Abstract

The properties of silver and aluminium wire-grid polarizers are examined in the volume plasmon frequency region where the transmittances of field with polarizations parallel and perpendicular to the grid lines are reversed with respect to their behavior outside the plasma region. Analysis of the behavior is conducted with effective approximate refractive index formulae and by simulations with rigorous Fourier modal method. The parallel polarization behaves as in a homogenous thin metal film while the perpendicular field is absorbed in the plasma region and transmitted otherwise. We further explain the performance by viewing the distribution of the field intensities inside the grating.

© 2009 Optical Society of America

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    [CrossRef]
  4. L. Chen, J. J. Wang, F. Walters, X. Deng, M. Buonanno, S. Tai, and X. Liu, "Large flexible nanowire grid visible polarizer made by nanoimprint lithography," Appl. Phys. Lett. 90, 063111, (2007).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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  14. M. Honkanen, V. Kettunen, M. Kuittinen, J. Lautanen, J. Turunen, B. Schnabel, and F. Wyrowski, "Inverse metalstripe polarizers," Appl. Phys. B 68, 81-85 (1999).
    [CrossRef]
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    [CrossRef]
  17. A. Christ, S. G. Tikhodeev, N. A. Gippius, J. Kuhl, and H. Giessen, "Plasmon polaritons in a metallic photonic crystal slab," Phys. Stat. Solidi C 0, 1393-1396 (2003).
    [CrossRef]
  18. E. A. Taft and H. R. Phillip, "Optical constants of silver," Phys. Rev. 121, 1100-1103 (1961).
    [CrossRef]
  19. F. Wooten, Optical Properties of Solids (Academic press, New York, 1972).
  20. ed-in-chief D. R. Lide, Handbook of Chemistry and Physics, 85th edit. (CRC Press, Boca Raton, 2005).
  21. M. Kuittinen, J. Turunen, and P. Vahimaa, "Subwavelength-structured elements" in Diffractive Optics for Industrial and Commercial Applications, J. Turunen, F. Wyrowski, eds. (Cambridge university press, New York, 1998).
  22. J. Turunen, "Diffraction theory of microrelief gratings" in Micro-Optics, Elements, Systems, and Applications, H. P. Herzig, ed. (Taylor & Francis, London, 1997).
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    [CrossRef]

2007 (2)

L. Chen, J. J. Wang, F. Walters, X. Deng, M. Buonanno, S. Tai, and X. Liu, "Large flexible nanowire grid visible polarizer made by nanoimprint lithography," Appl. Phys. Lett. 90, 063111, (2007).
[CrossRef]

C. Ropers, C. C. Neacsu, T. Elsaesser, M. Albrecht, M. B. Raschke, and C. Lienau, "Grating-coupling of surface plasmons onto metallic tips: a nanoconfined light source," Nano Lett. 7, 2784-2788 (2007).
[CrossRef] [PubMed]

2003 (3)

J. Homola, "Present and future of surface plasmon resonance biosensors," Anal. Bioanal. Chem. 377, 528-539 (2003).
[CrossRef] [PubMed]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

A. Christ, S. G. Tikhodeev, N. A. Gippius, J. Kuhl, and H. Giessen, "Plasmon polaritons in a metallic photonic crystal slab," Phys. Stat. Solidi C 0, 1393-1396 (2003).
[CrossRef]

2001 (2)

G. Schider, J. R. Krenn, W. Gotschy, B. Lamprecht, H. Ditlbacher, A. Leitner, and F. R. Aussenegg, "Optical properties of Ag and Au nanowire gratings," J. Appl. Phys. 90, 3825-3830 (2001).
[CrossRef]

C. Pentico, E. Gardner, D. Hansen, and R. Perkins, "New, high performance, durable polarizers for projection displays," SID Int. Symp. Digest Tech. Papers 32, 1287-1289, (2001).
[CrossRef]

1999 (2)

