond using continuous-wave light,” Nano Lett. 9(9), 3323–3329 (2009).
[Crossref] [PubMed]

W. Dai and C. M. Soukoulis, “Theoretical analysis of the surface wave along a metal-dielectric interface,” Phys. Rev. B Condens. Matter Mater. Phys. 80(15), 155407 (2009).
[Crossref]

2008 (2)

E. Verhagen, J. A. Dionne, L. K. Kuipers, H. A. Atwater, and A. Polman, “Near-field visualization of strongly confined surface plasmon polaritons in metal-insulator-metal waveguides,” Nano Lett. 8(9), 2925–2929 (2008).
[Crossref] [PubMed]

B. A. Fairchild, P. Olivero, S. Rubanov, A. D. Greentree, F. Waldermann, R. A. Taylor, I. Walmsley, J. M. Smith, S. Huntington, B. C. Gibson, D. N. Jamieson, and S. Prawer, “Fabrication of ultrathin single-crystal diamond membranes,” Adv. Mater. 20(24), 4793–4798 (2008).
[Crossref]

2007 (1)

Y. Fu, W. Zhou, L. E. N. Lim, C. L. Du, and X. G. Luo, “Plasmonic microzone plate: superfocusing at visible regime,” Appl. Phys. Lett. 91(6), 061124 (2007).
[Crossref]

2005 (1)

2004 (1)

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,” Phys. Rev. Lett. 92(10), 107401 (2004).
[Crossref] [PubMed]

2003 (2)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref] [PubMed]

A. V. Zayats and I. I. Smolyaninov, “Near-field photonics: surface plasmon polaritons and localized surface plasmons,” J. Opt. A, Pure Appl. Opt. 5(4), S16–S50 (2003).
[Crossref]

2000 (1)

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[Crossref] [PubMed]

1998 (1)

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[Crossref]

1997 (1)

A. Gruber, A. Drabenstedt, C. Tietz, L. Fleury, J. Wrachtrup, and C. vonBorczyskowski, “Scanning confocal optical microscopy and magnetic resonance on single defect centers,” Science 276(5321), 2012–2014 (1997).
[Crossref]

1964 (2)

H. R. Phillip and E. A. Taft, “Kramers-Kronig analysis of reflectance data for diamond,” Phys. Rev. A Gen. Phys. 136(5A), 1445 (1964).
[Crossref]

J. O. Linde, “The effective mass of the conduction electrons in metals and the theory of superconductivity,” Phys. Lett. 11(3), 199–201 (1964).
[Crossref]

Abeysinghe, D. C.

W. Chen, D. C. Abeysinghe, R. L. Nelson, and Q. Zhan, “Plasmonic lens made of multiple concentric metallic rings under radially polarized illumination,” Nano Lett. 9(12), 4320–4325 (2009).
[Crossref] [PubMed]

Atwater, H. A.

E. Verhagen, J. A. Dionne, L. K. Kuipers, H. A. Atwater, and A. Polman, “Near-field visualization of strongly confined surface plasmon polaritons in metal-insulator-metal waveguides,” Nano Lett. 8(9), 2925–2929 (2008).
[Crossref] [PubMed]

Balatsky, A. V.

S. S. Borysov, R. M. Geilhufe, and A. V. Balatsky, “Organic materials database: an open-access online database for data mining,” PLoS One 12(2), e0171501 (2017).
[Crossref] [PubMed]

Barnes, W. L.

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,” Phys. Rev. Lett. 92(10), 107401 (2004).
[Crossref] [PubMed]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref] [PubMed]

Berini, P.

P. Berini, “Long-range surface plasmon polaritons,” Adv. Opt. Photonics 1(3), 484–588 (2009).
[Crossref]

Borysov, S. S.

S. S. Borysov, R. M. Geilhufe, and A. V. Balatsky, “Organic materials database: an open-access online database for data mining,” PLoS One 12(2), e0171501 (2017).
[Crossref] [PubMed]

Chang, S. H.

Chen, W.

W. Chen, D. C. Abeysinghe, R. L. Nelson, and Q. Zhan, “Plasmonic lens made of multiple concentric metallic rings under radially polarized illumination,” Nano Lett. 9(12), 4320–4325 (2009).
[Crossref] [PubMed]

Dai, W.

W. Dai and C. M. Soukoulis, “Theoretical analysis of the surface wave along a metal-dielectric interface,” Phys. Rev. B Condens. Matter Mater. Phys. 80(15), 155407 (2009).
[Crossref]

Davis, T. J.

