Abstract

A normalized admittance diagram assists in describing and designing multilayered structures to excite long-range surface-plasmon-polariton (LRSPP) waves of either the p- or the s-polarization state. These structures comprise symmetric periodic multilayers on one or both sides of a metal thin film in either the Kretschmann or the Sarid configuration. The normalized admittance diagram even assists in designing structures that can be used to excite LRSPP waves of both polarization states simultaneously.

© 2009 Optical Society of America

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References

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  1. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer, 1983).
  2. D. Sarid, “Long-range surface-plasma waves on very thin metal films,” Phys. Rev. Lett. 47, 1927-1930 (1981).
    [CrossRef]
  3. C. R. Williams, S. R. Andrews, S. A. Maier, A. I. Fernández-Domínguez, L. Martín-Moreno, and F. J. García-Vidal, “Highly confined guiding of terahertz surface plasmon polaritons on structured metal surfaces,” Nat. Photonics. 2, 175-179 (2008).
    [CrossRef]
  4. R. F. Oulton, V. J. Sorger, D. A. Genov, D. F. P. Pile, and X. Zhang, “A hybrid plasmonic waveguide for subwavelength confinement and long-range propagation,” Nat. Photonics 2, 496-500 (2008).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  10. M. Takabayashi, M. Haraguchi, and M. Fukui, “Propagation length of guided waves in lossy Si film sandwiched by identical dielectrics,” J. Opt. Soc. Am. B 12, 2406-2411 (1995).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  14. M. A. Motyka and A. Lakhtakia, “Multiple trains of same-color surface plasmon-polaritons guided by the planar interface of a metal and a sculptured nematic thin film,” J. Nanophoton 2, 021910 (2008).
    [CrossRef]
  15. A. Lakhtakia, Y.-J. Jen, and C.-F. Lin, “Multiple trains of same-color surface plasmon-polaritons guided by the planar interface of a metal and a sculptured nematic thin film. Part III: Experimental evidence,” J. Nanophoton 3, 033506 (2009).
    [CrossRef]

2009 (1)

A. Lakhtakia, Y.-J. Jen, and C.-F. Lin, “Multiple trains of same-color surface plasmon-polaritons guided by the planar interface of a metal and a sculptured nematic thin film. Part III: Experimental evidence,” J. Nanophoton 3, 033506 (2009).
[CrossRef]

2008 (3)

M. A. Motyka and A. Lakhtakia, “Multiple trains of same-color surface plasmon-polaritons guided by the planar interface of a metal and a sculptured nematic thin film,” J. Nanophoton 2, 021910 (2008).
[CrossRef]

C. R. Williams, S. R. Andrews, S. A. Maier, A. I. Fernández-Domínguez, L. Martín-Moreno, and F. J. García-Vidal, “Highly confined guiding of terahertz surface plasmon polaritons on structured metal surfaces,” Nat. Photonics. 2, 175-179 (2008).
[CrossRef]

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

2007 (1)

2006 (1)

1999 (1)

1997 (1)

Z. Salamon, H. A. Macleod, and G. Tollin, “Coupled plasmon-waveguide resonators: A new spectroscopic tool for probing proteolipids film structure and properties,” Biophys. J. 73, 2791-2797 (1997).
[CrossRef] [PubMed]

1995 (1)

1991 (1)

F. Yang, J. R. Sambles, and G. W. Bradberry, “Long-range surface modes supported by thin films,” Phys. Rev. B 44, 5855-5872 (1991).
[CrossRef]

1983 (1)

1981 (1)

D. Sarid, “Long-range surface-plasma waves on very thin metal films,” Phys. Rev. Lett. 47, 1927-1930 (1981).
[CrossRef]

Adato, R.

Andrews, S. R.

C. R. Williams, S. R. Andrews, S. A. Maier, A. I. Fernández-Domínguez, L. Martín-Moreno, and F. J. García-Vidal, “Highly confined guiding of terahertz surface plasmon polaritons on structured metal surfaces,” Nat. Photonics. 2, 175-179 (2008).
[CrossRef]

Anemogiannis, E.

Bradberry, G. W.

F. Yang, J. R. Sambles, and G. W. Bradberry, “Long-range surface modes supported by thin films,” Phys. Rev. B 44, 5855-5872 (1991).
[CrossRef]

Fernández-Domínguez, A. I.

