Abstract

We report on the development of a new coating design for applications in the vacuum ultraviolet that yields significantly higher reflectivity over selectable bandwidths. We demonstrate that the concept can be used to fabricate high-performance narrow-band and broadband reflection filters, whose spectral properties can be greatly enhanced by utilizing several of these filters in tandem. For example, we have fabricated a narrow-band filter at the location of the O I 135.6-nm line with a 3.2-nm bandwidth, a peak transmittance of 39.3%, and out-of-band wavelength blocking of better than 10−4 %. The principle of our design approach is to use a combination of high (H) and low (L) refractive-index dielectric pairs so that H + L = λr/2, where H/L < 1. H and L designate the optical thicknesses of high- and low-index film materials. This kind of choice for the high–low ratio reduces the effects of absorption for the H films for which the extinction coefficient in the vacuum ultraviolet is much higher than for the low-index film material MgF2. The reduced absorption of multilayers with H/L < 1 results in a significant increase in reflectivity compared with the classical quarter-wave stack for which H/L = 1.

© 1992 Optical Society of America

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References

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  1. Optical Filters Catalog (Acton Research Corporation, Acton, Mass., 1989).
  2. A. Malherbe, “Interference filters for the far ultraviolet,” Appl. Opt. 13, 1275–1276 (1974).
    [Crossref] [PubMed]
  3. A. Malherbe, “Multidielectric components for the far ultraviolet,” Appl. Opt. 13, 1276–1276 (1974).
    [Crossref] [PubMed]
  4. E. Spiller, “Interference filters for the ultraviolet and the surface plasmon of aluminum,” Appl. Opt. 13, 1209–1215 (1974).
    [Crossref] [PubMed]
  5. L. R. Elias, R. Flach, W. M. Yen, “Variable bandwidth transmission filter for the vacuum ultraviolet: La1−xCexF3,” Appl. Opt. 12, 138–139 (1973).
    [Crossref] [PubMed]
  6. E. T. Fairchild, “Interference filters for the VUV (1200–1900 Å),” Appl. Opt. 12, 2240–2241 (1973).
    [Crossref] [PubMed]
  7. B. K. Flint, “Special application coatings for the vacuum ultraviolet (VUV),” Opt. Eng. 18, 92–97 (1979).
  8. B. K. Flint, “Recent developments in ultraviolet filters and coatings,” Adv. Space Res. 2, 135–142 (1983).
    [Crossref]
  9. W. R. Hunter, “Review of vacuum ultraviolet optics,” in Optical Coatings: Applications and Utilization II, G. W. De Bell, D. H. Harrison, eds., Proc. Soc. Photo-Opt. Instrum. Eng.140, 122–130 (1978).
  10. M. Zukic, D. G. Torr, J. F. Spann, M. R. Torr, “VUV thin films. Part 2: Vacuum ultraviolet all-dielectric narrowband filters,” Appl. Opt. 29, 4293–4302 (1990).
    [Crossref] [PubMed]
  11. E. Spiller, “Multilayer interference coatings for the vacuum ultraviolet,” in Space Optics, Proceedings of the Ninth International Congress of the International Commission for Optics, B. J. Thompson, R. R. Shannon, eds. (National Academy of Sciences, Washington, D.C., 1974), pp. 581–597.
  12. W. R. Hunter, “Design criteria for reflection polarizers and analyzers in the vacuum ultraviolet,” Appl. Opt. 17, 1259–1270 (1978).
    [Crossref] [PubMed]
  13. M. Zukic, D. G. Torr, “VUV thin films,” in Thin Films, K. H. Guenther, ed., Springer Topics in Applied Physics, (Springer-Verlag, Berlin, 1991), Chap. 7.
  14. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1983), Chap. 1.
  15. H. A. Macleod, Thin-Film Optical Filters (Macmillan, New York, 1986), Chaps. 2, 5, 6.
    [Crossref]
  16. L. Young, “Prediction of absorption loss in multilayer interference filters,” J. Opt. Soc. Am. 52, 753–761 (1962).
    [Crossref]
  17. C. K. Carniglia, J. H. Apfel, “Maximum reflectance of multilayer dielectric mirrors in the presence of slight absorption,” J. Opt. Soc. Am. 70, 523–534 (1980).
    [Crossref]
  18. G. Koppelmann, “On the theory of multilayers consisting of weakly absorbing materials and their use as interferometer mirrors,” Ann. Phys. Leipzig 5, 388–396 (1960).
    [Crossref]
  19. J. H. Apfel, “Optical coatings design with reduced electric field intensity,” Appl. Opt. 16, 1880–1885 (1977).
    [Crossref] [PubMed]
  20. P. H. Lissberger, “The ultimate reflectance of multilayer dielectric mirror,” Opt. Acta 25, 291–298 (1978).
    [Crossref]
  21. M. Sparks, M. Flannery, “Simplified description of multilayer dielectric reflectors,” J. Opt. Soc. Am. 69, 993–1006 (1979).
    [Crossref]
  22. M. Zukic, D. G. Torr, J. F. Spann, M. R. Torr, “VUV thin films. Part 1: Optical constants of BaF2, CaF2, LaF3, MgF2, A12O3, HfO2, and SiO2 thin films,” Appl. Opt. 29, 4284–4292 (1991).
    [Crossref]
  23. P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988), Chaps. 6 and 7.
  24. 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]