T. J. Davis, “Surface plasmon modes in multi-layer thin-films,” Opt. Commun. 282(1), 135–140 (2009).
[Crossref]

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref] [PubMed]

Devaux, E.

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,” Phys. Rev. Lett. 92(10), 107401 (2004).
[Crossref] [PubMed]

Dintinger, J.

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,” Phys. Rev. Lett. 92(10), 107401 (2004).
[Crossref] [PubMed]

Dionne, J. A.

E. Verhagen, J. A. Dionne, L. K. Kuipers, H. A. Atwater, and A. Polman, “Near-field visualization of strongly confined surface plasmon polaritons in metal-insulator-metal waveguides,” Nano Lett. 8(9), 2925–2929 (2008).
[Crossref] [PubMed]

Djalalian-Assl, A.

A. Djalalian-Assl, “Dipole emission to surface plasmon-coupled enhanced transmission in diamond substrates with nitrogen vacancy center- near the surface,” Photonics 4(4), 10 (2017).
[Crossref]

Drabenstedt, A.

A. Gruber, A. Drabenstedt, C. Tietz, L. Fleury, J. Wrachtrup, and C. vonBorczyskowski, “Scanning confocal optical microscopy and magnetic resonance on single defect centers,” Science 276(5321), 2012–2014 (1997).
[Crossref]

Du, C. L.

Y. Fu, W. Zhou, L. E. N. Lim, C. L. Du, and X. G. Luo, “Plasmonic microzone plate: superfocusing at visible regime,” Appl. Phys. Lett. 91(6), 061124 (2007).
[Crossref]

Ebbesen, T. W.

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,” Phys. Rev. Lett. 92(10), 107401 (2004).
[Crossref] [PubMed]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref] [PubMed]

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[Crossref]

Eggeling, C.

K. Y. Han, K. I. Willig, E. Rittweger, F. Jelezko, C. Eggeling, and S. W. Hell, “Three-dimensional stimulated emission depletion microscopy of nitrogen-vacancy centers in diamond using continuous-wave light,” Nano Lett. 9(9), 3323–3329 (2009).
[Crossref] [PubMed]

Fairchild, B. A.

B. A. Fairchild, P. Olivero, S. Rubanov, A. D. Greentree, F. Waldermann, R. A. Taylor, I. Walmsley, J. M. Smith, S. Huntington, B. C. Gibson, D. N. Jamieson, and S. Prawer, “Fabrication of ultrathin single-crystal diamond membranes,” Adv. Mater. 20(24), 4793–4798 (2008).
[Crossref]

Fleury, L.

A. Gruber, A. Drabenstedt, C. Tietz, L. Fleury, J. Wrachtrup, and C. vonBorczyskowski, “Scanning confocal optical microscopy and magnetic resonance on single defect centers,” Science 276(5321), 2012–2014 (1997).
[Crossref]

Fu, Y.

Y. Fu, W. Zhou, L. E. N. Lim, C. L. Du, and X. G. Luo, “Plasmonic microzone plate: superfocusing at visible regime,” Appl. Phys. Lett. 91(6), 061124 (2007).
[Crossref]

Garcia-Meca, C.

R. Ortuño, C. Garcia-Meca, F. J. Rodriguez-Fortuno, J. Marti, and A. Martinez, “Role of surface plasmon polaritons on optical transmission through double layer metallic hole arrays,” Phys. Rev. B Condens. Matter Mater. Phys. 79(7), 075425 (2009).
[Crossref]

García-Vidal, F. J.

A. Y. Nikitin, F. J. García-Vidal, and L. Martín-Moreno, “Surface electromagnetic field radiated by a subwavelength hole in a metal film,” Phys. Rev. Lett. 105(7), 073902 (2010).
[Crossref] [PubMed]

Geilhufe, R. M.

S. S. Borysov, R. M. Geilhufe, and A. V. Balatsky, “Organic materials database: an open-access online database for data mining,” PLoS One 12(2), e0171501 (2017).
[Crossref] [PubMed]

Ghaemi, H. F.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[Crossref]

Gibson, B. C.

B. A. Fairchild, P. Olivero, S. Rubanov, A. D. Greentree, F. Waldermann, R. A. Taylor, I. Walmsley, J. M. Smith, S. Huntington, B. C. Gibson, D. N. Jamieson, and S. Prawer, “Fabrication of ultrathin single-crystal diamond membranes,” Adv. Mater. 20(24), 4793–4798 (2008).
[Crossref]

Gray, S.

