Abstract

We show theoretically and numerically that a planar structure consisting of two isotropic dielectric layers can be used to minimize parasitic scattering of surface plasmon polaritons for arbitrary incidence angle. The average scattering losses are reduced by an order-of-magnitude down to 1–3%. The surface plasmon refraction with the scattering suppression can be accurately described by an analytical model based on the Fresnel equations. The proposed approach can be used for the design of plasmonic lenses, reflectors, plasmonic crystals and plasmonic laser cavities.

© 2014 Optical Society of America

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References

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  1. R.-M. Ma, R. F. Oulton, V. J. Sorger, X. Zhang, “Plasmon lasers: coherent light source at molecular scales,” Laser Photonics Rev. 7(1), 1–21 (2013).
    [CrossRef]
  2. Z. Xie, W. Yu, T. Wang, H. Zhang, Y. Fu, H. Liu, F. Li, Z. Lu, Q. Sun, “Plasmonic nanolithography: a review,” Plasmonics 6(3), 565–580 (2011).
    [CrossRef]
  3. Z. Han, S. I. Bozhevolnyi, “Radiation guiding with surface plasmon polaritons,” Rep. Prog. Phys. 76(1), 016402 (2013).
    [CrossRef] [PubMed]
  4. H. A. Atwater, A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010).
    [CrossRef] [PubMed]
  5. R. F. Oulton, D. F. P. Pile, Y. Liu, X. Zhang, “Scattering of surface plasmon polaritons at abrupt surface interfaces: Implications for nanoscale cavities,” Phys. Rev. B 76(3), 035408 (2007).
    [CrossRef]
  6. J. Elser, V. A. Podolskiy, “Scattering-free plasmonic optics with anisotropic metamaterials,” Phys. Rev. Lett. 100(6), 066402 (2008).
    [CrossRef] [PubMed]
  7. M. Zhong-Tuan, W. Pei, C. Yong, T. Hong-Gao, M. Hai, “Pure Reflection and Refraction of a Surface Polariton by a Matched Waveguide Structure,” Chin. Phys. Lett. 23(9), 2545–2548 (2006).
    [CrossRef]
  8. S. Thongrattanasiri, J. Elser, V. A. Podolskiy, “Quasi-planar optics: computing light propagation and scattering in planar waveguide arrays,” J. Opt. Soc. Am. B 26(12), B102–B110 (2009).
    [CrossRef]
  9. A. V. Novitsky, “Conversion from surface wave to surface wave on reflection,” J. Opt. 12(11), 115705 (2010).
    [CrossRef]
  10. E. A. Bezus, L. L. Doskolovich, N. L. Kazanskiy, “Scattering suppression in plasmonic optics using a simple two-layer dielectric structure,” Appl. Phys. Lett. 98(22), 221108 (2011).
    [CrossRef]
  11. E. A. Bezus, L. L. Doskolovich, N. L. Kazanskiy, V. A. Soifer, “Scattering in elements of plasmon optics suppressed by two-layer dielectric structures,” Tech. Phys. Lett. 37(12), 1091–1095 (2011).
    [CrossRef]
  12. A. Salandrino, D. N. Christodoulides, “Airy plasmon: a nondiffracting surface wave,” Opt. Lett. 35(12), 2082–2084 (2010).
    [CrossRef] [PubMed]
  13. C. E. Garcia-Ortiz, V. Coello, Z. Han, S. I. Bozhevolnyi, “Generation of diffraction-free plasmonic beams with one-dimensional Bessel profiles,” Opt. Lett. 38(6), 905–907 (2013).
    [CrossRef] [PubMed]
  14. I. Avrutsky, R. Soref, W. Buchwald, “Sub-wavelength plasmonic modes in a conductor-gap-dielectric system with a nanoscale gap,” Opt. Express 18(1), 348–363 (2010).
    [CrossRef] [PubMed]
  15. D. G. Sannikov, D. I. Sementsov, “The surface mode of a dielectric waveguide with metal substrate,” Tech. Phys. Lett. 29(5), 353–356 (2003).
    [CrossRef]
  16. P. B. Johnson, R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
    [CrossRef]
  17. M. N. Polyanskiy, “Refractive index database,” http://refractiveindex.info .
  18. R. Zia, A. Chandran, M. L. Brongersma, “Dielectric waveguide model for guided surface polaritons,” Opt. Lett. 30(12), 1473–1475 (2005).
    [CrossRef] [PubMed]
  19. M. G. Moharam, E. B. Grann, D. A. Pommet, T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A 12(5), 1068–1076 (1995).
    [CrossRef]
  20. L. Li, “Use of Fourier series in the analysis of discontinuous periodic structures,” J. Opt. Soc. Am. A 13(9), 1870–1876 (1996).
    [CrossRef]
  21. E. Silberstein, P. Lalanne, J.-P. Hugonin, Q. Cao, “Use of grating theories in integrated optics,” J. Opt. Soc. Am. A 18(11), 2865–2875 (2001).
    [CrossRef] [PubMed]
  22. E. A. Bezus, L. L. Doskolovich, N. L. Kazanskiy, V. A. Soifer, S. I. Kharitonov, “Design of diffractive lenses for focusing surface plasmons,” J. Opt. 12(1), 015001 (2010).
    [CrossRef]

