Abstract

We numerically investigate the optical field enhancement by a metal/dielectric multilayered zone plate. The optical field enhancement at the focal point of a zone plate originates not only from surface plasmon polaritons (SPPs)-assisted diffraction process along the propagation direction of incident light, but also from multiple scattering and coupling of surface plasmons (SPs) along the metal/dielectric multilayer films. By comparing multilayered zone plates to a conventional monolayered zone plate, we present the effects associated with the number of building blocks and different dielectric materials in the building block on the efficiency of the transmission.

© 2009 Optical Society of America

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  1. Y. Fu, W. Zhou, and L. E. N. Lim, "Near-field behavior of zone-plate-like plasmonic nanostructures," J. Opt. Soc. Am. A 25, 238-249 (2008).
    [CrossRef]
  2. H. C. Kim, H. Ko, and M. Cheng, "Optical focusing of plasmonic Fresnel zone plate-based metallic structure covered with a dielectric layer," J. Vac. Sci. Technol. B 26, 2197-2203 (2008).
    [CrossRef]
  3. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature (London) 391, 667-669 (1998).
    [CrossRef]
  4. E. Ozbay, "Plasmonics: Merging Photonics and Electronics at Nanoscale Dimensions," Science 311, 189-193 (2006).
    [CrossRef] [PubMed]
  5. Z. H. Tang, R. W. Peng, Z. Wang, X. Wu, Y. J. Bao, Q. J. Wang, Z. J. Zhang, W. H. Sun, and M. Wang, "Coupling of surface plasmons in nanostructured metal/dielectric multilayers with subwavelength hole arrays," Phys. Rev. B 76, 195405-195408 (2007).
    [CrossRef]
  6. E. D. Palik, Handbook of Optical Constants of Solids (Academic, New York, 1985).
  7. J. M. Steele, Z. Liu, Y. Wang, and X. Zhang, "Resonant and non-resonant generation and focusing of surface plasmons with circular gratings," Opt. Express 14, 5664-5670 (2006).
    [CrossRef] [PubMed]
  8. 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, 061124-061123 (2007).
    [CrossRef]
  9. D.-Z. Lin, C.-H. Chen, C.-K. Chang, T.-D. Cheng, C.-S. Yeh, and C.-K. Lee, "Subwavelength nondiffraction beam generated by a plasmonic lens," Appl. Phys. Lett. 92, 233106-233103 (2008).
    [CrossRef]
  10. S. Seo, H. C. Kim, H. Ko, and M. Cheng, "Subwavelength proximity nanolithography using a plasmonic lens," J. Vac. Sci. Technol. B 25, 2271-2276 (2007).
    [CrossRef]
  11. Z. Liu, J. M. Steele, W. Srituravanich, Y. Pikus, C. Sun, and X. Zhang, "Focusing Surface Plasmons with a Plasmonic Lens," Nano Lett. 5, 1726-1729 (2005).
    [CrossRef] [PubMed]
  12. C. Liu, N. Chen, and C. Sheppard, "Nanoillumination based on self-focus and field enhancement inside a subwavelength metallic structure," Appl. Phys. Lett. 90, 011501-011503 (2007).
    [CrossRef]
  13. P. K. Tien, "Integrated optics and new wave phenomena in optical waveguides," Rev. Mod. Phys. 49, 361 (1977).
    [CrossRef]
  14. R. Gordon and A. Brolo, "Increased cut-off wavelength for a subwavelength hole in a real metal," Opt. Express 13, 1933-1938 (2005).
    [CrossRef] [PubMed]
  15. H. Shi, C. Wang, C. Du, X. Luo, X. Dong, and H. Gao, "Beam manipulating by metallic nano-slits with variant widths," Opt. Express 13, 6815-6820 (2005).
    [CrossRef] [PubMed]
  16. B. Ung and Y. Sheng, "Mechanism of coupling and interference in nano-slit," in Holography and Diffractive Optics III, (SPIE, 2007), 68320E-68328.
  17. J. Park, H. Kim, I.-M. Lee, S. Kim, J. Jung, and B. Lee, "Resonant tunneling of surface plasmon polariton in the plasmonic nano-cavity," Opt. Express 16, 16903-16915 (2008).
    [CrossRef] [PubMed]

2008

D.-Z. Lin, C.-H. Chen, C.-K. Chang, T.-D. Cheng, C.-S. Yeh, and C.-K. Lee, "Subwavelength nondiffraction beam generated by a plasmonic lens," Appl. Phys. Lett. 92, 233106-233103 (2008).
[CrossRef]

