Abstract

Band rejection filters with a bandwidth as narrow as <5% that operate in the UV region can be constructed from multiple thin metal films and insulating layers. A physical model is derived to illustrate the dependence of the wavelength of maximum reflectance and rejection bandwidth on the optical constants of metal and dielectrics, on the thickness, and on the number of repetitive layers. This design prevails over conventional dielectric–dielectric coatings because of its development and simplicity in the fabricating process and its applicability to large spectral ranges.

© 1992 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, 1103–1105 (1989).
    [CrossRef]
  2. J. S. Sheng, J. T. Lue, J. H. Tyan, “Design criteria for band rejection filters made from multilayers of dielectric and ultrathin metal films,” Appl. Opt. 30, 1746–1748 (1991).
    [CrossRef] [PubMed]
  3. E. Spiller, “Interference filters for the ultraviolet and the surface plasmon of aluminum,” Appl. Opt. 13, 1209–1215 (1974).
    [CrossRef] [PubMed]
  4. E. Spiller, “Reflective multilayer coatings for the far UV region,” Appl. Opt. 15, 2333–2338 (1976).
    [CrossRef] [PubMed]
  5. L. J. Epstein, “The design of optical filters,” J. Opt. Soc. Am. 45, 360–365 (1955).
    [CrossRef]
  6. A. Thelen, “Equivalent layers in multilayer filters,” J. Opt. Soc. Am. 56, 1533–1537 (1966).
    [CrossRef]
  7. R. Frazer, W. Duncan, A. Collar, Elementary Matrices and Some Applications to Dynamics and Differential Equations (Cambridge U. Press, Cambridge, 1963), chap. V.
  8. L. Epstein, “The design of optical filters,” J. Opt. Soc. Am. 42, 806–810 (1952).
    [CrossRef]
  9. E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic, New York, 1985), pp. 356, 398.
  10. K. Ploog, “Molecular beam epitaxy of III–V compounds,” in Crystals: Growth, Properties, and Applications, H. C. Freyhardt, ed. (Springer-Verlag, Berlin, 1980), Vol. 3, p. 73.
  11. J. T. Lue, “Voltage readout of a temperature controlled thin film thickness monitor,” J. Phys. E 10, 101–105 (1977).
    [CrossRef]
  12. G. J. Davies, D. Williams, “III–V MBE growth systems,” in The Technology and Physics of Molecular Beam Epitaxy, E. H. C. Parker, ed. (Plenum, New York, 1985), Chap. 2, p. 17.
  13. J. Szczyrbowski, K. Schmalzbauer, H. Hoffmann, “Optical transmittance and reflectance and dynamic current density for thin metallic films,” Phys. Rev. B 32, 763–770 (1985).
    [CrossRef]
  14. J. T. Lue, J. S. Sheng, “Coupled surface plasmon polariton waves and optical size effect,” Phys. Rev. B 45, 14,241–14,244 (1991).

1991 (2)

J. T. Lue, J. S. Sheng, “Coupled surface plasmon polariton waves and optical size effect,” Phys. Rev. B 45, 14,241–14,244 (1991).

J. S. Sheng, J. T. Lue, J. H. Tyan, “Design criteria for band rejection filters made from multilayers of dielectric and ultrathin metal films,” Appl. Opt. 30, 1746–1748 (1991).
[CrossRef] [PubMed]

1989 (1)

1985 (1)

J. Szczyrbowski, K. Schmalzbauer, H. Hoffmann, “Optical transmittance and reflectance and dynamic current density for thin metallic films,” Phys. Rev. B 32, 763–770 (1985).
[CrossRef]

1977 (1)

J. T. Lue, “Voltage readout of a temperature controlled thin film thickness monitor,” J. Phys. E 10, 101–105 (1977).
[CrossRef]

1976 (1)

1974 (1)

1966 (1)

1955 (1)

1952 (1)

Collar, A.

R. Frazer, W. Duncan, A. Collar, Elementary Matrices and Some Applications to Dynamics and Differential Equations (Cambridge U. Press, Cambridge, 1963), chap. V.

Davies, G. J.