2013

R.-M. Ma, R. F. Oulton, V. J. Sorger, X. Zhang, “Plasmon lasers: coherent light source at molecular scales,” Laser Photonics Rev. 7(1), 1–21 (2013).
[CrossRef]

Z. Han, S. I. Bozhevolnyi, “Radiation guiding with surface plasmon polaritons,” Rep. Prog. Phys. 76(1), 016402 (2013).
[CrossRef] [PubMed]

C. E. Garcia-Ortiz, V. Coello, Z. Han, S. I. Bozhevolnyi, “Generation of diffraction-free plasmonic beams with one-dimensional Bessel profiles,” Opt. Lett. 38(6), 905–907 (2013).
[CrossRef] [PubMed]

2011

E. A. Bezus, L. L. Doskolovich, N. L. Kazanskiy, “Scattering suppression in plasmonic optics using a simple two-layer dielectric structure,” Appl. Phys. Lett. 98(22), 221108 (2011).
[CrossRef]

E. A. Bezus, L. L. Doskolovich, N. L. Kazanskiy, V. A. Soifer, “Scattering in elements of plasmon optics suppressed by two-layer dielectric structures,” Tech. Phys. Lett. 37(12), 1091–1095 (2011).
[CrossRef]

Z. Xie, W. Yu, T. Wang, H. Zhang, Y. Fu, H. Liu, F. Li, Z. Lu, Q. Sun, “Plasmonic nanolithography: a review,” Plasmonics 6(3), 565–580 (2011).
[CrossRef]

2010

H. A. Atwater, A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010).
[CrossRef] [PubMed]

A. V. Novitsky, “Conversion from surface wave to surface wave on reflection,” J. Opt. 12(11), 115705 (2010).
[CrossRef]

A. Salandrino, D. N. Christodoulides, “Airy plasmon: a nondiffracting surface wave,” Opt. Lett. 35(12), 2082–2084 (2010).
[CrossRef] [PubMed]

I. Avrutsky, R. Soref, W. Buchwald, “Sub-wavelength plasmonic modes in a conductor-gap-dielectric system with a nanoscale gap,” Opt. Express 18(1), 348–363 (2010).
[CrossRef] [PubMed]

E. A. Bezus, L. L. Doskolovich, N. L. Kazanskiy, V. A. Soifer, S. I. Kharitonov, “Design of diffractive lenses for focusing surface plasmons,” J. Opt. 12(1), 015001 (2010).
[CrossRef]

2009

2008

J. Elser, V. A. Podolskiy, “Scattering-free plasmonic optics with anisotropic metamaterials,” Phys. Rev. Lett. 100(6), 066402 (2008).
[CrossRef] [PubMed]

2007

R. F. Oulton, D. F. P. Pile, Y. Liu, X. Zhang, “Scattering of surface plasmon polaritons at abrupt surface interfaces: Implications for nanoscale cavities,” Phys. Rev. B 76(3), 035408 (2007).
[CrossRef]

2006

M. Zhong-Tuan, W. Pei, C. Yong, T. Hong-Gao, M. Hai, “Pure Reflection and Refraction of a Surface Polariton by a Matched Waveguide Structure,” Chin. Phys. Lett. 23(9), 2545–2548 (2006).
[CrossRef]

2005

2003

D. G. Sannikov, D. I. Sementsov, “The surface mode of a dielectric waveguide with metal substrate,” Tech. Phys. Lett. 29(5), 353–356 (2003).
[CrossRef]

2001

1996

1995

1972

P. B. Johnson, R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Atwater, H. A.

H. A. Atwater, A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010).
[CrossRef] [PubMed]

Avrutsky, I.