Greentree, A. D.

B. A. Fairchild, P. Olivero, S. Rubanov, A. D. Greentree, F. Waldermann, R. A. Taylor, I. Walmsley, J. M. Smith, S. Huntington, B. C. Gibson, D. N. Jamieson, and S. Prawer, “Fabrication of ultrathin single-crystal diamond membranes,” Adv. Mater. 20(24), 4793–4798 (2008).
[Crossref]

Gruber, A.

A. Gruber, A. Drabenstedt, C. Tietz, L. Fleury, J. Wrachtrup, and C. vonBorczyskowski, “Scanning confocal optical microscopy and magnetic resonance on single defect centers,” Science 276(5321), 2012–2014 (1997).
[Crossref]

Han, K. Y.

K. Y. Han, K. I. Willig, E. Rittweger, F. Jelezko, C. Eggeling, and S. W. Hell, “Three-dimensional stimulated emission depletion microscopy of nitrogen-vacancy centers in diamond using continuous-wave light,” Nano Lett. 9(9), 3323–3329 (2009).
[Crossref] [PubMed]

Hell, S. W.

K. Y. Han, K. I. Willig, E. Rittweger, F. Jelezko, C. Eggeling, and S. W. Hell, “Three-dimensional stimulated emission depletion microscopy of nitrogen-vacancy centers in diamond using continuous-wave light,” Nano Lett. 9(9), 3323–3329 (2009).
[Crossref] [PubMed]

Huntington, S.

B. A. Fairchild, P. Olivero, S. Rubanov, A. D. Greentree, F. Waldermann, R. A. Taylor, I. Walmsley, J. M. Smith, S. Huntington, B. C. Gibson, D. N. Jamieson, and S. Prawer, “Fabrication of ultrathin single-crystal diamond membranes,” Adv. Mater. 20(24), 4793–4798 (2008).
[Crossref]

Jamieson, D. N.

B. A. Fairchild, P. Olivero, S. Rubanov, A. D. Greentree, F. Waldermann, R. A. Taylor, I. Walmsley, J. M. Smith, S. Huntington, B. C. Gibson, D. N. Jamieson, and S. Prawer, “Fabrication of ultrathin single-crystal diamond membranes,” Adv. Mater. 20(24), 4793–4798 (2008).
[Crossref]

Jelezko, F.

K. Y. Han, K. I. Willig, E. Rittweger, F. Jelezko, C. Eggeling, and S. W. Hell, “Three-dimensional stimulated emission depletion microscopy of nitrogen-vacancy centers in diamond using continuous-wave light,” Nano Lett. 9(9), 3323–3329 (2009).
[Crossref] [PubMed]

Kuipers, L. K.

E. Verhagen, J. A. Dionne, L. K. Kuipers, H. A. Atwater, and A. Polman, “Near-field visualization of strongly confined surface plasmon polaritons in metal-insulator-metal waveguides,” Nano Lett. 8(9), 2925–2929 (2008).
[Crossref] [PubMed]

Lezec, H. J.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[Crossref]

Lim, L. E. N.

Y. Fu, W. Zhou, L. E. N. Lim, C. L. Du, and X. G. Luo, “Plasmonic microzone plate: superfocusing at visible regime,” Appl. Phys. Lett. 91(6), 061124 (2007).
[Crossref]

Linde, J. O.

J. O. Linde, “The effective mass of the conduction electrons in metals and the theory of superconductivity,” Phys. Lett. 11(3), 199–201 (1964).
[Crossref]

Luo, X. G.

Y. Fu, W. Zhou, L. E. N. Lim, C. L. Du, and X. G. Luo, “Plasmonic microzone plate: superfocusing at visible regime,” Appl. Phys. Lett. 91(6), 061124 (2007).
[Crossref]

Marti, J.

R. Ortuño, C. Garcia-Meca, F. J. Rodriguez-Fortuno, J. Marti, and A. Martinez, “Role of surface plasmon polaritons on optical transmission through double layer metallic hole arrays,” Phys. Rev. B Condens. Matter Mater. Phys. 79(7), 075425 (2009).
[Crossref]

Martinez, A.