G. J. Davies, D. Williams, “III–V MBE growth systems,” in The Technology and Physics of Molecular Beam Epitaxy, E. H. C. Parker, ed. (Plenum, New York, 1985), Chap. 2, p. 17.

Duncan, W.

R. Frazer, W. Duncan, A. Collar, Elementary Matrices and Some Applications to Dynamics and Differential Equations (Cambridge U. Press, Cambridge, 1963), chap. V.

Epstein, L.

Epstein, L. J.

Frazer, R.

R. Frazer, W. Duncan, A. Collar, Elementary Matrices and Some Applications to Dynamics and Differential Equations (Cambridge U. Press, Cambridge, 1963), chap. V.

Hoffmann, H.

J. Szczyrbowski, K. Schmalzbauer, H. Hoffmann, “Optical transmittance and reflectance and dynamic current density for thin metallic films,” Phys. Rev. B 32, 763–770 (1985).
[CrossRef]

Hor, Y. S.

Lue, J. T.

Ploog, K.

K. Ploog, “Molecular beam epitaxy of III–V compounds,” in Crystals: Growth, Properties, and Applications, H. C. Freyhardt, ed. (Springer-Verlag, Berlin, 1980), Vol. 3, p. 73.

Schmalzbauer, K.

J. Szczyrbowski, K. Schmalzbauer, H. Hoffmann, “Optical transmittance and reflectance and dynamic current density for thin metallic films,” Phys. Rev. B 32, 763–770 (1985).
[CrossRef]

Sheng, J. S.

J. T. Lue, J. S. Sheng, “Coupled surface plasmon polariton waves and optical size effect,” Phys. Rev. B 45, 14,241–14,244 (1991).

J. S. Sheng, J. T. Lue, J. H. Tyan, “Design criteria for band rejection filters made from multilayers of dielectric and ultrathin metal films,” Appl. Opt. 30, 1746–1748 (1991).
[CrossRef] [PubMed]

Spiller, E.

Szczyrbowski, J.

J. Szczyrbowski, K. Schmalzbauer, H. Hoffmann, “Optical transmittance and reflectance and dynamic current density for thin metallic films,” Phys. Rev. B 32, 763–770 (1985).
[CrossRef]

Thelen, A.

Tyan, J. H.

Williams, D.

G. J. Davies, D. Williams, “III–V MBE growth systems,” in The Technology and Physics of Molecular Beam Epitaxy, E. H. C. Parker, ed. (Plenum, New York, 1985), Chap. 2, p. 17.

Appl. Opt. (3)

J. Opt. Soc. Am. (3)

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

J. Phys. E (1)

J. T. Lue, “Voltage readout of a temperature controlled thin film thickness monitor,” J. Phys. E 10, 101–105 (1977).
[CrossRef]

Phys. Rev. B (2)

J. Szczyrbowski, K. Schmalzbauer, H. Hoffmann, “Optical transmittance and reflectance and dynamic current density for thin metallic films,” Phys. Rev. B 32, 763–770 (1985).
[CrossRef]

J. T. Lue, J. S. Sheng, “Coupled surface plasmon polariton waves and optical size effect,” Phys. Rev. B 45, 14,241–14,244 (1991).

Other (4)

G. J. Davies, D. Williams, “III–V MBE growth systems,” in The Technology and Physics of Molecular Beam Epitaxy, E. H. C. Parker, ed. (Plenum, New York, 1985), Chap. 2, p. 17.

E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic, New York, 1985), pp. 356, 398.

K. Ploog, “Molecular beam epitaxy of III–V compounds,” in Crystals: Growth, Properties, and Applications, H. C. Freyhardt, ed. (Springer-Verlag, Berlin, 1980), Vol. 3, p. 73.

R. Frazer, W. Duncan, A. Collar, Elementary Matrices and Some Applications to Dynamics and Differential Equations (Cambridge U. Press, Cambridge, 1963), chap. V.

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Figures (8)

Fig. 1
Fig. 1

Construction of the band rejection filter composed of multiple layers of dielectric–metal films. A and B designate metal and dielectric materials, respectively.

