Abstract

Narrowband rejection filters can be constructed from multilayers of dielectric and ultrathin metal films operating in the anomalous skin effect region constrained by the optical size effect. The wavelength of the main reflecting spectrum is wholly determined by the dielectric thickness, and the bandwidth can be reduced by increasing the total number of layers and selecting the dielectric film with high refractive index while diminishing the thickness of the metal film.

© 1991 Optical Society of America

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References

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  1. J.-T. Lue, Y.-S. Hor, “Optical Filters Constructed from Multilayers of Dielectric and Thin Metallic Films Operating in the Anomalous Skin Effect Region,” J. Opt. Soc. Am. B 6, 1103 (1989).
    [CrossRef]
  2. J. Szczyrbowski, K. Schmalzbauer, H. Haffmann, “Optical Transmittance and Reflectance and Dynamic Current Density for Thin Metallic Films,” Phys. Rev. B 32, 763–770 (1985).
    [CrossRef]
  3. M. S. D. Lucas, “Electrical Conductivity of Thin Metallic Films with Unlike Surfaces,” J. Appl. Phys. 36, 1632–1635 (1965).
    [CrossRef]
  4. C. R. Tellier, A. J. Tosser, Size Effects in Thin Films (Elsevier, Amsterdam, 1982), p. 13.
  5. S. H. Mahmood, A. Malkawi, I. Abu-Aljarayesh, “Evolution and Splitting of Plasmon Bands in Metallic Superlattices,” Phys. Rev. B 40, 988–992 (1989).
    [CrossRef]
  6. J. Dryzek, R. Dimmich, “Effect of Surface Scattering on Optical Properties of Metallic Double-Layer Films,” Phys. Rev. B. 34, 843–856 (1986).
    [CrossRef]
  7. H. A. Macleod, “A New Approach to the Design of Metal-Dielectric Thin Film Optical Coatings,” Opt. Acta 25, 93–106 (1978).
    [CrossRef]

1989

S. H. Mahmood, A. Malkawi, I. Abu-Aljarayesh, “Evolution and Splitting of Plasmon Bands in Metallic Superlattices,” Phys. Rev. B 40, 988–992 (1989).
[CrossRef]

J.-T. Lue, Y.-S. Hor, “Optical Filters Constructed from Multilayers of Dielectric and Thin Metallic Films Operating in the Anomalous Skin Effect Region,” J. Opt. Soc. Am. B 6, 1103 (1989).
[CrossRef]

1986

J. Dryzek, R. Dimmich, “Effect of Surface Scattering on Optical Properties of Metallic Double-Layer Films,” Phys. Rev. B. 34, 843–856 (1986).
[CrossRef]

1985

J. Szczyrbowski, K. Schmalzbauer, H. Haffmann, “Optical Transmittance and Reflectance and Dynamic Current Density for Thin Metallic Films,” Phys. Rev. B 32, 763–770 (1985).
[CrossRef]

1978

H. A. Macleod, “A New Approach to the Design of Metal-Dielectric Thin Film Optical Coatings,” Opt. Acta 25, 93–106 (1978).
[CrossRef]

1965

M. S. D. Lucas, “Electrical Conductivity of Thin Metallic Films with Unlike Surfaces,” J. Appl. Phys. 36, 1632–1635 (1965).
[CrossRef]

Abu-Aljarayesh, I.

S. H. Mahmood, A. Malkawi, I. Abu-Aljarayesh, “Evolution and Splitting of Plasmon Bands in Metallic Superlattices,” Phys. Rev. B 40, 988–992 (1989).
[CrossRef]

Dimmich, R.

J. Dryzek, R. Dimmich, “Effect of Surface Scattering on Optical Properties of Metallic Double-Layer Films,” Phys. Rev. B. 34, 843–856 (1986).
[CrossRef]

Dryzek, J.

J. Dryzek, R. Dimmich, “Effect of Surface Scattering on Optical Properties of Metallic Double-Layer Films,” Phys. Rev. B. 34, 843–856 (1986).
[CrossRef]

Haffmann, H.

J. Szczyrbowski, K. Schmalzbauer, H. Haffmann, “Optical Transmittance and Reflectance and Dynamic Current Density for Thin Metallic Films,” Phys. Rev. B 32, 763–770 (1985).
[CrossRef]

Hor, Y.-S.

Lucas, M. S. D.

M. S. D. Lucas, “Electrical Conductivity of Thin Metallic Films with Unlike Surfaces,” J. Appl. Phys. 36, 1632–1635 (1965).
[CrossRef]

Lue, J.-T.

Macleod, H. A.

H. A. Macleod, “A New Approach to the Design of Metal-Dielectric Thin Film Optical Coatings,” Opt. Acta 25, 93–106 (1978).
[CrossRef]

Mahmood, S. H.

S. H. Mahmood, A. Malkawi, I. Abu-Aljarayesh, “Evolution and Splitting of Plasmon Bands in Metallic Superlattices,” Phys. Rev. B 40, 988–992 (1989).
[CrossRef]

Malkawi, A.