M. Honkanen, V. Kettunen, M. Kuittinen, J. Lautanen, J. Turunen, B. Schnabel, and F. Wyrowski, "Inverse metalstripe polarizers," Appl. Phys. B 68, 81-85 (1999).
[CrossRef]

F. J. García-Vidal, J. Sánchez-Dehesa, A. Dechelette, E. Bustarret, T. López-Ríos, T. Fournier, and B. Pannetier, "Localized surface plasmons in lamellar metallic gratings," J. Lightwave Technol. 17, 2191-2195 (1999).
[CrossRef]

1996 (1)

1968 (1)

R. H. Ritchie, E. T. Arakawa, J. J. Kowan, and R. N. Hamm, "Surface plasmon resonance effect in grating diffraction," Phys. Rev. Let. 21, 1530-1533 (1968).
[CrossRef]

1965 (1)

1961 (1)

E. A. Taft and H. R. Phillip, "Optical constants of silver," Phys. Rev. 121, 1100-1103 (1961).
[CrossRef]

1960 (1)

1956 (1)

D. Pines, "Collective energy losses in solids," Rev. Mod. Phys. 28, 184-199 (1956).
[CrossRef]

1941 (1)

1902 (1)

R. W. Wood, "On a remarkable case of uneven distribution of light in a diffraction grating spectrum," Phil. Mag. 4, 396-402 (1902).

Albrecht, M.

C. Ropers, C. C. Neacsu, T. Elsaesser, M. Albrecht, M. B. Raschke, and C. Lienau, "Grating-coupling of surface plasmons onto metallic tips: a nanoconfined light source," Nano Lett. 7, 2784-2788 (2007).
[CrossRef] [PubMed]

Arakawa, E. T.

R. H. Ritchie, E. T. Arakawa, J. J. Kowan, and R. N. Hamm, "Surface plasmon resonance effect in grating diffraction," Phys. Rev. Let. 21, 1530-1533 (1968).
[CrossRef]

Aussenegg, F. R.

G. Schider, J. R. Krenn, W. Gotschy, B. Lamprecht, H. Ditlbacher, A. Leitner, and F. R. Aussenegg, "Optical properties of Ag and Au nanowire gratings," J. Appl. Phys. 90, 3825-3830 (2001).
[CrossRef]

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

Bird, G. R.

Buonanno, M.

L. Chen, J. J. Wang, F. Walters, X. Deng, M. Buonanno, S. Tai, and X. Liu, "Large flexible nanowire grid visible polarizer made by nanoimprint lithography," Appl. Phys. Lett. 90, 063111, (2007).
[CrossRef]

Bustarret, E.

Chen, L.

L. Chen, J. J. Wang, F. Walters, X. Deng, M. Buonanno, S. Tai, and X. Liu, "Large flexible nanowire grid visible polarizer made by nanoimprint lithography," Appl. Phys. Lett. 90, 063111, (2007).
[CrossRef]

Christ, A.

A. Christ, S. G. Tikhodeev, N. A. Gippius, J. Kuhl, and H. Giessen, "Plasmon polaritons in a metallic photonic crystal slab," Phys. Stat. Solidi C 0, 1393-1396 (2003).
[CrossRef]

Dechelette, A.

Deng, X.

L. Chen, J. J. Wang, F. Walters, X. Deng, M. Buonanno, S. Tai, and X. Liu, "Large flexible nanowire grid visible polarizer made by nanoimprint lithography," Appl. Phys. Lett. 90, 063111, (2007).
[CrossRef]

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

Ditlbacher, H.

G. Schider, J. R. Krenn, W. Gotschy, B. Lamprecht, H. Ditlbacher, A. Leitner, and F. R. Aussenegg, "Optical properties of Ag and Au nanowire gratings," J. Appl. Phys. 90, 3825-3830 (2001).
[CrossRef]

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

Elsaesser, T.

C. Ropers, C. C. Neacsu, T. Elsaesser, M. Albrecht, M. B. Raschke, and C. Lienau, "Grating-coupling of surface plasmons onto metallic tips: a nanoconfined light source," Nano Lett. 7, 2784-2788 (2007).
[CrossRef] [PubMed]

Fano, U.

