Abstract

The potential transmittance of a given absorbing film depends only on the load admittance of the optical structure with which it is backed, in addition to the optical parameters of the film itself. Utilizing appropriately designed backings of nonabsorbing multilayer films, admittances for light of a specified wavelength can be obtained which greatly increase the potential transmittance of certain materials, notably metals with high k/n ratios. A high transmittance of the specified monochromatic radiation results if the given film plus backing is subsequently antireflected by a second nonabsorbing multilayer combination added on the side of incidence. This procedure introduces the basic principles of “induced transmission.” These principles are applied directly to the problem of improving the efficiency of metal band pass filters. The resulting designs are discussed from different points of view.

© 1957 Optical Society of America

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References

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  1. A. F. Turner and P. H. Berning, J. Opt. Soc. Am. 45, 408(A) (1955).
  2. P. H. Berning, J. Opt. Soc. Am. 43, 819(A) (1953).
  3. F. Abelès, Ann. phys. Ser. 12, 5, 634 (1950).
  4. A. F. Turner, J. phys. radium 11, 444 (1950).
    [Crossref]
  5. Berning, Berning, and Epstein, J. Opt. Soc. Am. 45, 407(A) (1955).
  6. W. Geffcken, Z. angew. Phys. 6, 249 (1954).
  7. A. Hermansen, Kgl. Danske Videnskabs. Selskab Mat.-fys. Medd. 29, No. 13 (1955).
  8. A. F. Turner and O. A. Ullrich, J. Opt. Soc. Am. 38, 662 (A) (1948). R. Gradman, Optica Acta 3, 30 (1956).
    [Crossref]

1955 (3)

A. F. Turner and P. H. Berning, J. Opt. Soc. Am. 45, 408(A) (1955).

Berning, Berning, and Epstein, J. Opt. Soc. Am. 45, 407(A) (1955).

A. Hermansen, Kgl. Danske Videnskabs. Selskab Mat.-fys. Medd. 29, No. 13 (1955).

1954 (1)

W. Geffcken, Z. angew. Phys. 6, 249 (1954).

1953 (1)

P. H. Berning, J. Opt. Soc. Am. 43, 819(A) (1953).

1950 (2)

F. Abelès, Ann. phys. Ser. 12, 5, 634 (1950).

A. F. Turner, J. phys. radium 11, 444 (1950).
[Crossref]

1948 (1)

A. F. Turner and O. A. Ullrich, J. Opt. Soc. Am. 38, 662 (A) (1948). R. Gradman, Optica Acta 3, 30 (1956).
[Crossref]

Abelès, F.

F. Abelès, Ann. phys. Ser. 12, 5, 634 (1950).

Berning,

Berning, Berning, and Epstein, J. Opt. Soc. Am. 45, 407(A) (1955).

Berning, Berning, and Epstein, J. Opt. Soc. Am. 45, 407(A) (1955).

Berning, P. H.

A. F. Turner and P. H. Berning, J. Opt. Soc. Am. 45, 408(A) (1955).

P. H. Berning, J. Opt. Soc. Am. 43, 819(A) (1953).

Epstein,

Berning, Berning, and Epstein, J. Opt. Soc. Am. 45, 407(A) (1955).

Geffcken, W.

W. Geffcken, Z. angew. Phys. 6, 249 (1954).

Hermansen, A.

A. Hermansen, Kgl. Danske Videnskabs. Selskab Mat.-fys. Medd. 29, No. 13 (1955).

Turner, A. F.

A. F. Turner and P. H. Berning, J. Opt. Soc. Am. 45, 408(A) (1955).

A. F. Turner, J. phys. radium 11, 444 (1950).
[Crossref]

A. F. Turner and O. A. Ullrich, J. Opt. Soc. Am. 38, 662 (A) (1948). R. Gradman, Optica Acta 3, 30 (1956).
[Crossref]

Ullrich, O. A.

A. F. Turner and O. A. Ullrich, J. Opt. Soc. Am. 38, 662 (A) (1948). R. Gradman, Optica Acta 3, 30 (1956).
[Crossref]

Ann. phys. Ser. (1)

F. Abelès, Ann. phys. Ser. 12, 5, 634 (1950).

J. Opt. Soc. Am. (4)

A. F. Turner and P. H. Berning, J. Opt. Soc. Am. 45, 408(A) (1955).

P. H. Berning, J. Opt. Soc. Am. 43, 819(A) (1953).

Berning, Berning, and Epstein, J. Opt. Soc. Am. 45, 407(A) (1955).

A. F. Turner and O. A. Ullrich, J. Opt. Soc. Am. 38, 662 (A) (1948). R. Gradman, Optica Acta 3, 30 (1956).
[Crossref]

J. phys. radium (1)

A. F. Turner, J. phys. radium 11, 444 (1950).
[Crossref]

Kgl. Danske Videnskabs. Selskab Mat.-fys. Medd. (1)

A. Hermansen, Kgl. Danske Videnskabs. Selskab Mat.-fys. Medd. 29, No. 13 (1955).

Z. angew. Phys. (1)

W. Geffcken, Z. angew. Phys. 6, 249 (1954).

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Figures (16)

Fig. 1
Fig. 1

Schematic representation of a simple metal-spacer-metal interference filter.

Fig. 2
Fig. 2

Schematic representation of the definition of half-filter.

Fig. 3
Fig. 3

Schematic representation of an arbitrary film combination.

Fig. 4
Fig. 4

Schematic representation of a metal-spacer-metal interference filter with dielectric stacks added on each side to enhance peak transmittance.