Bezus, E. A.

E. A. Bezus, L. L. Doskolovich, N. L. Kazanskiy, V. A. Soifer, “Scattering in elements of plasmon optics suppressed by two-layer dielectric structures,” Tech. Phys. Lett. 37(12), 1091–1095 (2011).
[CrossRef]

E. A. Bezus, L. L. Doskolovich, N. L. Kazanskiy, “Scattering suppression in plasmonic optics using a simple two-layer dielectric structure,” Appl. Phys. Lett. 98(22), 221108 (2011).
[CrossRef]

E. A. Bezus, L. L. Doskolovich, N. L. Kazanskiy, V. A. Soifer, S. I. Kharitonov, “Design of diffractive lenses for focusing surface plasmons,” J. Opt. 12(1), 015001 (2010).
[CrossRef]

Bozhevolnyi, S. I.

Brongersma, M. L.

Buchwald, W.

Cao, Q.

Chandran, A.

Christodoulides, D. N.

Christy, R. W.

P. B. Johnson, R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Coello, V.

Doskolovich, L. L.

E. A. Bezus, L. L. Doskolovich, N. L. Kazanskiy, V. A. Soifer, “Scattering in elements of plasmon optics suppressed by two-layer dielectric structures,” Tech. Phys. Lett. 37(12), 1091–1095 (2011).
[CrossRef]

E. A. Bezus, L. L. Doskolovich, N. L. Kazanskiy, “Scattering suppression in plasmonic optics using a simple two-layer dielectric structure,” Appl. Phys. Lett. 98(22), 221108 (2011).
[CrossRef]

E. A. Bezus, L. L. Doskolovich, N. L. Kazanskiy, V. A. Soifer, S. I. Kharitonov, “Design of diffractive lenses for focusing surface plasmons,” J. Opt. 12(1), 015001 (2010).
[CrossRef]

Elser, J.

Fu, Y.

Z. Xie, W. Yu, T. Wang, H. Zhang, Y. Fu, H. Liu, F. Li, Z. Lu, Q. Sun, “Plasmonic nanolithography: a review,” Plasmonics 6(3), 565–580 (2011).
[CrossRef]

Garcia-Ortiz, C. E.

Gaylord, T. K.

Grann, E. B.

Hai, M.

M. Zhong-Tuan, W. Pei, C. Yong, T. Hong-Gao, M. Hai, “Pure Reflection and Refraction of a Surface Polariton by a Matched Waveguide Structure,” Chin. Phys. Lett. 23(9), 2545–2548 (2006).
[CrossRef]

Han, Z.

Hong-Gao, T.

M. Zhong-Tuan, W. Pei, C. Yong, T. Hong-Gao, M. Hai, “Pure Reflection and Refraction of a Surface Polariton by a Matched Waveguide Structure,” Chin. Phys. Lett. 23(9), 2545–2548 (2006).
[CrossRef]

Hugonin, J.-P.

Johnson, P. B.

P. B. Johnson, R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Kazanskiy, N. L.

E. A. Bezus, L. L. Doskolovich, N. L. Kazanskiy, V. A. Soifer, “Scattering in elements of plasmon optics suppressed by two-layer dielectric structures,” Tech. Phys. Lett. 37(12), 1091–1095 (2011).
[CrossRef]

E. A. Bezus, L. L. Doskolovich, N. L. Kazanskiy, “Scattering suppression in plasmonic optics using a simple two-layer dielectric structure,” Appl. Phys. Lett. 98(22), 221108 (2011).
[CrossRef]

E. A. Bezus, L. L. Doskolovich, N. L. Kazanskiy, V. A. Soifer, S. I. Kharitonov, “Design of diffractive lenses for focusing surface plasmons,” J. Opt. 12(1), 015001 (2010).
[CrossRef]

Kharitonov, S. I.