R. Ortuño, C. Garcia-Meca, F. J. Rodriguez-Fortuno, J. Marti, and A. Martinez, “Role of surface plasmon polaritons on optical transmission through double layer metallic hole arrays,” Phys. Rev. B Condens. Matter Mater. Phys. 79(7), 075425 (2009).
[Crossref]

Martín-Moreno, L.

A. Y. Nikitin, F. J. García-Vidal, and L. Martín-Moreno, “Surface electromagnetic field radiated by a subwavelength hole in a metal film,” Phys. Rev. Lett. 105(7), 073902 (2010).
[Crossref] [PubMed]

Murray, W. A.

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,” Phys. Rev. Lett. 92(10), 107401 (2004).
[Crossref] [PubMed]

Nelson, R. L.

W. Chen, D. C. Abeysinghe, R. L. Nelson, and Q. Zhan, “Plasmonic lens made of multiple concentric metallic rings under radially polarized illumination,” Nano Lett. 9(12), 4320–4325 (2009).
[Crossref] [PubMed]

Nikitin, A. Y.

A. Y. Nikitin, F. J. García-Vidal, and L. Martín-Moreno, “Surface electromagnetic field radiated by a subwavelength hole in a metal film,” Phys. Rev. Lett. 105(7), 073902 (2010).
[Crossref] [PubMed]

Olivero, P.

B. A. Fairchild, P. Olivero, S. Rubanov, A. D. Greentree, F. Waldermann, R. A. Taylor, I. Walmsley, J. M. Smith, S. Huntington, B. C. Gibson, D. N. Jamieson, and S. Prawer, “Fabrication of ultrathin single-crystal diamond membranes,” Adv. Mater. 20(24), 4793–4798 (2008).
[Crossref]

Ortuño, R.

R. Ortuño, C. Garcia-Meca, F. J. Rodriguez-Fortuno, J. Marti, and A. Martinez, “Role of surface plasmon polaritons on optical transmission through double layer metallic hole arrays,” Phys. Rev. B Condens. Matter Mater. Phys. 79(7), 075425 (2009).
[Crossref]

Pendry, J. B.

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[Crossref] [PubMed]

Petek, H.

L. M. Wang, L. X. Zhang, T. Seideman, and H. Petek, “Dynamics of coupled plasmon polariton wave packets excited at a subwavelength slit in optically thin metal films,” Phys. Rev. B Condens. Matter Mater. Phys. 86(16), 165408 (2012).
[Crossref]

Phillip, H. R.

H. R. Phillip and E. A. Taft, “Kramers-Kronig analysis of reflectance data for diamond,” Phys. Rev. A Gen. Phys. 136(5A), 1445 (1964).
[Crossref]

Polman, A.

E. Verhagen, J. A. Dionne, L. K. Kuipers, H. A. Atwater, and A. Polman, “Near-field visualization of strongly confined surface plasmon polaritons in metal-insulator-metal waveguides,” Nano Lett. 8(9), 2925–2929 (2008).
[Crossref] [PubMed]

Prawer, S.

B. A. Fairchild, P. Olivero, S. Rubanov, A. D. Greentree, F. Waldermann, R. A. Taylor, I. Walmsley, J. M. Smith, S. Huntington, B. C. Gibson, D. N. Jamieson, and S. Prawer, “Fabrication of ultrathin single-crystal diamond membranes,” Adv. Mater. 20(24), 4793–4798 (2008).
[Crossref]

Rittweger, E.

K. Y. Han, K. I. Willig, E. Rittweger, F. Jelezko, C. Eggeling, and S. W. Hell, “Three-dimensional stimulated emission depletion microscopy of nitrogen-vacancy centers in diamond using continuous-wave light,” Nano Lett. 9(9), 3323–3329 (2009).
[Crossref] [PubMed]

Rodriguez-Fortuno, F. J.

R. Ortuño, C. Garcia-Meca, F. J. Rodriguez-Fortuno, J. Marti, and A. Martinez, “Role of surface plasmon polaritons on optical transmission through double layer metallic hole arrays,” Phys. Rev. B Condens. Matter Mater. Phys. 79(7), 075425 (2009).
[Crossref]

Rubanov, S.

B. A. Fairchild, P. Olivero, S. Rubanov, A. D. Greentree, F. Waldermann, R. A. Taylor, I. Walmsley, J. M. Smith, S. Huntington, B. C. Gibson, D. N. Jamieson, and S. Prawer, “Fabrication of ultrathin single-crystal diamond membranes,” Adv. Mater. 20(24), 4793–4798 (2008).
[Crossref]

Schatz, G.