Fournier, T.

García-Vidal, F. J.

Gardner, E.

C. Pentico, E. Gardner, D. Hansen, and R. Perkins, "New, high performance, durable polarizers for projection displays," SID Int. Symp. Digest Tech. Papers 32, 1287-1289, (2001).
[CrossRef]

Giessen, H.

A. Christ, S. G. Tikhodeev, N. A. Gippius, J. Kuhl, and H. Giessen, "Plasmon polaritons in a metallic photonic crystal slab," Phys. Stat. Solidi C 0, 1393-1396 (2003).
[CrossRef]

Gippius, N. A.

A. Christ, S. G. Tikhodeev, N. A. Gippius, J. Kuhl, and H. Giessen, "Plasmon polaritons in a metallic photonic crystal slab," Phys. Stat. Solidi C 0, 1393-1396 (2003).
[CrossRef]

Gotschy, W.

G. Schider, J. R. Krenn, W. Gotschy, B. Lamprecht, H. Ditlbacher, A. Leitner, and F. R. Aussenegg, "Optical properties of Ag and Au nanowire gratings," J. Appl. Phys. 90, 3825-3830 (2001).
[CrossRef]

Graham, H. A.

Hamm, R. N.

R. H. Ritchie, E. T. Arakawa, J. J. Kowan, and R. N. Hamm, "Surface plasmon resonance effect in grating diffraction," Phys. Rev. Let. 21, 1530-1533 (1968).
[CrossRef]

Hansen, D.

C. Pentico, E. Gardner, D. Hansen, and R. Perkins, "New, high performance, durable polarizers for projection displays," SID Int. Symp. Digest Tech. Papers 32, 1287-1289, (2001).
[CrossRef]

Homola, J.

J. Homola, "Present and future of surface plasmon resonance biosensors," Anal. Bioanal. Chem. 377, 528-539 (2003).
[CrossRef] [PubMed]

Honkanen, M.

M. Honkanen, V. Kettunen, M. Kuittinen, J. Lautanen, J. Turunen, B. Schnabel, and F. Wyrowski, "Inverse metalstripe polarizers," Appl. Phys. B 68, 81-85 (1999).
[CrossRef]

Kettunen, V.

M. Honkanen, V. Kettunen, M. Kuittinen, J. Lautanen, J. Turunen, B. Schnabel, and F. Wyrowski, "Inverse metalstripe polarizers," Appl. Phys. B 68, 81-85 (1999).
[CrossRef]

Kowan, J. J.

R. H. Ritchie, E. T. Arakawa, J. J. Kowan, and R. N. Hamm, "Surface plasmon resonance effect in grating diffraction," Phys. Rev. Let. 21, 1530-1533 (1968).
[CrossRef]

Krenn, J. R.

G. Schider, J. R. Krenn, W. Gotschy, B. Lamprecht, H. Ditlbacher, A. Leitner, and F. R. Aussenegg, "Optical properties of Ag and Au nanowire gratings," J. Appl. Phys. 90, 3825-3830 (2001).
[CrossRef]

Kuhl, J.

A. Christ, S. G. Tikhodeev, N. A. Gippius, J. Kuhl, and H. Giessen, "Plasmon polaritons in a metallic photonic crystal slab," Phys. Stat. Solidi C 0, 1393-1396 (2003).
[CrossRef]

Kuittinen, M.

M. Honkanen, V. Kettunen, M. Kuittinen, J. Lautanen, J. Turunen, B. Schnabel, and F. Wyrowski, "Inverse metalstripe polarizers," Appl. Phys. B 68, 81-85 (1999).
[CrossRef]

Lalanne, P.

Lamprecht, B.

G. Schider, J. R. Krenn, W. Gotschy, B. Lamprecht, H. Ditlbacher, A. Leitner, and F. R. Aussenegg, "Optical properties of Ag and Au nanowire gratings," J. Appl. Phys. 90, 3825-3830 (2001).
[CrossRef]

Lautanen, J.