E. A. Bezus, L. L. Doskolovich, N. L. Kazanskiy, V. A. Soifer, S. I. Kharitonov, “Design of diffractive lenses for focusing surface plasmons,” J. Opt. 12(1), 015001 (2010).
[CrossRef]

Lalanne, P.

Li, F.

Z. Xie, W. Yu, T. Wang, H. Zhang, Y. Fu, H. Liu, F. Li, Z. Lu, Q. Sun, “Plasmonic nanolithography: a review,” Plasmonics 6(3), 565–580 (2011).
[CrossRef]

Li, L.

Liu, H.

Z. Xie, W. Yu, T. Wang, H. Zhang, Y. Fu, H. Liu, F. Li, Z. Lu, Q. Sun, “Plasmonic nanolithography: a review,” Plasmonics 6(3), 565–580 (2011).
[CrossRef]

Liu, Y.

R. F. Oulton, D. F. P. Pile, Y. Liu, X. Zhang, “Scattering of surface plasmon polaritons at abrupt surface interfaces: Implications for nanoscale cavities,” Phys. Rev. B 76(3), 035408 (2007).
[CrossRef]

Lu, Z.

Z. Xie, W. Yu, T. Wang, H. Zhang, Y. Fu, H. Liu, F. Li, Z. Lu, Q. Sun, “Plasmonic nanolithography: a review,” Plasmonics 6(3), 565–580 (2011).
[CrossRef]

Ma, R.-M.

R.-M. Ma, R. F. Oulton, V. J. Sorger, X. Zhang, “Plasmon lasers: coherent light source at molecular scales,” Laser Photonics Rev. 7(1), 1–21 (2013).
[CrossRef]

Moharam, M. G.

Novitsky, A. V.

A. V. Novitsky, “Conversion from surface wave to surface wave on reflection,” J. Opt. 12(11), 115705 (2010).
[CrossRef]

Oulton, R. F.

R.-M. Ma, R. F. Oulton, V. J. Sorger, X. Zhang, “Plasmon lasers: coherent light source at molecular scales,” Laser Photonics Rev. 7(1), 1–21 (2013).
[CrossRef]

R. F. Oulton, D. F. P. Pile, Y. Liu, X. Zhang, “Scattering of surface plasmon polaritons at abrupt surface interfaces: Implications for nanoscale cavities,” Phys. Rev. B 76(3), 035408 (2007).
[CrossRef]

Pei, W.

M. Zhong-Tuan, W. Pei, C. Yong, T. Hong-Gao, M. Hai, “Pure Reflection and Refraction of a Surface Polariton by a Matched Waveguide Structure,” Chin. Phys. Lett. 23(9), 2545–2548 (2006).
[CrossRef]

Pile, D. F. P.

R. F. Oulton, D. F. P. Pile, Y. Liu, X. Zhang, “Scattering of surface plasmon polaritons at abrupt surface interfaces: Implications for nanoscale cavities,” Phys. Rev. B 76(3), 035408 (2007).
[CrossRef]

Podolskiy, V. A.

Polman, A.

H. A. Atwater, A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010).
[CrossRef] [PubMed]

Pommet, D. A.

Salandrino, A.

Sannikov, D. G.

D. G. Sannikov, D. I. Sementsov, “The surface mode of a dielectric waveguide with metal substrate,” Tech. Phys. Lett. 29(5), 353–356 (2003).
[CrossRef]

Sementsov, D. I.

D. G. Sannikov, D. I. Sementsov, “The surface mode of a dielectric waveguide with metal substrate,” Tech. Phys. Lett. 29(5), 353–356 (2003).
[CrossRef]

Silberstein, E.

Soifer, V. A.

E. A. Bezus, L. L. Doskolovich, N. L. Kazanskiy, V. A. Soifer, “Scattering in elements of plasmon optics suppressed by two-layer dielectric structures,” Tech. Phys. Lett. 37(12), 1091–1095 (2011).
[CrossRef]

E. A. Bezus, L. L. Doskolovich, N. L. Kazanskiy, V. A. Soifer, S. I. Kharitonov, “Design of diffractive lenses for focusing surface plasmons,” J. Opt. 12(1), 015001 (2010).
[CrossRef]

Soref, R.

Sorger, V. J.