Seideman, T.

L. M. Wang, L. X. Zhang, T. Seideman, and H. Petek, “Dynamics of coupled plasmon polariton wave packets excited at a subwavelength slit in optically thin metal films,” Phys. Rev. B Condens. Matter Mater. Phys. 86(16), 165408 (2012).
[Crossref]

Shapere, A.

A. Shapere and F. Wilczek, “Classical time crystals,” Phys. Rev. Lett. 109(16), 160402 (2012).
[Crossref] [PubMed]

Smith, J. M.

B. A. Fairchild, P. Olivero, S. Rubanov, A. D. Greentree, F. Waldermann, R. A. Taylor, I. Walmsley, J. M. Smith, S. Huntington, B. C. Gibson, D. N. Jamieson, and S. Prawer, “Fabrication of ultrathin single-crystal diamond membranes,” Adv. Mater. 20(24), 4793–4798 (2008).
[Crossref]

Smolyaninov, I. I.

A. V. Zayats and I. I. Smolyaninov, “Near-field photonics: surface plasmon polaritons and localized surface plasmons,” J. Opt. A, Pure Appl. Opt. 5(4), S16–S50 (2003).
[Crossref]

Soukoulis, C. M.

W. Dai and C. M. Soukoulis, “Theoretical analysis of the surface wave along a metal-dielectric interface,” Phys. Rev. B Condens. Matter Mater. Phys. 80(15), 155407 (2009).
[Crossref]

Taft, E. A.

H. R. Phillip and E. A. Taft, “Kramers-Kronig analysis of reflectance data for diamond,” Phys. Rev. A Gen. Phys. 136(5A), 1445 (1964).
[Crossref]

Taylor, R. A.

B. A. Fairchild, P. Olivero, S. Rubanov, A. D. Greentree, F. Waldermann, R. A. Taylor, I. Walmsley, J. M. Smith, S. Huntington, B. C. Gibson, D. N. Jamieson, and S. Prawer, “Fabrication of ultrathin single-crystal diamond membranes,” Adv. Mater. 20(24), 4793–4798 (2008).
[Crossref]

Thio, T.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[Crossref]

Tietz, C.

A. Gruber, A. Drabenstedt, C. Tietz, L. Fleury, J. Wrachtrup, and C. vonBorczyskowski, “Scanning confocal optical microscopy and magnetic resonance on single defect centers,” Science 276(5321), 2012–2014 (1997).
[Crossref]

Verhagen, E.

E. Verhagen, J. A. Dionne, L. K. Kuipers, H. A. Atwater, and A. Polman, “Near-field visualization of strongly confined surface plasmon polaritons in metal-insulator-metal waveguides,” Nano Lett. 8(9), 2925–2929 (2008).
[Crossref] [PubMed]

vonBorczyskowski, C.

A. Gruber, A. Drabenstedt, C. Tietz, L. Fleury, J. Wrachtrup, and C. vonBorczyskowski, “Scanning confocal optical microscopy and magnetic resonance on single defect centers,” Science 276(5321), 2012–2014 (1997).
[Crossref]

Waldermann, F.

B. A. Fairchild, P. Olivero, S. Rubanov, A. D. Greentree, F. Waldermann, R. A. Taylor, I. Walmsley, J. M. Smith, S. Huntington, B. C. Gibson, D. N. Jamieson, and S. Prawer, “Fabrication of ultrathin single-crystal diamond membranes,” Adv. Mater. 20(24), 4793–4798 (2008).
[Crossref]

Walmsley, I.

B. A. Fairchild, P. Olivero, S. Rubanov, A. D. Greentree, F. Waldermann, R. A. Taylor, I. Walmsley, J. M. Smith, S. Huntington, B. C. Gibson, D. N. Jamieson, and S. Prawer, “Fabrication of ultrathin single-crystal diamond membranes,” Adv. Mater. 20(24), 4793–4798 (2008).
[Crossref]

Wang, L. M.

L. M. Wang, L. X. Zhang, T. Seideman, and H. Petek, “Dynamics of coupled plasmon polariton wave packets excited at a subwavelength slit in optically thin metal films,” Phys. Rev. B Condens. Matter Mater. Phys. 86(16), 165408 (2012).
[Crossref]

Wilczek, F.