M. Honkanen, V. Kettunen, M. Kuittinen, J. Lautanen, J. Turunen, B. Schnabel, and F. Wyrowski, "Inverse metalstripe polarizers," Appl. Phys. B 68, 81-85 (1999).
[CrossRef]

Leitner, A.

G. Schider, J. R. Krenn, W. Gotschy, B. Lamprecht, H. Ditlbacher, A. Leitner, and F. R. Aussenegg, "Optical properties of Ag and Au nanowire gratings," J. Appl. Phys. 90, 3825-3830 (2001).
[CrossRef]

Lienau, C.

C. Ropers, C. C. Neacsu, T. Elsaesser, M. Albrecht, M. B. Raschke, and C. Lienau, "Grating-coupling of surface plasmons onto metallic tips: a nanoconfined light source," Nano Lett. 7, 2784-2788 (2007).
[CrossRef] [PubMed]

Liu, X.

L. Chen, J. J. Wang, F. Walters, X. Deng, M. Buonanno, S. Tai, and X. Liu, "Large flexible nanowire grid visible polarizer made by nanoimprint lithography," Appl. Phys. Lett. 90, 063111, (2007).
[CrossRef]

López-Ríos, T.

Morris, G. M.

Neacsu, C. C.

C. Ropers, C. C. Neacsu, T. Elsaesser, M. Albrecht, M. B. Raschke, and C. Lienau, "Grating-coupling of surface plasmons onto metallic tips: a nanoconfined light source," Nano Lett. 7, 2784-2788 (2007).
[CrossRef] [PubMed]

Pannetier, B.

Parrish, M.

Pentico, C.

C. Pentico, E. Gardner, D. Hansen, and R. Perkins, "New, high performance, durable polarizers for projection displays," SID Int. Symp. Digest Tech. Papers 32, 1287-1289, (2001).
[CrossRef]

Perkins, R.

C. Pentico, E. Gardner, D. Hansen, and R. Perkins, "New, high performance, durable polarizers for projection displays," SID Int. Symp. Digest Tech. Papers 32, 1287-1289, (2001).
[CrossRef]

Peterson, E. W.

Phillip, H. R.

E. A. Taft and H. R. Phillip, "Optical constants of silver," Phys. Rev. 121, 1100-1103 (1961).
[CrossRef]

Pines, D.

D. Pines, "Collective energy losses in solids," Rev. Mod. Phys. 28, 184-199 (1956).
[CrossRef]

Raschke, M. B.

C. Ropers, C. C. Neacsu, T. Elsaesser, M. Albrecht, M. B. Raschke, and C. Lienau, "Grating-coupling of surface plasmons onto metallic tips: a nanoconfined light source," Nano Lett. 7, 2784-2788 (2007).
[CrossRef] [PubMed]

Ritchie, R. H.

R. H. Ritchie, E. T. Arakawa, J. J. Kowan, and R. N. Hamm, "Surface plasmon resonance effect in grating diffraction," Phys. Rev. Let. 21, 1530-1533 (1968).
[CrossRef]

Ropers, C.

C. Ropers, C. C. Neacsu, T. Elsaesser, M. Albrecht, M. B. Raschke, and C. Lienau, "Grating-coupling of surface plasmons onto metallic tips: a nanoconfined light source," Nano Lett. 7, 2784-2788 (2007).
[CrossRef] [PubMed]

Sánchez-Dehesa, J.

Schider, G.

G. Schider, J. R. Krenn, W. Gotschy, B. Lamprecht, H. Ditlbacher, A. Leitner, and F. R. Aussenegg, "Optical properties of Ag and Au nanowire gratings," J. Appl. Phys. 90, 3825-3830 (2001).
[CrossRef]

Schnabel, B.

M. Honkanen, V. Kettunen, M. Kuittinen, J. Lautanen, J. Turunen, B. Schnabel, and F. Wyrowski, "Inverse metalstripe polarizers," Appl. Phys. B 68, 81-85 (1999).
[CrossRef]

Taft, E. A.