Fig. 2
Fig. 2

Real (n) and imaginary (k) parts of the refractive index of Ag film.

Fig. 3
Fig. 3

Real (n) and imaginary (k) parts of the refractive index of Al film.

Fig. 4
Fig. 4

Curve (a) normal and curve (b) inclined (incident angle θ = 45°) reflectance for the (Ag/dielectric)N system with nB = 1.5, N = 30, dA = 4 × 10−9 m, dB = 0.9 × 10−7 m.

Fig. 5
Fig. 5

Curve (a) normal and curve (b) inclined (θ = 45°) reflectance of the same system as in Fig. 4 but for the construction of the (dielectric/Ag)N form.

Fig. 6
Fig. 6

Curve (a) normal and curve (b) inclined (θ = 45°) reflectance of the (dielectric/Al)N system with nB = 1.5, N = 30, dA = 4 × 10−9 m, dB = 1.0 × 10−7 m.

Fig. 7
Fig. 7

Reflectance of the (dielectric/Al)N system with nB = 1.5, N = 30, dA = 2 × 10−9 m, dB = 1.0 × 10−7 m.

Fig. 8
Fig. 8

Reflectance for curve (a) the (dielectric/Ag)N system with N = 50, nB = 1.5, dA = 4 × 10−9 m, dB = 1.15 × 10−7 m, and curve (b) the (dielectric/Al)N system with N = 50, nB = 2.3, dA = 2 × 10−9, dB = 0.78 × 10−7 m.

Equations (16)

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M N = ( M A M B ) N = [ m 11 m 12 m 21 m 22 ] ,
M A = [ cos ϕ A j sin ϕ A n A j n A sin ϕ A cos ϕ A ] , M B = [ cos ϕ B j sin ϕ B n B j n B   sin ϕ B cos ϕ B ] .
M = M A · M B = ( m 110 m 120 m 210 m 220 ) ,
m 110 = cos ϕ A cos ϕ B - n B N A sin ϕ A sin ϕ B , m 120 = j ( cos ϕ A sin ϕ B n B + sin ϕ A cos ϕ B N A ) , m 210 = j ( N A sin ϕ A   cos ϕ B + n B   cos ϕ A sin ϕ B ) , m 220 = cos ϕ A   cos ϕ B - N A n B sin ϕ A   sin ϕ B , ϕ A = 2 π N A d A / λ cos θ A , ϕ B = 2 π n B d B / λ cos θ B , θ A , B = sin - 1 ( n 0 N A , B sin θ ) ,
ρ = ( m 11 + m 12 n s ) n 0 - ( m 21 + m 22 n s ) ( m 11 + m 12 n s ) n 0 + ( m 21 + m 22 n s ) .
M N = [ S N - 1 ( x ) ] M - [ S N - 2 ( x ) ] I ,
m 110 + m 120 = | 2 cos ϕ A   cos ϕ B - ( n B N A + N A n B ) sin ϕ A   sin ϕ B | 2.
cos ϕ A cos ϕ B - 1 2 ( n B N A + N A n B ) sin ϕ A sin ϕ B = ± 1.
ϕ A + ϕ B = m π for m = 1 , 2 .
k ( n B 2 - k 2 ) n B ( n 2 + k 2 ) sin 2 ϕ B = 0.
( i ) k = 0 , ( ii ) k = n B , or ( iii ) sin 2 ϕ B = 0.
N A   sin ϕ A cos ϕ B + n B   sin ϕ B     cos ϕ A = 0.
( n - j k ) ( sin ϕ 1 cosh ϕ 2 - j cos ϕ 1 sinh ϕ 2 ) cos ϕ B + n B ( cos ϕ 1   cosh ϕ 2 + j sin ϕ 1 sinh ϕ 2 ) sin ϕ B = 0.
( n sin ϕ B   cosh ϕ 2 + k cos ϕ B   sinh ϕ 2 ) cos ϕ B - n B   cos ϕ B   cosh ϕ 2   sin ϕ B = 0 ,
tan ϕ B = k tanh ϕ 2 ( n B - n ) .
BW = 2 Δ g π = 2 π tan - 1 | k tanh ϕ 2 n B - n | .

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