A. Shapere and F. Wilczek, “Classical time crystals,” Phys. Rev. Lett. 109(16), 160402 (2012).
[Crossref] [PubMed]

F. Wilczek, “Quantum time crystals,” Phys. Rev. Lett. 109(16), 160401 (2012).
[Crossref] [PubMed]

Willig, K. I.

K. Y. Han, K. I. Willig, E. Rittweger, F. Jelezko, C. Eggeling, and S. W. Hell, “Three-dimensional stimulated emission depletion microscopy of nitrogen-vacancy centers in diamond using continuous-wave light,” Nano Lett. 9(9), 3323–3329 (2009).
[Crossref] [PubMed]

Wolff, P. A.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[Crossref]

Wrachtrup, J.

A. Gruber, A. Drabenstedt, C. Tietz, L. Fleury, J. Wrachtrup, and C. vonBorczyskowski, “Scanning confocal optical microscopy and magnetic resonance on single defect centers,” Science 276(5321), 2012–2014 (1997).
[Crossref]

Zayats, A. V.

A. V. Zayats and I. I. Smolyaninov, “Near-field photonics: surface plasmon polaritons and localized surface plasmons,” J. Opt. A, Pure Appl. Opt. 5(4), S16–S50 (2003).
[Crossref]

Zhan, Q.

W. Chen, D. C. Abeysinghe, R. L. Nelson, and Q. Zhan, “Plasmonic lens made of multiple concentric metallic rings under radially polarized illumination,” Nano Lett. 9(12), 4320–4325 (2009).
[Crossref] [PubMed]

Zhang, L. X.

L. M. Wang, L. X. Zhang, T. Seideman, and H. Petek, “Dynamics of coupled plasmon polariton wave packets excited at a subwavelength slit in optically thin metal films,” Phys. Rev. B Condens. Matter Mater. Phys. 86(16), 165408 (2012).
[Crossref]

Zhou, W.

Y. Fu, W. Zhou, L. E. N. Lim, C. L. Du, and X. G. Luo, “Plasmonic microzone plate: superfocusing at visible regime,” Appl. Phys. Lett. 91(6), 061124 (2007).
[Crossref]

Adv. Mater. (1)

B. A. Fairchild, P. Olivero, S. Rubanov, A. D. Greentree, F. Waldermann, R. A. Taylor, I. Walmsley, J. M. Smith, S. Huntington, B. C. Gibson, D. N. Jamieson, and S. Prawer, “Fabrication of ultrathin single-crystal diamond membranes,” Adv. Mater. 20(24), 4793–4798 (2008).
[Crossref]

Adv. Opt. Photonics (1)

P. Berini, “Long-range surface plasmon polaritons,” Adv. Opt. Photonics 1(3), 484–588 (2009).
[Crossref]

Appl. Phys. Lett. (1)

Y. Fu, W. Zhou, L. E. N. Lim, C. L. Du, and X. G. Luo, “Plasmonic microzone plate: superfocusing at visible regime,” Appl. Phys. Lett. 91(6), 061124 (2007).
[Crossref]

J. Opt. A, Pure Appl. Opt. (1)

A. V. Zayats and I. I. Smolyaninov, “Near-field photonics: surface plasmon polaritons and localized surface plasmons,” J. Opt. A, Pure Appl. Opt. 5(4), S16–S50 (2003).
[Crossref]

Nano Lett. (3)

K. Y. Han, K. I. Willig, E. Rittweger, F. Jelezko, C. Eggeling, and S. W. Hell, “Three-dimensional stimulated emission depletion microscopy of nitrogen-vacancy centers in diamond using continuous-wave light,” Nano Lett. 9(9), 3323–3329 (2009).
[Crossref] [PubMed]

E. Verhagen, J. A. Dionne, L. K. Kuipers, H. A. Atwater, and A. Polman, “Near-field visualization of strongly confined surface plasmon polaritons in metal-insulator-metal waveguides,” Nano Lett. 8(9), 2925–2929 (2008).
[Crossref] [PubMed]

W. Chen, D. C. Abeysinghe, R. L. Nelson, and Q. Zhan, “Plasmonic lens made of multiple concentric metallic rings under radially polarized illumination,” Nano Lett. 9(12), 4320–4325 (2009).
[Crossref] [PubMed]

Nature (2)

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391(6668), 667–669 (1998).
[Crossref]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003).
[Crossref] [PubMed]

Opt. Commun. (1)

