Abstract

The reflectivity of metallic films, as calculated from standard equations, is discussed in the case of infrared radiation. We derive the minimum thickness of a metallic film for infrared reflectors and show the reason that metallic films cannot be used to make Fabry-Perot filters in the infrared.

© 1977 Optical Society of America

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References

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  1. M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), Sec. 13.4.
  2. L. N. Hadley and D. M. Dennison, “Reflection and Transmission Interference Filters, Part I, Theory,” J. Opt. Soc. Am. 37, 451 (1947).
    [Crossref]
  3. M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), Sec. 7.6.
  4. J. Millman and H. Taub, Pulse Digital and Switching Waveforms (McGraw-Hill, Tokyo, 1965), Sec. 3.15.

1947 (1)

Born, M.

M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), Sec. 13.4.

M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), Sec. 7.6.

Dennison, D. M.

Hadley, L. N.

Millman, J.

J. Millman and H. Taub, Pulse Digital and Switching Waveforms (McGraw-Hill, Tokyo, 1965), Sec. 3.15.

Taub, H.

J. Millman and H. Taub, Pulse Digital and Switching Waveforms (McGraw-Hill, Tokyo, 1965), Sec. 3.15.

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), Sec. 7.6.

M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), Sec. 13.4.

J. Opt. Soc. Am. (1)

Other (3)

M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), Sec. 13.4.

M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), Sec. 7.6.

J. Millman and H. Taub, Pulse Digital and Switching Waveforms (McGraw-Hill, Tokyo, 1965), Sec. 3.15.

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Figures (3)

FIG. 1
FIG. 1

Illustrating a plane wave incident on a metallic film of thickness h.

FIG. 2
FIG. 2

Transmissivity, reflectivity, and absorption of a metallic film as a function of f*.

FIG. 3
FIG. 3

The minimum thickness necessary to obtain a reflectivity R as a function of ( 1 R ). The four curves refer to four different materials: solid curve, silver; dash-dot-dash, gold; dashed, aluminium; and dotted, nickel. The values of the penetration depth and of ( 1 R max ) are marked, respectively at the bottom and on the right of the figure, for the four materials at several wavelengths.

Equations (23)

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R = ρ 12 2 e 2 υ 2 η + ρ 23 2 e 2 υ 2 η + 2 ρ 12 ρ 23 cos ( ϕ 23 ϕ 12 + 2 u 2 η ) e 2 υ 2 η + ρ 12 2 ρ 23 2 e 2 υ 2 η + 2 ρ 12 ρ 23 cos ( ϕ 23 + ϕ 12 + 2 u 2 η ) ,
T = C τ 12 2 τ 33 2 e 2 υ 2 η + ρ 12 2 ρ 23 2 e 2 υ 2 η + 2 ρ 12 ρ 23 cos ( ϕ 23 + ϕ 12 + 2 u 2 η ) ,
R = ρ 12 2 + ρ 23 2 + 2 ρ 12 ρ 23 cos ( ϕ 23 ϕ 12 ) 1 + ρ 12 2 ρ 23 2 + 2 ρ 12 ρ 23 cos ( ϕ 23 + ϕ 12 ) = ρ 13 2 ,
R = ρ 12 2 ,
h > λ 0 / 4 π n κ = d ,
n ̂ = ( μ σ / ν ) 1 / 2 + i ( μ σ / ν ) 1 / 2 ,
ρ 12 = 1 n 1 cos θ 1 n κ + 1 2 ( n 1 cos θ 1 n κ ) 2 , ρ 23 = 1 n 3 cos θ 3 n κ + 1 2 ( n 3 cos θ 3 n κ ) 2 , e 2 υ 2 η = 1 + 2 n κ η + 2 n 2 κ 2 η 2 , e 2 υ 2 η = 1 2 n κ η + 2 n 2 κ 2 η 2 , cos ( ϕ 23 ± ϕ 12 + 2 u 2 η ) = 1 ( n 3 cos θ 3 n κ ± n 1 cos θ 1 n κ + 2 n κ η ) 2 / 2 .
R = ( 2 f + n 3 cos θ 3 n 1 cos θ 1 2 f + n 3 cos θ 3 + n 1 cos θ 1 ) 2 ,
f = 60 π [ ohms ] r [ ohms ] .
T = 4 n 1 n 3 cos θ 1 cos θ 3 ( 2 f + n 3 cos θ 3 + n 1 cos θ 1 ) 2 ,
a = 1 R T = 8 f n 1 cos θ 1 ( 2 f + n 3 cos θ 3 + n 1 cos θ 1 ) 2 .
R = ( 2 f cos θ 1 cos θ 3 + n 3 cos θ 1 n 1 cos θ 3 2 f cos θ 1 cos θ 3 + n 3 cos θ 1 + n 1 cos θ 3 ) 2 , T = 4 n 1 n 3 cos θ 1 cos θ 3 ( 2 f cos θ 1 cos θ 3 + n 3 cos θ 1 + n 1 cos θ 3 ) 2 a = 8 f n 1 cos θ 1 cos 2 θ 3 ( 2 f cos θ 1 cos θ 3 + n 3 cos θ 1 + n 1 cos θ 3 ) 2 .
R = ( f * f * + 1 ) 2 , T = ( 1 f * + 1 ) 2 , and a = 2 f * ( f * + 1 ) 2 ,
h min = ( 1 + R ) R / ( 1 R ) 60 π σ ,
h min = 1 / ( 1 R ) 30 π σ .
R = [ f * / ( 1 + f * ) ] 2 ,
a = 2 f * / ( 1 + f * ) 2
T = 1 / ( 1 + f * ) 2 .
τ = ( 1 a 1 R ) 2 .
τ = 1 / ( 1 + 2 f * ) .
Z = Z k / ( Z + k ) .
R = | k Z k + Z | 2 = x 2 ( x + 2 ) 2 ,
T = ( 1 R ) Z Z + k = 4 ( x + 2 ) 2 , a = ( 1 R ) k Z + k = 4 x ( x + 2 ) 2 .