1991 (1)

1990 (1)

1983 (1)

B. K. Flint, “Recent developments in ultraviolet filters and coatings,” Adv. Space Res. 2, 135–142 (1983).
[Crossref]

1980 (1)

1979 (2)

M. Sparks, M. Flannery, “Simplified description of multilayer dielectric reflectors,” J. Opt. Soc. Am. 69, 993–1006 (1979).
[Crossref]

B. K. Flint, “Special application coatings for the vacuum ultraviolet (VUV),” Opt. Eng. 18, 92–97 (1979).

1978 (2)

W. R. Hunter, “Design criteria for reflection polarizers and analyzers in the vacuum ultraviolet,” Appl. Opt. 17, 1259–1270 (1978).
[Crossref] [PubMed]

P. H. Lissberger, “The ultimate reflectance of multilayer dielectric mirror,” Opt. Acta 25, 291–298 (1978).
[Crossref]

1977 (1)

1974 (3)

1973 (2)

1966 (1)

1962 (1)

1960 (1)

G. Koppelmann, “On the theory of multilayers consisting of weakly absorbing materials and their use as interferometer mirrors,” Ann. Phys. Leipzig 5, 388–396 (1960).
[Crossref]

Apfel, J. H.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1983), Chap. 1.

Carniglia, C. K.

Elias, L. R.

Fairchild, E. T.

Flach, R.

Flannery, M.

Flint, B. K.

B. K. Flint, “Recent developments in ultraviolet filters and coatings,” Adv. Space Res. 2, 135–142 (1983).
[Crossref]

B. K. Flint, “Special application coatings for the vacuum ultraviolet (VUV),” Opt. Eng. 18, 92–97 (1979).

Heath, D. F.

Hunter, W. R.

W. R. Hunter, “Design criteria for reflection polarizers and analyzers in the vacuum ultraviolet,” Appl. Opt. 17, 1259–1270 (1978).
[Crossref] [PubMed]

W. R. Hunter, “Review of vacuum ultraviolet optics,” in Optical Coatings: Applications and Utilization II, G. W. De Bell, D. H. Harrison, eds., Proc. Soc. Photo-Opt. Instrum. Eng.140, 122–130 (1978).

Koppelmann, G.

G. Koppelmann, “On the theory of multilayers consisting of weakly absorbing materials and their use as interferometer mirrors,” Ann. Phys. Leipzig 5, 388–396 (1960).
[Crossref]

Lissberger, P. H.

P. H. Lissberger, “The ultimate reflectance of multilayer dielectric mirror,” Opt. Acta 25, 291–298 (1978).
[Crossref]

Macleod, H. A.

H. A. Macleod, Thin-Film Optical Filters (Macmillan, New York, 1986), Chaps. 2, 5, 6.
[Crossref]

Malherbe, A.

Sacher, P. A.

Spann, J. F.

Sparks, M.

Spiller, E.

E. Spiller, “Interference filters for the ultraviolet and the surface plasmon of aluminum,” Appl. Opt. 13, 1209–1215 (1974).
[Crossref] [PubMed]

E. Spiller, “Multilayer interference coatings for the vacuum ultraviolet,” in Space Optics, Proceedings of the Ninth International Congress of the International Commission for Optics, B. J. Thompson, R. R. Shannon, eds. (National Academy of Sciences, Washington, D.C., 1974), pp. 581–597.

Torr, D. G.

Torr, M. R.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1983), Chap. 1.

Yeh, P.

P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988), Chaps. 6 and 7.

Yen, W. M.

Young, L.

Zukic, M.