C. R. Williams, S. R. Andrews, S. A. Maier, A. I. Fernández-Domínguez, L. Martín-Moreno, and F. J. García-Vidal, “Highly confined guiding of terahertz surface plasmon polaritons on structured metal surfaces,” Nat. Photonics. 2, 175-179 (2008).
[CrossRef]

Fukui, M.

García-Vidal, F. J.

C. R. Williams, S. R. Andrews, S. A. Maier, A. I. Fernández-Domínguez, L. Martín-Moreno, and F. J. García-Vidal, “Highly confined guiding of terahertz surface plasmon polaritons on structured metal surfaces,” Nat. Photonics. 2, 175-179 (2008).
[CrossRef]

Gaylord, T. K.

Genov, D. A.

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

Glytsis, E. N.

Guo, J.

Haraguchi, M.

Jen, Y.-J.

A. Lakhtakia, Y.-J. Jen, and C.-F. Lin, “Multiple trains of same-color surface plasmon-polaritons guided by the planar interface of a metal and a sculptured nematic thin film. Part III: Experimental evidence,” J. Nanophoton 3, 033506 (2009).
[CrossRef]

Lakhtakia, A.

A. Lakhtakia, Y.-J. Jen, and C.-F. Lin, “Multiple trains of same-color surface plasmon-polaritons guided by the planar interface of a metal and a sculptured nematic thin film. Part III: Experimental evidence,” J. Nanophoton 3, 033506 (2009).
[CrossRef]

M. A. Motyka and A. Lakhtakia, “Multiple trains of same-color surface plasmon-polaritons guided by the planar interface of a metal and a sculptured nematic thin film,” J. Nanophoton 2, 021910 (2008).
[CrossRef]

Lin, C.-F.

A. Lakhtakia, Y.-J. Jen, and C.-F. Lin, “Multiple trains of same-color surface plasmon-polaritons guided by the planar interface of a metal and a sculptured nematic thin film. Part III: Experimental evidence,” J. Nanophoton 3, 033506 (2009).
[CrossRef]

Macleod, H. A.

Z. Salamon, H. A. Macleod, and G. Tollin, “Coupled plasmon-waveguide resonators: A new spectroscopic tool for probing proteolipids film structure and properties,” Biophys. J. 73, 2791-2797 (1997).
[CrossRef] [PubMed]

H. A. Macleod, Thin-Film Optical Filters, 2nd ed. (Adam Hilger, 1986).
[CrossRef]

Maier, S. A.

C. R. Williams, S. R. Andrews, S. A. Maier, A. I. Fernández-Domínguez, L. Martín-Moreno, and F. J. García-Vidal, “Highly confined guiding of terahertz surface plasmon polaritons on structured metal surfaces,” Nat. Photonics. 2, 175-179 (2008).
[CrossRef]

Maradudin, A. A.

Martín-Moreno, L.

C. R. Williams, S. R. Andrews, S. A. Maier, A. I. Fernández-Domínguez, L. Martín-Moreno, and F. J. García-Vidal, “Highly confined guiding of terahertz surface plasmon polaritons on structured metal surfaces,” Nat. Photonics. 2, 175-179 (2008).
[CrossRef]

Motyka, M. A.

M. A. Motyka and A. Lakhtakia, “Multiple trains of same-color surface plasmon-polaritons guided by the planar interface of a metal and a sculptured nematic thin film,” J. Nanophoton 2, 021910 (2008).
[CrossRef]

Oulton, R. F.

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

Pile, D. F. P.

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

Raether, H.

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer, 1983).

Salamon, Z.

Z. Salamon, H. A. Macleod, and G. Tollin, “Coupled plasmon-waveguide resonators: A new spectroscopic tool for probing proteolipids film structure and properties,” Biophys. J. 73, 2791-2797 (1997).
[CrossRef] [PubMed]

Sambles, J. R.

F. Yang, J. R. Sambles, and G. W. Bradberry, “Long-range surface modes supported by thin films,” Phys. Rev. B 44, 5855-5872 (1991).
[CrossRef]

Sarid, D.

D. Sarid, “Long-range surface-plasma waves on very thin metal films,” Phys. Rev. Lett. 47, 1927-1930 (1981).
[CrossRef]

Sorger, V. J.

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

Stegeman, G. I.

Takabayashi, M.

Tollin, G.

Z. Salamon, H. A. Macleod, and G. Tollin, “Coupled plasmon-waveguide resonators: A new spectroscopic tool for probing proteolipids film structure and properties,” Biophys. J. 73, 2791-2797 (1997).
[CrossRef] [PubMed]

Wallis, R. F.

