Abstract

We report the design and performance of narrowband transmission filters employing the rapidly changing extinction coefficient that is characteristic of BaF2 and SiO2 films within certain wavelength intervals in the vacuum ultraviolet. We demonstrate the design concept for two filters centered at 135nm for BaF2 and at 141 nm for SiO2. It is found that these filters provide excellent narrowband spectral performance when combined with narrowband reflection filters. The filter centered at 135 nm has a peak transmittance of 24% and a bandwidth of 4 nm at full width at half-maximum for collimated incident light. The transmittance for λ0 ≤ 130 nm is <0.1% and for 138 ≤ λ0 ≤ 230 nm the average transmittance is <3%. Another filter centered at 141 nm has a peak transmittance of 25% and a bandwidth of 3.5 nm.

© 1990 Optical Society of America

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References

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  1. D. F. Heath, P. A. Sacher, “Effects of a Simulated High-Energy Space Environment on the Ultraviolet Transmittance of Optical Materials Between 1050 Å and 3000 Å,” Appl. Opt. 5, 937–943 (1966).
    [CrossRef] [PubMed]
  2. M. Zukic, D. G. Torr, J. F. Spann, M. R. Torr, “Vacuum Ultraviolet Thin Films. 1: Optical Constants of BaF2, CaF2, LaF3, MgF2, Al2O3, HfO2, and SiO2 Thin Films,” Appl. Opt. 29, 0000–0000 (1990), same issue.
  3. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), p. 60.
  4. Ref. 3, p. 616.
  5. Z. Knittl, Optics of Thin Films (Wiley, New York, 1976), Chaps. 5 and 6.
  6. H. A. Macleod, Thin-Film Optical Filters (Adam Hilger, Bristol, 1969), Chaps. 2 and 7.
  7. Ref. 3, p. 347.
  8. Ref. 6, p. 98.

1990

M. Zukic, D. G. Torr, J. F. Spann, M. R. Torr, “Vacuum Ultraviolet Thin Films. 1: Optical Constants of BaF2, CaF2, LaF3, MgF2, Al2O3, HfO2, and SiO2 Thin Films,” Appl. Opt. 29, 0000–0000 (1990), same issue.

1966

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), p. 60.

Heath, D. F.

Knittl, Z.

Z. Knittl, Optics of Thin Films (Wiley, New York, 1976), Chaps. 5 and 6.

Macleod, H. A.

H. A. Macleod, Thin-Film Optical Filters (Adam Hilger, Bristol, 1969), Chaps. 2 and 7.

Sacher, P. A.

Spann, J. F.

M. Zukic, D. G. Torr, J. F. Spann, M. R. Torr, “Vacuum Ultraviolet Thin Films. 1: Optical Constants of BaF2, CaF2, LaF3, MgF2, Al2O3, HfO2, and SiO2 Thin Films,” Appl. Opt. 29, 0000–0000 (1990), same issue.

Torr, D. G.

M. Zukic, D. G. Torr, J. F. Spann, M. R. Torr, “Vacuum Ultraviolet Thin Films. 1: Optical Constants of BaF2, CaF2, LaF3, MgF2, Al2O3, HfO2, and SiO2 Thin Films,” Appl. Opt. 29, 0000–0000 (1990), same issue.

Torr, M. R.

M. Zukic, D. G. Torr, J. F. Spann, M. R. Torr, “Vacuum Ultraviolet Thin Films. 1: Optical Constants of BaF2, CaF2, LaF3, MgF2, Al2O3, HfO2, and SiO2 Thin Films,” Appl. Opt. 29, 0000–0000 (1990), same issue.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), p. 60.

Zukic, M.

M. Zukic, D. G. Torr, J. F. Spann, M. R. Torr, “Vacuum Ultraviolet Thin Films. 1: Optical Constants of BaF2, CaF2, LaF3, MgF2, Al2O3, HfO2, and SiO2 Thin Films,” Appl. Opt. 29, 0000–0000 (1990), same issue.

Appl. Opt.

M. Zukic, D. G. Torr, J. F. Spann, M. R. Torr, “Vacuum Ultraviolet Thin Films. 1: Optical Constants of BaF2, CaF2, LaF3, MgF2, Al2O3, HfO2, and SiO2 Thin Films,” Appl. Opt. 29, 0000–0000 (1990), same issue.

D. F. Heath, P. A. Sacher, “Effects of a Simulated High-Energy Space Environment on the Ultraviolet Transmittance of Optical Materials Between 1050 Å and 3000 Å,” Appl. Opt. 5, 937–943 (1966).
[CrossRef] [PubMed]

Other

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980), p. 60.

Ref. 3, p. 616.

Z. Knittl, Optics of Thin Films (Wiley, New York, 1976), Chaps. 5 and 6.

H. A. Macleod, Thin-Film Optical Filters (Adam Hilger, Bristol, 1969), Chaps. 2 and 7.

Ref. 3, p. 347.