Fig. 5
Fig. 5

Calculated complex amplitude reflectance, r1=u1+iv1=|r1|e1, of the combination: GFLHLH(1.75L)|Ag|A as a function of the dielectric film thickness in units of phase, where the silver film thickness hAg=0.0549λ.

Fig. 6
Fig. 6

Calculated complex amplitude reflectance, r1=u1+iv1=|r1|e1, of the combination: GHLHLH(1.75L)|Ag|A as a function of the dielectric film thickness in units of phase, where the silver film thickness=0.0641λ.

Fig. 7
Fig. 7

Schematic representation of a “spacerless” filter.

Fig. 8
Fig. 8

Calculated transmittance: T22 cos2(argY0) of the filter: GHLHLH(1.75L)|Ag|(1.75L)HLHLHG, where the silver film thickness hAg=0.1098λ.

Fig. 9
Fig. 9

Calculated transmittance: T22 cos2(argY0) of the filter: GHLHLH(1.75L)|Ag|(1.75L)HLHLHG, where the silver film thickness hAg=0.1282λ.

Fig. 10
Fig. 10

Calculated transmittance: T22 cos2(argY0) of the filter: GLHLHL(0.7H)|Ag|(0.7H)LHLHLG where the silver film thickness hAg=0.1098λ.

Fig. 11
Fig. 11

Calculated transmittance: T22 cos2(argY0) of the filter: GLHLHL(0.7H)|Ag|(0.7H)LHLHLG where the silver film thickness hAg=0.1282λ.

Fig. 12
Fig. 12

Calculated transmittance: T22 cos2(argY0) of the filter: G|Ag|(1.46L)|Ag|G, where the silver film thickness hAg=0.0641λ.

Fig. 13
Fig. 13

Calculated transmittance: T22 cos2(argY0) of the filter: G|Ag|(3.46L)|Ag|G, where the silver film thickness hAg=0.0641λ.

Fig. 14
Fig. 14

Calculated transmittance: T22 cos2(argY0) of the filter G: |Ag|(1.46L)|2 Ag|(1.46L)|Ag|G, where the silver film thickness hAg=0.0641λ.

Fig. 15
Fig. 15

Measured transmittance of the filter,

Fig. 16
Fig. 16

Measured transmittance of the filter,

Tables (1)

Tables Icon

Table I Maximum theoretical transmittance of modified filter (Fig. 4) compared with unmodified (Fig. 1).

Equations (28)

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T = T 0 2 ( 1 - R 0 ) 2 + 4 R 0 sin 2 ρ 0 ,
T = ( T 0 1 - R 0 ) 2 ( 1 1 + 4 R 0 sin 2 ρ 0 [ 1 - R 0 ] 2 ) .
T max = ( T 0 1 - R 0 ) 2 ,
T min = ( T 0 1 + R 0 ) 2 .
T 0 / ( 1 - R 0 ) = P m / P 0 .
T 0 1 - R 0 = j n j , k j > 0 ( P j P j - 1 )
Ψ j = 1 - r j 2 - 2 ( k j / n j ) r j sin ρ j exp ( 4 π k j h j λ ) - r j 2 exp ( - 4 π k j h j λ ) - 2 k j n j r j sin ( ρ j - 4 π n j h j λ ) ,
r j = r j e i ρ j = N j - Y j N j + Y j .
Ψ max ( N j , h j ) = μ j - ( μ j 2 - 1 ) 1 2 = exp ( - cosh - 1 μ j ) ,
μ j = cosh ( 4 π k j h j λ ) + k j 2 n j 2 cos ( 4 π n j h j λ ) 1 + ( k j 2 / n j 2 ) .
0 Ψ j Ψ max ( N j , h j ) < 1 ,
T 0 1 - R 0 = Ψ j = 1 1 + A 0 / T 0 .
0 < T 0 1 - R 0 = Ψ j Ψ max ( N j , h j )
A 0 + R 0 + T 0 = 1.
Y j - 1 = Y j + i N j tan ( 2 π N j h j / λ ) 1 + i Y j N j tan ( 2 π N j h j / λ ) .
T = Ψ 2 2 [ 1 1 + 4 R 0 sin 2 ρ 0 ( 1 - R 0 ) 2 ] ,
T = Ψ 2 2 cos 2 [ arg Y 0 ] ,
T max = Ψ 2 2 .
( cos Φ 2 i N 2 sin Φ 2 i N 2 sin Φ 2 cos Φ 2 )
T / ( 1 - R ) = Ψ = Ψ max ( N 2 , 2 h 2 ) ,
cos 2 ( arg Y 0 ) = μ 2 2 μ 2 2 + ( k 2 2 / n 2 2 ) ( μ 2 - cos [ 4 π n 2 h 2 λ ] ) 2
μ 2 = cosh ( 4 π k 2 h 2 λ ) + k 2 2 n 2 2 cos ( 4 π n 2 h 2 λ ) 1 + ( k 2 2 / n 2 2 ) .
4 Δ ϕ 1 = 2 sin - 1 ( 1 - R 0 2 ( R 0 ) 1 2 ) ,
Δ ϕ 1 = Δ 2 π n 1 h 1 / λ .
G Ag ( 1.46 L ) 2 Ag ( 1.46 L ) Ag G ,
( h / λ ) Ag = 0.0641.
G H L H L H ( 1.75 L ) Ag ( 1.75 L ) H L H L H G ,
G L H L H L ( 0.7 H ) Ag ( 0.7 H ) L H L H L G ,