Williams, C. R.

C. R. Williams, S. R. Andrews, S. A. Maier, A. I. Fernández-Domínguez, L. Martín-Moreno, and F. J. García-Vidal, “Highly confined guiding of terahertz surface plasmon polaritons on structured metal surfaces,” Nat. Photonics. 2, 175-179 (2008).
[CrossRef]

Yang, F.

F. Yang, J. R. Sambles, and G. W. Bradberry, “Long-range surface modes supported by thin films,” Phys. Rev. B 44, 5855-5872 (1991).
[CrossRef]

Zhang, X.

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

Biophys. J. (1)

Z. Salamon, H. A. Macleod, and G. Tollin, “Coupled plasmon-waveguide resonators: A new spectroscopic tool for probing proteolipids film structure and properties,” Biophys. J. 73, 2791-2797 (1997).
[CrossRef] [PubMed]

J. Lightwave Technol. (1)

J. Nanophoton (2)

M. A. Motyka and A. Lakhtakia, “Multiple trains of same-color surface plasmon-polaritons guided by the planar interface of a metal and a sculptured nematic thin film,” J. Nanophoton 2, 021910 (2008).
[CrossRef]

A. Lakhtakia, Y.-J. Jen, and C.-F. Lin, “Multiple trains of same-color surface plasmon-polaritons guided by the planar interface of a metal and a sculptured nematic thin film. Part III: Experimental evidence,” J. Nanophoton 3, 033506 (2009).
[CrossRef]

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

Nat. Photonics (1)

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

Nat. Photonics. (1)

C. R. Williams, S. R. Andrews, S. A. Maier, A. I. Fernández-Domínguez, L. Martín-Moreno, and F. J. García-Vidal, “Highly confined guiding of terahertz surface plasmon polaritons on structured metal surfaces,” Nat. Photonics. 2, 175-179 (2008).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. B (1)

F. Yang, J. R. Sambles, and G. W. Bradberry, “Long-range surface modes supported by thin films,” Phys. Rev. B 44, 5855-5872 (1991).
[CrossRef]

Phys. Rev. Lett. (1)

D. Sarid, “Long-range surface-plasma waves on very thin metal films,” Phys. Rev. Lett. 47, 1927-1930 (1981).
[CrossRef]

Other (3)

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer, 1983).

H. A. Macleod, Thin-Film Optical Filters, 2nd ed. (Adam Hilger, 1986).
[CrossRef]

Optical Thin-Film Software: The Essential Macleod (Thin Film Center Inc., Version 8.18.0), http://www.thinfilmcenter.com/GMacleod.asp.

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Figures (13)

Fig. 1
Fig. 1

Normalized admittance diagram for a metal film of refractive index N = n i k , for normal incidence. Many different loci are shown, each for a different substrate admittance.

Fig. 2
Fig. 2

Normalized admittance diagram to explain typical design for LRSPP propagation.

Fig. 3
Fig. 3

p-polarization reflectance as a function of the angle of incidence, and the normalized admittance diagram of a silver thin film, for a typical Kretschmann structure {glass prism/silver ( 53.43 nm ) /air} at 632.8 - nm wavelength when θ i = 42.98329 ° .

Fig. 4
Fig. 4

Normalized admittance diagrams for a Sarid structure {glass prism / Si O 2 ( 1164.50 nm ) / silver ( 20 nm ) Si O 2 } for the p-polarization state at 632.8       nm wavelength when θ i = 76.66892 ° . Upper left, beginning of the locus for the silver film; right, locus for the silver film; lower left, end of the locus for the silver film and the entire locus of the Si O 2 coupling layer.

Fig. 5
Fig. 5

Imaginary part of the Herpin index E of the unit cell [ Ti O 2 ( X * 34.71 nm ) Si O 2 ( X * 108.58 nm ) Ti O 2 ( X * 34.71 nm ) ] as a function of X for the p-polarization state at 632.8     nm wavelength, when θ i = 41.32273 ° . The real part of E is not shown, as it is very small.

Fig. 6
Fig. 6

Normalized admittance diagrams for a Sarid structure {glass prism/ [ Ti O 2 ( X * 34.71 nm ) Si O 2 ( X * 108.58 nm ) Ti O 2 ( X * 34.71 nm ) ] 16 /silver ( 20 nm ) /air} for p polarization at 632.8         nm wavelength when X = 1.296 and θ i = 41.32273 ° . Upper left, beginning of the locus for the silver film; right, locus for the silver film; lower left, end of the locus for the silver film and the jumps due to successive unit cells in the coupling multilayer.