H. C. Kim, H. Ko, and M. Cheng, "Optical focusing of plasmonic Fresnel zone plate-based metallic structure covered with a dielectric layer," J. Vac. Sci. Technol. B 26, 2197-2203 (2008).
[CrossRef]

Y. Fu, W. Zhou, and L. E. N. Lim, "Near-field behavior of zone-plate-like plasmonic nanostructures," J. Opt. Soc. Am. A 25, 238-249 (2008).
[CrossRef]

J. Park, H. Kim, I.-M. Lee, S. Kim, J. Jung, and B. Lee, "Resonant tunneling of surface plasmon polariton in the plasmonic nano-cavity," Opt. Express 16, 16903-16915 (2008).
[CrossRef] [PubMed]

2007

Z. H. Tang, R. W. Peng, Z. Wang, X. Wu, Y. J. Bao, Q. J. Wang, Z. J. Zhang, W. H. Sun, and M. Wang, "Coupling of surface plasmons in nanostructured metal/dielectric multilayers with subwavelength hole arrays," Phys. Rev. B 76, 195405-195408 (2007).
[CrossRef]

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, 061124-061123 (2007).
[CrossRef]

S. Seo, H. C. Kim, H. Ko, and M. Cheng, "Subwavelength proximity nanolithography using a plasmonic lens," J. Vac. Sci. Technol. B 25, 2271-2276 (2007).
[CrossRef]

C. Liu, N. Chen, and C. Sheppard, "Nanoillumination based on self-focus and field enhancement inside a subwavelength metallic structure," Appl. Phys. Lett. 90, 011501-011503 (2007).
[CrossRef]

2006

2005

1998

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

1977

P. K. Tien, "Integrated optics and new wave phenomena in optical waveguides," Rev. Mod. Phys. 49, 361 (1977).
[CrossRef]

Bao, Y. J.

Z. H. Tang, R. W. Peng, Z. Wang, X. Wu, Y. J. Bao, Q. J. Wang, Z. J. Zhang, W. H. Sun, and M. Wang, "Coupling of surface plasmons in nanostructured metal/dielectric multilayers with subwavelength hole arrays," Phys. Rev. B 76, 195405-195408 (2007).
[CrossRef]

Brolo, A.

Chang, C.-K.

D.-Z. Lin, C.-H. Chen, C.-K. Chang, T.-D. Cheng, C.-S. Yeh, and C.-K. Lee, "Subwavelength nondiffraction beam generated by a plasmonic lens," Appl. Phys. Lett. 92, 233106-233103 (2008).
[CrossRef]

Chen, C.-H.

D.-Z. Lin, C.-H. Chen, C.-K. Chang, T.-D. Cheng, C.-S. Yeh, and C.-K. Lee, "Subwavelength nondiffraction beam generated by a plasmonic lens," Appl. Phys. Lett. 92, 233106-233103 (2008).
[CrossRef]

Chen, N.

C. Liu, N. Chen, and C. Sheppard, "Nanoillumination based on self-focus and field enhancement inside a subwavelength metallic structure," Appl. Phys. Lett. 90, 011501-011503 (2007).
[CrossRef]

Cheng, M.

H. C. Kim, H. Ko, and M. Cheng, "Optical focusing of plasmonic Fresnel zone plate-based metallic structure covered with a dielectric layer," J. Vac. Sci. Technol. B 26, 2197-2203 (2008).
[CrossRef]

S. Seo, H. C. Kim, H. Ko, and M. Cheng, "Subwavelength proximity nanolithography using a plasmonic lens," J. Vac. Sci. Technol. B 25, 2271-2276 (2007).
[CrossRef]

Cheng, T.-D.

D.-Z. Lin, C.-H. Chen, C.-K. Chang, T.-D. Cheng, C.-S. Yeh, and C.-K. Lee, "Subwavelength nondiffraction beam generated by a plasmonic lens," Appl. Phys. Lett. 92, 233106-233103 (2008).
[CrossRef]

Dong, X.

Du, C.

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, 061124-061123 (2007).
[CrossRef]

Ebbesen, T. W.

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

Fu, Y.

Y. Fu, W. Zhou, and L. E. N. Lim, "Near-field behavior of zone-plate-like plasmonic nanostructures," J. Opt. Soc. Am. A 25, 238-249 (2008).
[CrossRef]

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, 061124-061123 (2007).
[CrossRef]

Gao, H.

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 (London) 391, 667-669 (1998).
[CrossRef]

Gordon, R.

Jung, J.

Kim, H.

Kim, H. C.