Ref. 6, p. 98.

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Figures (20)

Fig. 1
Fig. 1

Reflectance and absorptance of the QW stack as functions of the number of (HL) pairs: H = barium fluoride and L = magnesium fluoride.

Fig. 2
Fig. 2

Reflectance and absorptance of the QW stack as functions of the number of (HL) pairs: H = lanthanum fluoride and L = magnesium fluoride.

Fig. 3
Fig. 3

Reflectance and absorptance of the QW stack as functions of the number of (HL) pairs: H = silicon dioxide and L = magnesium. fluoride.

Fig. 4
Fig. 4

Reflectance and absorptance of the TW stack as functions of the number of (HL) pairs: H = barium fluoride and L = magnesium fluoride.

Fig. 5
Fig. 5

Reflectance and absorptance of the TW stack as functions of the number of (HL) pairs: H = lanthanum fluoride and L = magnesium fluoride.

Fig. 6
Fig. 6

Reflectance and absorptance of the TW stack as functions of the number of (HL) pairs: H = silicon dioxide and L = magnesium fluoride.

Fig. 7
Fig. 7

Reflectances of the partial reflectors of the Fabry-Perot type filter as functions of the number of (HL) pairs: H = barium fluoride and L = magnesium fluoride.

Fig. 8
Fig. 8

Reflectances of the partial reflectors of the Fabry-Perot type filter as functions of the number of (HL) pairs: H = lanthanum fluoride and L = magnesium fluoride.

Fig. 9
Fig. 9

Reflectances of the partial reflectors of the Fabry-Perot. type filter as functions of the number of (HL) pairs: H = silicon dioxide and L = magnesium fluoride.

Fig. 10
Fig. 10

Maximum transmittance and bandwidth of the Fabry-Perot type filter calculated using Eqs. (62) and (67), respectively: H = barium fluoride and L = magnesium fluoride.

Fig. 11
Fig. 11

Maximum transmittance and bandwidth of the Fabry-Perot type filter calculated using Eqs. (62) and (67), respectively: H = lanthanum fluoride and L = magnesium fluoride.

Fig. 12
Fig. 12

Maximum transmittance and bandwidth of the Fabry-Perot type filter calculated using Eqs. (62) and (67), respectively: H = silicon dioxide and L = magnesium fluoride.

Fig. 13
Fig. 13

Twenty-five-layer Fabry-Perot type filter: H = barium fluoride and L = magnesium fluoride.

Fig. 14
Fig. 14

Twenty-nine-layer Fabry-Perot filter with two spacing layers: H = barium fluoride and L = magnesium fluoride.

Fig. 15
Fig. 15

Twenty-five-layer QW tuned filter with the high reflection zone centered at 140 nm: H = barium fluoride and L = magnesium fluoride.

Fig. 16
Fig. 16

Twenty-five-layer TW tuned filter with the high reflection zone centered at 147.5 nm: H = silicon dioxide and L = magnesium fluoride.

Fig. 17
Fig. 17

Twenty-five-layer QW tuned filter with the high reflection zone centered at 160 nm: H = lanthanum fluoride and L = magnesium fluoride.

Fig. 18
Fig. 18

Twenty-five-layer second-order QW tuned filter with the high reflection zone centered at 135 nm. The angle of incidence is 45°: H = lanthanum fluoride and L = magnesium fluoride.

Fig. 19
Fig. 19

Measured transmittance of the filters shown in Figs. 15 and 18 combined.

Fig. 20
Fig. 20

Combined filter centered at 141 nm.

Equations (76)