E. A. Taft and H. R. Phillip, "Optical constants of silver," Phys. Rev. 121, 1100-1103 (1961).
[CrossRef]

Tai, S.

L. Chen, J. J. Wang, F. Walters, X. Deng, M. Buonanno, S. Tai, and X. Liu, "Large flexible nanowire grid visible polarizer made by nanoimprint lithography," Appl. Phys. Lett. 90, 063111, (2007).
[CrossRef]

Tikhodeev, S. G.

A. Christ, S. G. Tikhodeev, N. A. Gippius, J. Kuhl, and H. Giessen, "Plasmon polaritons in a metallic photonic crystal slab," Phys. Stat. Solidi C 0, 1393-1396 (2003).
[CrossRef]

Turunen, J.

M. Honkanen, V. Kettunen, M. Kuittinen, J. Lautanen, J. Turunen, B. Schnabel, and F. Wyrowski, "Inverse metalstripe polarizers," Appl. Phys. B 68, 81-85 (1999).
[CrossRef]

Walters, F.

L. Chen, J. J. Wang, F. Walters, X. Deng, M. Buonanno, S. Tai, and X. Liu, "Large flexible nanowire grid visible polarizer made by nanoimprint lithography," Appl. Phys. Lett. 90, 063111, (2007).
[CrossRef]

Wang, J. J.

L. Chen, J. J. Wang, F. Walters, X. Deng, M. Buonanno, S. Tai, and X. Liu, "Large flexible nanowire grid visible polarizer made by nanoimprint lithography," Appl. Phys. Lett. 90, 063111, (2007).
[CrossRef]

Wood, R. W.

R. W. Wood, "On a remarkable case of uneven distribution of light in a diffraction grating spectrum," Phil. Mag. 4, 396-402 (1902).

Wyrowski, F.

M. Honkanen, V. Kettunen, M. Kuittinen, J. Lautanen, J. Turunen, B. Schnabel, and F. Wyrowski, "Inverse metalstripe polarizers," Appl. Phys. B 68, 81-85 (1999).
[CrossRef]

Young, J. B.

Anal. Bioanal. Chem. (1)

J. Homola, "Present and future of surface plasmon resonance biosensors," Anal. Bioanal. Chem. 377, 528-539 (2003).
[CrossRef] [PubMed]

Appl. Opt. (1)

Appl. Phys. B (1)

M. Honkanen, V. Kettunen, M. Kuittinen, J. Lautanen, J. Turunen, B. Schnabel, and F. Wyrowski, "Inverse metalstripe polarizers," Appl. Phys. B 68, 81-85 (1999).
[CrossRef]

Appl. Phys. Lett. (1)

L. Chen, J. J. Wang, F. Walters, X. Deng, M. Buonanno, S. Tai, and X. Liu, "Large flexible nanowire grid visible polarizer made by nanoimprint lithography," Appl. Phys. Lett. 90, 063111, (2007).
[CrossRef]

J. Appl. Phys. (1)

G. Schider, J. R. Krenn, W. Gotschy, B. Lamprecht, H. Ditlbacher, A. Leitner, and F. R. Aussenegg, "Optical properties of Ag and Au nanowire gratings," J. Appl. Phys. 90, 3825-3830 (2001).
[CrossRef]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. (2)

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

Nano Letters (1)

C. Ropers, C. C. Neacsu, T. Elsaesser, M. Albrecht, M. B. Raschke, and C. Lienau, "Grating-coupling of surface plasmons onto metallic tips: a nanoconfined light source," Nano Lett. 7, 2784-2788 (2007).
[CrossRef] [PubMed]

Nature (1)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

Phil. Mag. (1)

R. W. Wood, "On a remarkable case of uneven distribution of light in a diffraction grating spectrum," Phil. Mag. 4, 396-402 (1902).