Fig. 7
Fig. 7

Normalized admittance diagram for the silver film in the {glass prism/silver ( 39 nm ) [ Ti O 2 ( 69.42 nm ) Si O 2 ( 217.15 nm ) Ti O 2 ( 69.42 nm ) ] 2 /air} structure for s-polari zation at 632.8 nm wavelength when θ i = 65.91105 ° .

Fig. 8
Fig. 8

Normalized admittance diagrams for the {glass prism/ [ Ti O 2 ( 50.64 nm ) Si O 2 ( 158.41 nm ) Ti O 2 ( 50.64 nm ) ] 8 / silver ( 20 nm ) [ Ti O 2 ( 51.37 nm ) Si O 2 ( 160.69 nm ) Ti O 2 ( 51.37 nm ) ] 4 /air} structure for the s-polarization state at 632.8 nm wavelength when θ i = 41.42450 ° . Upper left, beginning of the locus for the silver thin film; right, locus for the silver film; lower left, end of the locus for the silver thin film and the jumps due to successive unit cells in the coupling multilayer of eight unit cells.

Fig. 9
Fig. 9

s-polarization reflectance as a function of the angle of incidence, of the {glass prism/ [ Ti O 2 ( 50.64 nm ) Si O 2 ( 158.41 nm ) Ti O 2 ( 50.64 nm ) ] 8 / silver ( 20.00 nm ) [ Ti O 2 ( 51.37 nm ) Si O 2 ( 160.69 nm ) Ti O 2 ( 51.37 nm ) ] 4 /air} structure at 632.8 nm wavelength.

Fig. 10
Fig. 10

Imaginary parts of the Herpin index E of the unit cell [ Ta 2 O 5 ( X * 74.15 nm ) Si O 2 ( X * 108.58 nm ) Ta 2 O 5 ( X * 74.15 nm ) ] against θ i at a wavelength of 632.8 nm , with X = 2.4674 , for the p- and s-polarization states. The real parts of E are not shown as they are very small in magnitude.

Fig. 11
Fig. 11

Normalized admittance diagrams for the {glass prism/ [ Ta 2 O 5 ( X * 74.15 nm ) Si O 2 ( X * 108.58 nm ) Ta 2 O 5 ( X * 74.15 nm ) ] 30 /silver film ( 35 nm ) [ Ta 2 O 5 ( Y * 74.15 nm ) Si O 2 ( Y * 108.58 nm ) Ta 2 O 5 ( Y * 74.15 nm ) ] 7 /air} structure for the p-polarization state at 632.8     nm wavelength with X = 4.928 and Y = 2.4674 when θ i = 43.24981 ° .

Fig. 12
Fig. 12

Normalized admittance diagrams for the {glass prism/ [ Ta 2 O 5 ( X * 74.15 nm ) Si O 2 ( X * 108.58 nm ) Ta 2 O 5 ( X * 74.15 nm ) ] 30 / silver ( 35 nm ) [ Ta 2 O 5 ( Y * 74.15 nm ) Si O 2 ( Y * 108.58 nm ) Ta 2 O 5 ( Y * 74.15 nm ) ] 7 / air} structure for the s-polarization state at 632.8     nm wavelength with X = 4.928 and Y = 2.4674 when θ i = 41.30433 ° .

Fig. 13
Fig. 13

p- and s-polarization reflectances as functions of the angle of incidence of the {glass prism/ [ Ta 2 O 5 ( X * 74.15 nm ) Si O 2 ( X * 108.58 nm ) Ta 2 O 5 ( X * 74.15 nm ) ] 30 / silver ( 35 nm ) [ Ta 2 O 5 ( Y * 74.15 nm ) Si O 2 ( Y * 108.58 nm ) Ta 2 O 5 ( Y * 74.15 nm ) ] 7 /air} structure at 632.8     nm wavelength with X = 4.928 and Y = 2.4674 .

Equations (2)

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η ̃ i = { η ̃ i char cos θ i η ̃ i char cos θ i } , η ̃ = { η ̃ char cos θ η ̃ char cos θ } , polarization = { p s }
η = { ( η ̃ cos θ i ) ε 0 μ 0 ( η ̃ cos θ i ) ε 0 μ 0 } , polarization = { p s } ,

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