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v = c N ,
k λ = ω c N
r = ( M 11 + M 12 η s ) η 0 - ( M 21 + M 22 η s ) ( M 11 + M 12 η s ) η 0 + ( M 21 + M 22 η s )
t = 2 η 0 ( M 11 + M 12 η s ) η 0 + ( M 21 + M 22 η s )
η 0 = n 0 cos θ 0 ,
η s = η s cos θ s
η 0 = cos θ 0 n 0 ,
η s = cos θ s n s ,
M = M 1 M 2 M P ,
M l = ( cos δ l i η l sin δ l i η l sin δ l cos δ l ) .
δ l = 2 π λ 0 N l d l cos Θ l ,
N l = n l ( 1 + i κ l ) = n l + i n l κ 1 = n l + i k l ,
sin Θ l = q l exp ( i γ l ) ,
N l sin Θ l = ( n l + i k l ) q l exp ( i γ l ) = n l - 1 sin Θ l - 1 .
n l q l cos γ l - k l q l sin γ l = n l - 1 sin Θ l - 1 ,
n l q l sin γ l + k l q l cos γ l = 0.
q l = n l - 1 sin Θ l - 1 n l 2 + k 1 2 ,
γ l = cos - 1 ( n l n l 2 + k l 2 ) .
q l = n l - 1 sin Θ l - 1 n l ,
γ l = 0 ,
r = r exp ( i ϕ r ) ,
t = t exp ( i ϕ t ) ,
R = r r * ,
T = η s η 0 t t * ,
A = 1 - ( R + T ) .
Θ H = Θ L = 0.
δ H = 2 π λ 0 ( n H + i k H ) d H
δ L = 2 π λ 0 ( n L + i k L ) d L .
n L d L = λ r 4 ,
n H d H = λ r 4 .
δ H = π 2 λ r λ 0 ( 1 + i k H n H ) ,
δ L = π 2 λ L λ 0 ( 1 + i k L n L ) .
κ H = k H n H ,
κ L = k L n L ,
δ H = π 2 λ r λ 0 ( 1 + i κ H ) ,
δ L = π 2 λ r λ 0 ( 1 + i κ L ) .
M H = ( - i sinh α H i N H cosh α H i N H cosh α H - i sinh α H ) ,
M L = ( - i sinh α L i N L cosh α L i N L cosh α L - i sinh α L ) ,
α H = π 2 k H n H = π 2 κ H ,
α L = π 2 k L n L = π 2 κ L .
M H = ( 0 i N H i N H 0 ) ,
M L = ( 0 i N L i N L 0 ) ,
M 1 = M H M L = ( - N L N H 0 0 - N H N L ) .
M P = ( M H M L ) P = [ ( - N L N H ) p 0 0 ( - N H N L ) p ] .
r = 1 - n s n 0 ( N H N L ) 2 p 1 + n s n 0 ( N H N L ) 2 p .
N H N L = n H n L ( 1 + i κ H ) ( 1 + i κ L ) = n H n L ( a 2 + b 2 ) 1 / 2 exp ( i β ) ,
a = 1 + κ H κ L 1 + κ L 2 ,
b = κ H - κ L 1 + κ L 2 ,
β = tan - 1 ( b a ) .
( N H N L ) p = F ( p ) exp [ i ψ ( p ) ] ,
F ( p ) = ( n H n L ) p ( a 2 + b 2 ) p / 2 ,
ψ ( p ) = p β .
r ( p ) = 1 - ( n s n 0 ) F ( 2 p ) exp [ i ψ ( 2 p ) ] 1 + ( n s n 0 ) F ( 2 p ) exp [ i ψ ( 2 p ) ] ,
R ( p ) = 1 - ( n s n 0 ) 2 F 2 ( 2 p ) - 2 ( n s n 0 ) F ( 2 p ) cos ψ ( 2 p ) 1 + ( n s n 0 ) 2 F 2 ( 2 p ) + 2 ( n s n 0 ) F ( 2 p ) cos ψ ( 2 p ) .
R ( 0 ) = ( 1 - n s n 0 ) 2 ( 1 + n s n 0 ) 2 .
ψ ( 2 p ) = ( l + ½ ) π ,
p = p 0 = π 4 [ tan - 1 ( κ H - κ L 1 + κ H κ L ) ] - 1 .
R ( p ) + A ( p ) 1.
n H d H = λ r 6 ,
n L d L = λ r 3 ,
T = T max 1 + F sin 2 Ψ ,
T max = T 1 T 2 ( 1 - R 1 R 2 ) 2 ,
F = 4 R 1 R 2 ( 1 - R 1 R 2 ) 2 ,
Ψ = δ - ϕ 1 + ϕ 2 2 .
Ψ = δ - ϕ = m π ,
ϕ = ϕ 1 + ϕ 2 2 ,
( Δ λ ) b = 2 λ 0 ( m ) [ π F | m - 1 π ( d d λ 0 ( λ 0 ϕ ) ) λ 0 = λ ( m ) | ] - 1
air [ H ( LH ) p 2 L ( HL ) p H ] substrate ,
air [ ( LH ) p 2 L ( HL ) p ] substrate ,
Φ ( λ 0 ) = λ 0 ϕ ( λ 0 )
[ d d λ 0 Φ ( λ 0 ) ] λ 0 = λ ( 1 ) = [ ϕ ( λ 0 ) ] λ 0 = λ ( 1 ) + [ λ 0 d d λ 0 ϕ ( λ 0 ) ] λ 0 = λ ( 1 ) ,
[ d d λ 0 Φ ( λ 0 ) ] λ 0 = λ ( 1 ) = [ Φ ( λ 0 + Δ λ ) - Φ ( λ 0 ) Δ λ ] λ 0 = λ ( 1 ) ,
air [ ( LH ) 6 2 L ( HL ) 6 ] substrate ,
air [ ( LH ) 4 2 L ( HL ) 5 H 2 L ( HL ) 4 ] substrate ,
( Δ λ ) H . R . = 4 λ 0 π sin - 1 ( n H - n L n H + n L ) ,
air [ 3 L 2 ( H 3 L ) 11 H 3 L 2 ] substrate ,

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