H. C. Kim, H. Ko, and M. Cheng, "Optical focusing of plasmonic Fresnel zone plate-based metallic structure covered with a dielectric layer," J. Vac. Sci. Technol. B 26, 2197-2203 (2008).
[CrossRef]

S. Seo, H. C. Kim, H. Ko, and M. Cheng, "Subwavelength proximity nanolithography using a plasmonic lens," J. Vac. Sci. Technol. B 25, 2271-2276 (2007).
[CrossRef]

Kim, S.

Ko, H.

H. C. Kim, H. Ko, and M. Cheng, "Optical focusing of plasmonic Fresnel zone plate-based metallic structure covered with a dielectric layer," J. Vac. Sci. Technol. B 26, 2197-2203 (2008).
[CrossRef]

S. Seo, H. C. Kim, H. Ko, and M. Cheng, "Subwavelength proximity nanolithography using a plasmonic lens," J. Vac. Sci. Technol. B 25, 2271-2276 (2007).
[CrossRef]

Lee, B.

Lee, C.-K.

D.-Z. Lin, C.-H. Chen, C.-K. Chang, T.-D. Cheng, C.-S. Yeh, and C.-K. Lee, "Subwavelength nondiffraction beam generated by a plasmonic lens," Appl. Phys. Lett. 92, 233106-233103 (2008).
[CrossRef]

Lee, I.-M.

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 (London) 391, 667-669 (1998).
[CrossRef]

Lim, L. E. N.

Y. Fu, W. Zhou, and L. E. N. Lim, "Near-field behavior of zone-plate-like plasmonic nanostructures," J. Opt. Soc. Am. A 25, 238-249 (2008).
[CrossRef]

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, 061124-061123 (2007).
[CrossRef]

Lin, D.-Z.

D.-Z. Lin, C.-H. Chen, C.-K. Chang, T.-D. Cheng, C.-S. Yeh, and C.-K. Lee, "Subwavelength nondiffraction beam generated by a plasmonic lens," Appl. Phys. Lett. 92, 233106-233103 (2008).
[CrossRef]

Liu, C.

C. Liu, N. Chen, and C. Sheppard, "Nanoillumination based on self-focus and field enhancement inside a subwavelength metallic structure," Appl. Phys. Lett. 90, 011501-011503 (2007).
[CrossRef]

Liu, Z.

J. M. Steele, Z. Liu, Y. Wang, and X. Zhang, "Resonant and non-resonant generation and focusing of surface plasmons with circular gratings," Opt. Express 14, 5664-5670 (2006).
[CrossRef] [PubMed]

Z. Liu, J. M. Steele, W. Srituravanich, Y. Pikus, C. Sun, and X. Zhang, "Focusing Surface Plasmons with a Plasmonic Lens," Nano Lett. 5, 1726-1729 (2005).
[CrossRef] [PubMed]

Luo, X.

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, 061124-061123 (2007).
[CrossRef]

Ozbay, E.

E. Ozbay, "Plasmonics: Merging Photonics and Electronics at Nanoscale Dimensions," Science 311, 189-193 (2006).
[CrossRef] [PubMed]

Park, J.

Peng, R. W.

Z. H. Tang, R. W. Peng, Z. Wang, X. Wu, Y. J. Bao, Q. J. Wang, Z. J. Zhang, W. H. Sun, and M. Wang, "Coupling of surface plasmons in nanostructured metal/dielectric multilayers with subwavelength hole arrays," Phys. Rev. B 76, 195405-195408 (2007).
[CrossRef]

Pikus, Y.

Z. Liu, J. M. Steele, W. Srituravanich, Y. Pikus, C. Sun, and X. Zhang, "Focusing Surface Plasmons with a Plasmonic Lens," Nano Lett. 5, 1726-1729 (2005).
[CrossRef] [PubMed]

Seo, S.

S. Seo, H. C. Kim, H. Ko, and M. Cheng, "Subwavelength proximity nanolithography using a plasmonic lens," J. Vac. Sci. Technol. B 25, 2271-2276 (2007).
[CrossRef]

Sheppard, C.

C. Liu, N. Chen, and C. Sheppard, "Nanoillumination based on self-focus and field enhancement inside a subwavelength metallic structure," Appl. Phys. Lett. 90, 011501-011503 (2007).
[CrossRef]

Shi, H.

Srituravanich, W.

Z. Liu, J. M. Steele, W. Srituravanich, Y. Pikus, C. Sun, and X. Zhang, "Focusing Surface Plasmons with a Plasmonic Lens," Nano Lett. 5, 1726-1729 (2005).
[CrossRef] [PubMed]

Steele, J. M.

