Abstract

The relative position of high- and low-transmittance bands in the transmittance spectrum of periodic multilayers is discussed. Conditions are derived for which two or more successive low-transmittance bands are suppressed. Specific designs are given and applications discussed.

© 1963 Optical Society of America

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References

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  1. J. A. Berning and P. H. Berning, J. Opt. Soc. Am. 50, 813 (1960).
    [CrossRef]
  2. L. I. Epstein, J. Opt. Soc. Am. 45, 360 (1955).
    [CrossRef]
  3. R. B. Muchmore, J. Opt. Soc. Am. 38, 20 (1948).
    [CrossRef]
  4. G. Hass and A. F. Turner, Ergebnisse der Hochvakuumtechnik und der Physik duenner Schichten (Wissenschaftliche Verlagsgesellschaft m. b. H. Stuttgart, 1957), p. 143.
  5. L. I. Epstein, J. Opt. Soc. Am. 42, 806 (1952).
    [CrossRef]

1960 (1)

1955 (1)

1952 (1)

1948 (1)

Berning, J. A.

Berning, P. H.

Epstein, L. I.

Hass, G.

G. Hass and A. F. Turner, Ergebnisse der Hochvakuumtechnik und der Physik duenner Schichten (Wissenschaftliche Verlagsgesellschaft m. b. H. Stuttgart, 1957), p. 143.

Muchmore, R. B.

Turner, A. F.

G. Hass and A. F. Turner, Ergebnisse der Hochvakuumtechnik und der Physik duenner Schichten (Wissenschaftliche Verlagsgesellschaft m. b. H. Stuttgart, 1957), p. 143.

J. Opt. Soc. Am. (4)

Other (1)

G. Hass and A. F. Turner, Ergebnisse der Hochvakuumtechnik und der Physik duenner Schichten (Wissenschaftliche Verlagsgesellschaft m. b. H. Stuttgart, 1957), p. 143.

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Figures (8)

Fig. 1
Fig. 1

Calculated transmittance of the design S ( A B ) 10 1 2 A M with nS=1.50, nM=1.00, nA=1.38, nB=2.30, as a function of the “relative wavenumber.”

Fig. 2
Fig. 2

Nomogram for the indices of refraction of a periodic multilayer with suppressed second- and third-order low-transmittance bands.

Fig. 3
Fig. 3

Calculated transmittance of the design SA(ABCBA)10M, with nS=1.50, nM=1.00, nA=1.38, nB=1.90, nC=2.30, as a function of the “relative wavenumber.”

Fig. 4
Fig. 4

Calculated transmittance of the design SA(AB2CBA)10M, with nS=1.50, nM=1.00, nA=1.38, nB=1.781, nC=2.30, as function of the “relative wavenumber.”

Fig. 5
Fig. 5

Calculated transmittance spectrum of a “red and blue solar cell reflector.” Design:

Fig. 6
Fig. 6

Calculated transmittance spectrum of a “single-stack heat reflector.” Design:

Fig. 7
Fig. 7

Calculated transmittance spectrum of a “double-stack heat reflector.” Design:

Fig. 8
Fig. 8

Calculated transmittance spectrum of a “triple-stack heat reflector.” Design:

Tables (1)

Tables Icon

Table I Infrared energy (in percent of total energy) of tungsten lamps with temperature T(°K) reflected away by various heat reflectors.

Equations (36)

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A B D C A A B D C A A B D C A A B D C A A B D C A             ( m times ) .
cos φ / t > 1 ,
t < 1.
φ = ( 2 π / λ ) n x = m π             m = 1 , 2 , 3 , .
λ 0 = 2 n x ,
λ = ( 2 / m ) n x = λ 0 / m             m = 1 , 2 , 3 , .
t = 1
A periodic multilayer has low transmittance bands at the design wavelength λ 0 , at λ 0 / 2 , λ 0 / 3 , and all higher orders except for those orders where the transmittance through a period is unity .
λ = ( 2 / m ) ( n A x A + n B x B )             m = 1 , 2 , 3 , ,
m = k ( a + b )             k = 1 , 2 , 3 , ,
( n A x A / n B x B ) = a / b .
relative wavenumber = ν / ν 0 = λ 0 / λ .
A B C B A .
n A x A = n B x B ,
n A n B = n S n M .
n A n B = n C n M .
tan 2 φ = tan 2 2 π λ n A x A = n A n B - n C 2 n B 2 - n A n C 2 / n B .
( 2 π / λ 1 ) n A x A = φ             and             ( 2 π / λ 2 ) n A x A = π - φ .
φ = π 1 + λ 1 / λ 2 .
tan 2 π 1 + λ 1 / λ 2 = n A n B - n C 2 n B 2 - n A n C 2 / n B .
4 n A x A + n C x C = 1 2 λ 0 .
( 2 π / λ 1 ) n A x A + ( 2 π / λ 2 ) n A x A = π ,
n A x A = λ 1 λ 2 / 2 ( λ 1 + λ 2 ) .
n C x C = ( λ 0 / 2 ) - 2 [ λ 1 λ 2 / ( λ 1 + λ 2 ) ] .
λ 1 = 1 2 λ 0             and             λ 2 = λ 0 / 3 ,
n A x A = n B x B = n C x C = λ 0 / 10.
n B 2 = n A n C = n M n S ,
n A x A = n B x B = n C x C = λ C / 4 ,
λ C = λ 0 / 3 ,
6 n A x A + n D x D = 1 2 λ 0 .
n D x D = 0 ,
configuration : A B 2 C B A , thickness : n A x A = λ 0 / 12 , index relation : n B = ( n A n C ) 1 2 .
S [ 0.565 ( 1 2 A B 1 2 A ) ] 2 [ 0.628 ( 1 2 A B 1 2 A ) ] 6 1.55 B [ 1.15 ( B C A C B ) ] ( B C A C B ) 6 [ 1.050 ( B C A C B ) ] M ,
S 1 2 A [ 1.125 ( 1 2 A B 1 2 A ) ] ( 1 2 A B 1 2 A ) 5 [ 1.1 ( 1 2 A B 1 2 A ) ] M ,
S 1 2 A [ 0.57 ( A B C B A ) ] 8 [ 1.125 ( 1 2 A C 1 2 A ) ] ( 1 2 A C 1 2 A ) 5 [ 1.1 ( 1 2 A C 1 2 A ) ] M ,
S 1 2 A [ 0.642 ( A B 2 C B A ) ] 8 [ 0.57 ( A D C D A ) ] 8 [ 1.25 ( 1 2 A C 1 2 A ) ] ( 1 2 A C 1 2 A ) 5 [ 1.1 ( 1 2 A C 1 2 A ) ] M ,