T. J. Davis, “Surface plasmon modes in multi-layer thin-films,” Opt. Commun. 282(1), 135–140 (2009).
[Crossref]

Opt. Express (1)

Photonics (1)

A. Djalalian-Assl, “Dipole emission to surface plasmon-coupled enhanced transmission in diamond substrates with nitrogen vacancy center- near the surface,” Photonics 4(4), 10 (2017).
[Crossref]

Phys. Lett. (1)

J. O. Linde, “The effective mass of the conduction electrons in metals and the theory of superconductivity,” Phys. Lett. 11(3), 199–201 (1964).
[Crossref]

Phys. Rev. A Gen. Phys. (1)

H. R. Phillip and E. A. Taft, “Kramers-Kronig analysis of reflectance data for diamond,” Phys. Rev. A Gen. Phys. 136(5A), 1445 (1964).
[Crossref]

Phys. Rev. B Condens. Matter Mater. Phys. (3)

W. Dai and C. M. Soukoulis, “Theoretical analysis of the surface wave along a metal-dielectric interface,” Phys. Rev. B Condens. Matter Mater. Phys. 80(15), 155407 (2009).
[Crossref]

L. M. Wang, L. X. Zhang, T. Seideman, and H. Petek, “Dynamics of coupled plasmon polariton wave packets excited at a subwavelength slit in optically thin metal films,” Phys. Rev. B Condens. Matter Mater. Phys. 86(16), 165408 (2012).
[Crossref]

R. Ortuño, C. Garcia-Meca, F. J. Rodriguez-Fortuno, J. Marti, and A. Martinez, “Role of surface plasmon polaritons on optical transmission through double layer metallic hole arrays,” Phys. Rev. B Condens. Matter Mater. Phys. 79(7), 075425 (2009).
[Crossref]

Phys. Rev. Lett. (5)

W. L. Barnes, W. A. Murray, J. Dintinger, E. Devaux, and T. W. Ebbesen, “Surface plasmon polaritons and their role in the enhanced transmission of light through periodic arrays of subwavelength holes in a metal film,” Phys. Rev. Lett. 92(10), 107401 (2004).
[Crossref] [PubMed]

A. Y. Nikitin, F. J. García-Vidal, and L. Martín-Moreno, “Surface electromagnetic field radiated by a subwavelength hole in a metal film,” Phys. Rev. Lett. 105(7), 073902 (2010).
[Crossref] [PubMed]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[Crossref] [PubMed]

F. Wilczek, “Quantum time crystals,” Phys. Rev. Lett. 109(16), 160401 (2012).
[Crossref] [PubMed]

A. Shapere and F. Wilczek, “Classical time crystals,” Phys. Rev. Lett. 109(16), 160402 (2012).
[Crossref] [PubMed]

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S. S. Borysov, R. M. Geilhufe, and A. V. Balatsky, “Organic materials database: an open-access online database for data mining,” PLoS One 12(2), e0171501 (2017).
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Science (1)

A. Gruber, A. Drabenstedt, C. Tietz, L. Fleury, J. Wrachtrup, and C. vonBorczyskowski, “Scanning confocal optical microscopy and magnetic resonance on single defect centers,” Science 276(5321), 2012–2014 (1997).
[Crossref]

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A. Djalalian-Assl, “Optical nano-antennas,” Ph.D. dissertation (University of Melbourne, 2015).

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J. H. Davies, The Physics of Low-Dimensional Semiconductors: An Introduction (Cambridge University Press, 1998), pp. xviii, 438p.

E. Hecht, Optics, 2nd ed. (Addison-Wesley, 1987).

Supplementary Material (1)

NameDescription
» Visualization 1       electric field Ex passing through a periodic charge screen (with periodicity 1/Kg) formed inside the 25 nm thick silver film .

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Figures (6)