Phys. Rev. (1)

E. A. Taft and H. R. Phillip, "Optical constants of silver," Phys. Rev. 121, 1100-1103 (1961).
[CrossRef]

Phys. Rev. Let. (1)

R. H. Ritchie, E. T. Arakawa, J. J. Kowan, and R. N. Hamm, "Surface plasmon resonance effect in grating diffraction," Phys. Rev. Let. 21, 1530-1533 (1968).
[CrossRef]

Phys. Status Solidi C (1)

A. Christ, S. G. Tikhodeev, N. A. Gippius, J. Kuhl, and H. Giessen, "Plasmon polaritons in a metallic photonic crystal slab," Phys. Stat. Solidi C 0, 1393-1396 (2003).
[CrossRef]

Rev. Mod. Phys. (1)

D. Pines, "Collective energy losses in solids," Rev. Mod. Phys. 28, 184-199 (1956).
[CrossRef]

SID Int. Symp. Digest Tech. Papers (1)

C. Pentico, E. Gardner, D. Hansen, and R. Perkins, "New, high performance, durable polarizers for projection displays," SID Int. Symp. Digest Tech. Papers 32, 1287-1289, (2001).
[CrossRef]

Other (6)

F. Wooten, Optical Properties of Solids (Academic press, New York, 1972).

ed-in-chief D. R. Lide, Handbook of Chemistry and Physics, 85th edit. (CRC Press, Boca Raton, 2005).

M. Kuittinen, J. Turunen, and P. Vahimaa, "Subwavelength-structured elements" in Diffractive Optics for Industrial and Commercial Applications, J. Turunen, F. Wyrowski, eds. (Cambridge university press, New York, 1998).

J. Turunen, "Diffraction theory of microrelief gratings" in Micro-Optics, Elements, Systems, and Applications, H. P. Herzig, ed. (Taylor & Francis, London, 1997).

S. E. Maier, Plasmonics: Fundamentals and Applications (Springer Science+Business Media LLC, New York, 2007).

edited by M. L. Brongersma and P. G. Kik Surface Plasmon Nanophotonics (Springer, Dordrecht, 2007).
[CrossRef]

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Figures (7)

Fig. 1.
Fig. 1.

Real part (solid line) and imaginary part (dashed line) of the complex permittivity for silver. The values are calculated from the refractive indexes given in [20].

Fig. 2.
Fig. 2.

Grating geometry.

Fig. 3.
Fig. 3.

Transmittance (a) and absorbance (b) of parallel (∥) and perpendicular (⊥) polarizations for a silver wire-grid grating on silica substrate with period 30 nm, depth 100 nm, and line width 5 nm.

Fig. 4.
Fig. 4.

Intensities in the cross-sectional view of the grating. (a) and (b) show the perpendicular field for the wavelengths 630 nm and 330 nm, respectively. (c) and (d) are for the parallel field for the same wavelengths 630 nm and 330 nm, respectively.

Fig. 5.
Fig. 5.

Effective refractive indexes as a function of wavelength for a silver grating with the same grating parameters as in Fig. 3. Black lines indicate the parallel field and red lines the perpendicular. Solid lines represents the real parts and dashed lines the imaginary parts.

Fig. 6.
Fig. 6.

Transmittances (a) and effective refractive indexes (b) for a silver grating with period 100 nm, fill factor 0.5 and height 100 nm.

Fig. 7.
Fig. 7.

Transmittances (a) and effective refractive indexes (b) for a self-supporting aluminium grating with period 40 nm, fill factor 0.5 and height 100 nm.

Equations (11)

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ε 1 = 0
ε 2 1 .
n = ε .
n eff = [ f n 1 2 + ( 1 f ) n 2 2 ] 1 / 2 ,
n eff = [ f n 1 2 + ( 1 f ) n 2 2 ] 1 / 2 ,
n ̂ eff = γ 0 / k ,
n eff 1 f .
D air = D Ag ε air E air = ε Ag E Ag ,
E Ag 2 E air 2 .
E Ag 2 E air 2 .
n eff n ̂ 1 f .

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