R.-M. Ma, R. F. Oulton, V. J. Sorger, X. Zhang, “Plasmon lasers: coherent light source at molecular scales,” Laser Photonics Rev. 7(1), 1–21 (2013).
[CrossRef]

Sun, Q.

Z. Xie, W. Yu, T. Wang, H. Zhang, Y. Fu, H. Liu, F. Li, Z. Lu, Q. Sun, “Plasmonic nanolithography: a review,” Plasmonics 6(3), 565–580 (2011).
[CrossRef]

Thongrattanasiri, S.

Wang, T.

Z. Xie, W. Yu, T. Wang, H. Zhang, Y. Fu, H. Liu, F. Li, Z. Lu, Q. Sun, “Plasmonic nanolithography: a review,” Plasmonics 6(3), 565–580 (2011).
[CrossRef]

Xie, Z.

Z. Xie, W. Yu, T. Wang, H. Zhang, Y. Fu, H. Liu, F. Li, Z. Lu, Q. Sun, “Plasmonic nanolithography: a review,” Plasmonics 6(3), 565–580 (2011).
[CrossRef]

Yong, C.

M. Zhong-Tuan, W. Pei, C. Yong, T. Hong-Gao, M. Hai, “Pure Reflection and Refraction of a Surface Polariton by a Matched Waveguide Structure,” Chin. Phys. Lett. 23(9), 2545–2548 (2006).
[CrossRef]

Yu, W.

Z. Xie, W. Yu, T. Wang, H. Zhang, Y. Fu, H. Liu, F. Li, Z. Lu, Q. Sun, “Plasmonic nanolithography: a review,” Plasmonics 6(3), 565–580 (2011).
[CrossRef]

Zhang, H.

Z. Xie, W. Yu, T. Wang, H. Zhang, Y. Fu, H. Liu, F. Li, Z. Lu, Q. Sun, “Plasmonic nanolithography: a review,” Plasmonics 6(3), 565–580 (2011).
[CrossRef]

Zhang, X.

R.-M. Ma, R. F. Oulton, V. J. Sorger, X. Zhang, “Plasmon lasers: coherent light source at molecular scales,” Laser Photonics Rev. 7(1), 1–21 (2013).
[CrossRef]

R. F. Oulton, D. F. P. Pile, Y. Liu, X. Zhang, “Scattering of surface plasmon polaritons at abrupt surface interfaces: Implications for nanoscale cavities,” Phys. Rev. B 76(3), 035408 (2007).
[CrossRef]

Zhong-Tuan, M.

M. Zhong-Tuan, W. Pei, C. Yong, T. Hong-Gao, M. Hai, “Pure Reflection and Refraction of a Surface Polariton by a Matched Waveguide Structure,” Chin. Phys. Lett. 23(9), 2545–2548 (2006).
[CrossRef]

Zia, R.

Appl. Phys. Lett.

E. A. Bezus, L. L. Doskolovich, N. L. Kazanskiy, “Scattering suppression in plasmonic optics using a simple two-layer dielectric structure,” Appl. Phys. Lett. 98(22), 221108 (2011).
[CrossRef]

Chin. Phys. Lett.

M. Zhong-Tuan, W. Pei, C. Yong, T. Hong-Gao, M. Hai, “Pure Reflection and Refraction of a Surface Polariton by a Matched Waveguide Structure,” Chin. Phys. Lett. 23(9), 2545–2548 (2006).
[CrossRef]

J. Opt.

A. V. Novitsky, “Conversion from surface wave to surface wave on reflection,” J. Opt. 12(11), 115705 (2010).
[CrossRef]

E. A. Bezus, L. L. Doskolovich, N. L. Kazanskiy, V. A. Soifer, S. I. Kharitonov, “Design of diffractive lenses for focusing surface plasmons,” J. Opt. 12(1), 015001 (2010).
[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Laser Photonics Rev.

R.-M. Ma, R. F. Oulton, V. J. Sorger, X. Zhang, “Plasmon lasers: coherent light source at molecular scales,” Laser Photonics Rev. 7(1), 1–21 (2013).
[CrossRef]

Nat. Mater.

H. A. Atwater, A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9(3), 205–213 (2010).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

Phys. Rev. B

P. B. Johnson, R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

R. F. Oulton, D. F. P. Pile, Y. Liu, X. Zhang, “Scattering of surface plasmon polaritons at abrupt surface interfaces: Implications for nanoscale cavities,” Phys. Rev. B 76(3), 035408 (2007).
[CrossRef]

Phys. Rev. Lett.