J. M. Steele, Z. Liu, Y. Wang, and X. Zhang, "Resonant and non-resonant generation and focusing of surface plasmons with circular gratings," Opt. Express 14, 5664-5670 (2006).
[CrossRef] [PubMed]

Z. Liu, J. M. Steele, W. Srituravanich, Y. Pikus, C. Sun, and X. Zhang, "Focusing Surface Plasmons with a Plasmonic Lens," Nano Lett. 5, 1726-1729 (2005).
[CrossRef] [PubMed]

Sun, C.

Z. Liu, J. M. Steele, W. Srituravanich, Y. Pikus, C. Sun, and X. Zhang, "Focusing Surface Plasmons with a Plasmonic Lens," Nano Lett. 5, 1726-1729 (2005).
[CrossRef] [PubMed]

Sun, W. H.

Z. H. Tang, R. W. Peng, Z. Wang, X. Wu, Y. J. Bao, Q. J. Wang, Z. J. Zhang, W. H. Sun, and M. Wang, "Coupling of surface plasmons in nanostructured metal/dielectric multilayers with subwavelength hole arrays," Phys. Rev. B 76, 195405-195408 (2007).
[CrossRef]

Tang, Z. H.

Z. H. Tang, R. W. Peng, Z. Wang, X. Wu, Y. J. Bao, Q. J. Wang, Z. J. Zhang, W. H. Sun, and M. Wang, "Coupling of surface plasmons in nanostructured metal/dielectric multilayers with subwavelength hole arrays," Phys. Rev. B 76, 195405-195408 (2007).
[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 (London) 391, 667-669 (1998).
[CrossRef]

Tien, P. K.

P. K. Tien, "Integrated optics and new wave phenomena in optical waveguides," Rev. Mod. Phys. 49, 361 (1977).
[CrossRef]

Wang, C.

Wang, M.

Z. H. Tang, R. W. Peng, Z. Wang, X. Wu, Y. J. Bao, Q. J. Wang, Z. J. Zhang, W. H. Sun, and M. Wang, "Coupling of surface plasmons in nanostructured metal/dielectric multilayers with subwavelength hole arrays," Phys. Rev. B 76, 195405-195408 (2007).
[CrossRef]

Wang, Q. J.

Z. H. Tang, R. W. Peng, Z. Wang, X. Wu, Y. J. Bao, Q. J. Wang, Z. J. Zhang, W. H. Sun, and M. Wang, "Coupling of surface plasmons in nanostructured metal/dielectric multilayers with subwavelength hole arrays," Phys. Rev. B 76, 195405-195408 (2007).
[CrossRef]

Wang, Y.

Wang, Z.

Z. H. Tang, R. W. Peng, Z. Wang, X. Wu, Y. J. Bao, Q. J. Wang, Z. J. Zhang, W. H. Sun, and M. Wang, "Coupling of surface plasmons in nanostructured metal/dielectric multilayers with subwavelength hole arrays," Phys. Rev. B 76, 195405-195408 (2007).
[CrossRef]

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 (London) 391, 667-669 (1998).
[CrossRef]

Wu, X.

Z. H. Tang, R. W. Peng, Z. Wang, X. Wu, Y. J. Bao, Q. J. Wang, Z. J. Zhang, W. H. Sun, and M. Wang, "Coupling of surface plasmons in nanostructured metal/dielectric multilayers with subwavelength hole arrays," Phys. Rev. B 76, 195405-195408 (2007).
[CrossRef]

Yeh, C.-S.

D.-Z. Lin, C.-H. Chen, C.-K. Chang, T.-D. Cheng, C.-S. Yeh, and C.-K. Lee, "Subwavelength nondiffraction beam generated by a plasmonic lens," Appl. Phys. Lett. 92, 233106-233103 (2008).
[CrossRef]

Zhang, X.

J. M. Steele, Z. Liu, Y. Wang, and X. Zhang, "Resonant and non-resonant generation and focusing of surface plasmons with circular gratings," Opt. Express 14, 5664-5670 (2006).
[CrossRef] [PubMed]

Z. Liu, J. M. Steele, W. Srituravanich, Y. Pikus, C. Sun, and X. Zhang, "Focusing Surface Plasmons with a Plasmonic Lens," Nano Lett. 5, 1726-1729 (2005).
[CrossRef] [PubMed]

Zhang, Z. J.