S. H. Mahmood, A. Malkawi, I. Abu-Aljarayesh, “Evolution and Splitting of Plasmon Bands in Metallic Superlattices,” Phys. Rev. B 40, 988–992 (1989).
[CrossRef]

Schmalzbauer, K.

J. Szczyrbowski, K. Schmalzbauer, H. Haffmann, “Optical Transmittance and Reflectance and Dynamic Current Density for Thin Metallic Films,” Phys. Rev. B 32, 763–770 (1985).
[CrossRef]

Szczyrbowski, J.

J. Szczyrbowski, K. Schmalzbauer, H. Haffmann, “Optical Transmittance and Reflectance and Dynamic Current Density for Thin Metallic Films,” Phys. Rev. B 32, 763–770 (1985).
[CrossRef]

Tellier, C. R.

C. R. Tellier, A. J. Tosser, Size Effects in Thin Films (Elsevier, Amsterdam, 1982), p. 13.

Tosser, A. J.

C. R. Tellier, A. J. Tosser, Size Effects in Thin Films (Elsevier, Amsterdam, 1982), p. 13.

J. Appl. Phys.

M. S. D. Lucas, “Electrical Conductivity of Thin Metallic Films with Unlike Surfaces,” J. Appl. Phys. 36, 1632–1635 (1965).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Acta

H. A. Macleod, “A New Approach to the Design of Metal-Dielectric Thin Film Optical Coatings,” Opt. Acta 25, 93–106 (1978).
[CrossRef]

Phys. Rev. B

J. Szczyrbowski, K. Schmalzbauer, H. Haffmann, “Optical Transmittance and Reflectance and Dynamic Current Density for Thin Metallic Films,” Phys. Rev. B 32, 763–770 (1985).
[CrossRef]

S. H. Mahmood, A. Malkawi, I. Abu-Aljarayesh, “Evolution and Splitting of Plasmon Bands in Metallic Superlattices,” Phys. Rev. B 40, 988–992 (1989).
[CrossRef]

Phys. Rev. B.

J. Dryzek, R. Dimmich, “Effect of Surface Scattering on Optical Properties of Metallic Double-Layer Films,” Phys. Rev. B. 34, 843–856 (1986).
[CrossRef]

Other

C. R. Tellier, A. J. Tosser, Size Effects in Thin Films (Elsevier, Amsterdam, 1982), p. 13.

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Figures (5)

Fig. 1
Fig. 1

Reflectance R and transmittance T for ten-layer Ag–Al2O3 films with ns = 1.52, d(Ag) = 5 nm, and d1(Al2O3) = 300 nm.

Fig. 2
Fig. 2

Forbidden dielectric thickness for obtaining a single value of reflecting spectrum in the visible wavelength region.

Fig. 3
Fig. 3

Reflectance R and transmittance T for ten-layer Ag–MgF2 films with nd = 1.38, ns = 1.52 m, d1 = 370 nm, d = 3 m, p = q = 1, and N = 20.

Fig. 4
Fig. 4

Reflectance R and transmittance T for nd = 1.38, ns = 1.52, d1 = 200 nm, d = 3 nm, p = q = 1, and N = 20.

Fig. 5
Fig. 5

Reflectance R and transmittance T for nd = 1.38, ns = 1.52, d1 = 160 nm, d = 3 nm, p = q = 1, and N = 10.

Equations (13)

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r = r 12 + r 23 Q exp ( 2 u w d ) 1 + r 12 r 23 exp ( 2 u w d ) , t = t 12 + t 23 exp ( u w d ) 1 + r 12 r 23 exp ( 2 u w d ) ,
r 12 = n 1 n ( o ) n 1 + n ( o ) , r 12 = n 1 n ( o ) n 1 + n ( o ) , r 23 = n ( d ) n 3 n ( d ) + n 3 , t i j = 1 + r i j , Q = n 1 + n ( o ) n 1 + n ( o ) .
n ( o ) = n b μ F ( u , p , q ) ,
n ( o ) = n b μ + F ( u , q , p ) ,
n ( d ) = n b μ + F ( u , p , q ) ,
n ( d ) = n b μ F ( u , q , p ) ,
F ( u , p , q ) = 3 4 ( ω p τ ω ) 2 V F c ( 1 p ) × [ I 0 ( 1 q ) exp ( u w d ) I 1 q I 2 ] ,
I k = 1 ( 1 S 3 1 S 5 ) exp ( k s w d ) 1 p q exp ( 2 s w d ) d s , with k = 0 , 1 , 2 ,
E K = h c 2 t k , k = 1 , 2 , 3 ,
Δ E i = ( E i ) 2 h c ( 2 N t ) .
Δ E i exp ( d / 3 . 3 ) n d d 1 E i 2 N 0 . 31 ,
R b n d · d .
| ξ = 3 4 ω P 2 τ 2 ( V F c ) 2 ω τ | 1

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