Fig. 1
Fig. 1 Schematics for the model under investigation.
Fig. 2
Fig. 2 (a) Surface charge density, s (x, t0), at an arbitrary time t0, calculated at the air/silver and glass/silver interfaces. (b) The envelope, |s(x)|, at the air/silver interface. The corresponding FFT of (c) the wave ƒ[ σ( x, t 0 ) ] and (d) the envelope ƒ[ | σ( x ) | ] [1]. Λ and 1/Λ = KSPP are wavelength and wavenumber obtained from FFT respectively.
Fig. 3
Fig. 3 ƒ[ σ( x, t 0 ) ]and ƒ[ | σ( x ) | ] calculated for (a)-(b) h = 50 nm on glass substrate, (c)-(d) h = 25 nm on glass substrate and (e)-(f) h = 25 nm on diamond substrate. Note that subscript ‘g’ is used to label the substrate in general [1]. Λ and 1/Λ = KSPP are wavelength and wavenumber obtained from FFT respectively.
Fig. 4
Fig. 4 Surface charge densities, |s (x)|, over the air/silver surface for h = {100, 50, 25} on glass substrate, h = 25 nm on diamond substrate and for PEC [1].
Fig. 5
Fig. 5 |E|2 ´10(V/m)2 Diffraction patterns of a transmitted Gaussian beam through (a) 25 nm silver film perforated with a slit, supported on a diamond substrate. (b) same as (a) with the maximum intensity of the Gaussian beam displaced to x = 680 nm away from the center of the slit. (c) In the absence of the slit [1].
Fig. 6
Fig. 6 Snapshot of electric field Ex passing through a periodic charge screen (with periodicity 1/Kg) formed inside the 25 nm thick silver film for (a) glass and (b) diamond substrates. Note that Ex was calculated at an arbitrary time with the maximum of its amplitude falling over the silver film (Visualization 1) [1].

Equations (28)

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k SPP = ε m ε d ε m + ε d k k SPP +i k SPP
k m ε m 2 ε m + ε d k k m +i k m
σ( x,t )A e i( k a x ω 0 t ) ±B e i( k a x ω 0 t+mπ )
σ( x )=[ 2 e i( ( k a + k g )x 2 ) cos( ( k a k g )x 2 ) ]
Δ ρ x ( k g , ω 0 )= ω 0 c ε 0 ε m '' [ ε d + ε m ε m + ε d ] E zg e i( k g x ω 0 t )
ΔN( k g , ω 0 )= Δ ρ x e = ω 0 c e ε 0 ε m '' [ ε m + ε d ε m + ε d ] E zg e i( k g x ω 0 t )
E F ( k g , ω 0 )= 3 2/3 h 2 8m π 2/3 ( N 0 +ΔN ) 2/3
ω p ( k g , ω 0 )= ( N 0 +ΔN ) e 2 ε 0 m e
E xg ( x, t 0 ):+,0,,0,+ E xi ( t 0 ):+,+,+,+,+ +,+,0,+,+
E xg ( x, t 0 +T/2 ):,0,+,0, E xi ( t 0 +T/2 ):,,,, ,,0,,
ξ j (t) ψ j ( R j ,t )= H (t) ψ j ( R j ,t )
i ψ j ( R j ,t ) t = H (t) ψ j ( R j ,t )
H = j [ 2 2m j 2 +V( R j ) ] + 1 2 j,k jk e 2 4πε| R j R k |
H (t)= j [ 2 2m j 2 +V( R j (t) ) ] + 1 2 j,k jk e 2 4πε| R j (t) R k (t) |
Ψ( x,t )=2 e i( ( k 1 + k 2 )x 2 ( ω 1 + ω 2 )t 2 ) cos( ( k 1 k 2 )x 2 )cos( ( ω 1 ω 2 )t 2 )
[ 2π/( k 1 k 2 ) ]=[ 4π/( k 1 + k 2 ) ]
[ 2π/( ω 1 ω 2 ) ]=[ 4π/( ω 1 + ω 2 ) ]
σ( x,t )= e i ω 0 t [ C a e i( k a x ) + C δg e i( k g x ) ]
σ( x )=[ 2 e i( ( k a + k g )x 2 ) cos( ( k a k g )x 2 ) ]
1/2 k a =2π/| ( k a k g ) |=4π/( k a + k g )
B m =( 0, B y ,0 ) e i( k x x+ k z z ω 0 t )
E m =( E x ,0, E z ) e i( k x x+ k z z ω 0 t )
× E m =( x y z )×( E x 0 E z )=( y E z x E z + z E x y E x )
× E m =( 0 i k x E z +i k z E x 0 )
F x = σ m ω 0 [ k x + k z ( i ε m ε d ) ] E z 2
F x = ω 0 ε 0 ε m '' c [ ε m ε d +i ε m ε m ε d ε m + ε d ] E z 2
Δ ρ x = ω 0 c ε 0 ε m '' [ ε d + ε m ε m + ε d ] E z
ΔN= Δ ρ x e = ω 0 c e ε 0 ε m '' [ ε d + ε m ε m + ε d ] E z

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