Z. H. Tang, R. W. Peng, Z. Wang, X. Wu, Y. J. Bao, Q. J. Wang, Z. J. Zhang, W. H. Sun, and M. Wang, "Coupling of surface plasmons in nanostructured metal/dielectric multilayers with subwavelength hole arrays," Phys. Rev. B 76, 195405-195408 (2007).
[CrossRef]

Zhou, W.

Y. Fu, W. Zhou, and L. E. N. Lim, "Near-field behavior of zone-plate-like plasmonic nanostructures," J. Opt. Soc. Am. A 25, 238-249 (2008).
[CrossRef]

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, 061124-061123 (2007).
[CrossRef]

Appl. Phys. Lett.

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, 061124-061123 (2007).
[CrossRef]

D.-Z. Lin, C.-H. Chen, C.-K. Chang, T.-D. Cheng, C.-S. Yeh, and C.-K. Lee, "Subwavelength nondiffraction beam generated by a plasmonic lens," Appl. Phys. Lett. 92, 233106-233103 (2008).
[CrossRef]

C. Liu, N. Chen, and C. Sheppard, "Nanoillumination based on self-focus and field enhancement inside a subwavelength metallic structure," Appl. Phys. Lett. 90, 011501-011503 (2007).
[CrossRef]

J. Opt. Soc. Am. A

J. Vac. Sci. Technol. B

H. C. Kim, H. Ko, and M. Cheng, "Optical focusing of plasmonic Fresnel zone plate-based metallic structure covered with a dielectric layer," J. Vac. Sci. Technol. B 26, 2197-2203 (2008).
[CrossRef]

S. Seo, H. C. Kim, H. Ko, and M. Cheng, "Subwavelength proximity nanolithography using a plasmonic lens," J. Vac. Sci. Technol. B 25, 2271-2276 (2007).
[CrossRef]

Nano Lett.

Z. Liu, J. M. Steele, W. Srituravanich, Y. Pikus, C. Sun, and X. Zhang, "Focusing Surface Plasmons with a Plasmonic Lens," Nano Lett. 5, 1726-1729 (2005).
[CrossRef] [PubMed]

Nature (London)

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

Opt. Express

Phys. Rev. B

Z. H. Tang, R. W. Peng, Z. Wang, X. Wu, Y. J. Bao, Q. J. Wang, Z. J. Zhang, W. H. Sun, and M. Wang, "Coupling of surface plasmons in nanostructured metal/dielectric multilayers with subwavelength hole arrays," Phys. Rev. B 76, 195405-195408 (2007).
[CrossRef]

Rev. Mod. Phys.

P. K. Tien, "Integrated optics and new wave phenomena in optical waveguides," Rev. Mod. Phys. 49, 361 (1977).
[CrossRef]

Science

E. Ozbay, "Plasmonics: Merging Photonics and Electronics at Nanoscale Dimensions," Science 311, 189-193 (2006).
[CrossRef] [PubMed]

Other

E. D. Palik, Handbook of Optical Constants of Solids (Academic, New York, 1985).

B. Ung and Y. Sheng, "Mechanism of coupling and interference in nano-slit," in Holography and Diffractive Optics III, (SPIE, 2007), 68320E-68328.

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Figures (4)

Fig. 1.
Fig. 1.

Schematic figures of the proposed multilayered zone plate structure: (a) Top down view in xy plane, and (b) cross-sectional view in xz plane (y = 4.0 μm).

Fig. 2.
Fig. 2.

Field distributions of the transmitted field in xz plane: (a) monolayered zone plate (Mono-ZP) and (b) multilayered zone plate (Multi-ZP) with N = 5, and (c) comparison of the normalized intensity for the Mono-ZP and Multi-ZP, respectively, along z direction. The inset shows real part and imaginary part of effective refractive index as a function of the width of two metal plates.

Fig. 3.
Fig. 3.

(a) Comparison of transmission efficiency (η) and spot size (FWHM) as a function of the building block for the Multi-ZP and corresponding thickness for the Mono-ZP, respectively. (b) The transmission efficiency and spot size when the focal planes of each building block coincide.

Fig. 4.
Fig. 4.

Comparison of the normalized intensity for the various dielectric materials along z direction: SiO2 (ε = 2.16), Al2O3 (ε = 3.20), HfO2 (ε = 3.92), and ZrO2 (ε = 5.15), respectively, with N = 5. The inset shows real part (Re(neff)) and imaginary part (Im(neff)) of effective refractive indices, and propagation lengths (Lspp) of SPPs as a function of the dielectric permittivity (εd) at w = 30 nm.

Equations (1)

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tanh ( β 2 k 0 2 ε d w / 2 ) = ε d β 2 k 0 2 ε m ε m β 2 k 0 2 ε d

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