J. Elser, V. A. Podolskiy, “Scattering-free plasmonic optics with anisotropic metamaterials,” Phys. Rev. Lett. 100(6), 066402 (2008).
[CrossRef] [PubMed]

Plasmonics

Z. Xie, W. Yu, T. Wang, H. Zhang, Y. Fu, H. Liu, F. Li, Z. Lu, Q. Sun, “Plasmonic nanolithography: a review,” Plasmonics 6(3), 565–580 (2011).
[CrossRef]

Rep. Prog. Phys.

Z. Han, S. I. Bozhevolnyi, “Radiation guiding with surface plasmon polaritons,” Rep. Prog. Phys. 76(1), 016402 (2013).
[CrossRef] [PubMed]

Tech. Phys. Lett.

E. A. Bezus, L. L. Doskolovich, N. L. Kazanskiy, V. A. Soifer, “Scattering in elements of plasmon optics suppressed by two-layer dielectric structures,” Tech. Phys. Lett. 37(12), 1091–1095 (2011).
[CrossRef]

D. G. Sannikov, D. I. Sementsov, “The surface mode of a dielectric waveguide with metal substrate,” Tech. Phys. Lett. 29(5), 353–356 (2003).
[CrossRef]

Other

M. N. Polyanskiy, “Refractive index database,” http://refractiveindex.info .

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Figures (6)

Fig. 1
Fig. 1

Geometry of the SPP propagation through a dielectric ridge (the considered structure is invariant in the y-direction). In the paper, also the case of SPP transmission through the interfaces between two media (from medium 1 to medium 2 and from medium 2 to medium 3) is considered.

Fig. 2
Fig. 2

Comparison of the refraction of an SPP and a TE-polarized plane wave on an interface between two media. SPP reflectance (thick solid blue lines), plane wave reflectance (thin solid green lines), SPP transmittance (thick dashed blue lines), plane wave transmittance (thin dashed green lines), and SPP scattering losses (thick dotted blue lines) vs. incidence angle θ are shown. SPP is incident from the surrounding dielectric to the two-layer medium ((a), (b)) or vice versa ((c), (d)). The cases of h 1 = 0 ((a), (c)) and h 1 = 62 nm ((b), (d)) are considered. The insets in (c) and (d) show the SPP scattering losses (S) near the total internal reflection critical angle θ T I R marked by vertical black dashed lines.

Fig. 3
Fig. 3

Comparison of the reflectance (R) and transmittance (T) of an SPP propagating through a dielectric ridge and a plane wave (PW) propagating through a plane-parallel plate vs. the angle of incidence θ and the ridge length (or plate thickness) l: h 1 = 0 (a), h 1 = 62 nm (b).

Fig. 4
Fig. 4

SPP scattering losses (S) vs. the angle of incidence θ and the ridge length l: h 1 = 0 (a), h 1 = 62 nm (b).

Fig. 5
Fig. 5

(a) Fragment of the SPP transmittance distribution at h 1 = 0 shown by white dashed rectangle in Fig. 3(a), black dashed lines are the dispersion curves of the DLSPPW modes, white dashed line shows the angle θ c r . (b) | E | 2 distributions in the dielectric ridge for SPP diffraction (left) and DLSPPW eigenmode (right) at the point depicted by white asterisk in Fig. 5(a). The dielectric ridge and the interface between the metal and the surrounding dielectric are shown by dashed white lines.

Fig. 6
Fig. 6

| E y | 2 distributions for SPP ((c), (d)) and PW ((a), (b)) lens arrays within one period. h 1 = 0 ((a), (c)) or h 1 = 62 nm ((b), (d)). Lenses are shown with solid white lines.

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

tan h ( γ 1 h 1 ) = γ 1 ε 1 ( ε 2 γ m + ε m γ 2 ) / ( ε 2 ε m γ 1 2 + ε 1 2 γ 2 γ m ) ,
r= n I cosθ n II cos θ t n I cosθ+ n II cos θ t , t= 2 n I cosθ n I cosθ+ n II cos θ t ,
Re{ n mode }x+Re{ n spp } y 2 + ( fx ) 2 =const,

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