Adv. Space Res. (1)

B. K. Flint, “Recent developments in ultraviolet filters and coatings,” Adv. Space Res. 2, 135–142 (1983).
[Crossref]

Ann. Phys. Leipzig (1)

G. Koppelmann, “On the theory of multilayers consisting of weakly absorbing materials and their use as interferometer mirrors,” Ann. Phys. Leipzig 5, 388–396 (1960).
[Crossref]

Appl. Opt. (10)

J. H. Apfel, “Optical coatings design with reduced electric field intensity,” Appl. Opt. 16, 1880–1885 (1977).
[Crossref] [PubMed]

W. R. Hunter, “Design criteria for reflection polarizers and analyzers in the vacuum ultraviolet,” Appl. Opt. 17, 1259–1270 (1978).
[Crossref] [PubMed]

M. Zukic, D. G. Torr, J. F. Spann, M. R. Torr, “VUV thin films. Part 2: Vacuum ultraviolet all-dielectric narrowband filters,” Appl. Opt. 29, 4293–4302 (1990).
[Crossref] [PubMed]

A. Malherbe, “Interference filters for the far ultraviolet,” Appl. Opt. 13, 1275–1276 (1974).
[Crossref] [PubMed]

A. Malherbe, “Multidielectric components for the far ultraviolet,” Appl. Opt. 13, 1276–1276 (1974).
[Crossref] [PubMed]

E. Spiller, “Interference filters for the ultraviolet and the surface plasmon of aluminum,” Appl. Opt. 13, 1209–1215 (1974).
[Crossref] [PubMed]

L. R. Elias, R. Flach, W. M. Yen, “Variable bandwidth transmission filter for the vacuum ultraviolet: La1−xCexF3,” Appl. Opt. 12, 138–139 (1973).
[Crossref] [PubMed]

E. T. Fairchild, “Interference filters for the VUV (1200–1900 Å),” Appl. Opt. 12, 2240–2241 (1973).
[Crossref] [PubMed]

M. Zukic, D. G. Torr, J. F. Spann, M. R. Torr, “VUV thin films. Part 1: Optical constants of BaF2, CaF2, LaF3, MgF2, A12O3, HfO2, and SiO2 thin films,” Appl. Opt. 29, 4284–4292 (1991).
[Crossref]

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]

J. Opt. Soc. Am. (3)

Opt. Acta (1)

P. H. Lissberger, “The ultimate reflectance of multilayer dielectric mirror,” Opt. Acta 25, 291–298 (1978).
[Crossref]

Opt. Eng. (1)

B. K. Flint, “Special application coatings for the vacuum ultraviolet (VUV),” Opt. Eng. 18, 92–97 (1979).

Other (7)

E. Spiller, “Multilayer interference coatings for the vacuum ultraviolet,” in Space Optics, Proceedings of the Ninth International Congress of the International Commission for Optics, B. J. Thompson, R. R. Shannon, eds. (National Academy of Sciences, Washington, D.C., 1974), pp. 581–597.

W. R. Hunter, “Review of vacuum ultraviolet optics,” in Optical Coatings: Applications and Utilization II, G. W. De Bell, D. H. Harrison, eds., Proc. Soc. Photo-Opt. Instrum. Eng.140, 122–130 (1978).

M. Zukic, D. G. Torr, “VUV thin films,” in Thin Films, K. H. Guenther, ed., Springer Topics in Applied Physics, (Springer-Verlag, Berlin, 1991), Chap. 7.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1983), Chap. 1.

H. A. Macleod, Thin-Film Optical Filters (Macmillan, New York, 1986), Chaps. 2, 5, 6.
[Crossref]

Optical Filters Catalog (Acton Research Corporation, Acton, Mass., 1989).

P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988), Chaps. 6 and 7.

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Figures (10)

Fig. 1
Fig. 1

Maximum reflectance of the π stack calculated for the zero angle of incidence at 145 nm. The diamonds represent 99-layer stacks, triangles 55-layer stacks, and squares 35-layer stacks: H is LaF2 and L is MgF2. The Koppelmann limit is 90.8%.

Fig. 2
Fig. 2

Maximum reflectance of the π stack calculated for a 45° angle of incidence at 135.6 nm. The diamonds represent 99-layer stacks, triangles 55-layer stacks, and squares 35-layer stacks. H is LaF2, and L is MgF2. The Koppelmann limit is 89.5%.

Fig. 3
Fig. 3

Full width at half of the reflectance maximum of the π stacks calculated for a 45° angle of incidence. The maximum reflectance of the stacks as a function of the H/L ratio is shown in Fig. 2.

Fig. 4
Fig. 4

Measured (squares) and calculated (diamonds) reflectance of the 35-layer π stack for a 45° angle of incidence centered at 135.6 nm. The optical thickness ratio H/L = 1/4, where H is LaF2 and L is MgF2.

Fig. 5
Fig. 5

Measured (squares) and calculated (diamonds) reflectance of the 29-layer π stack for 45° angle of incidence centered at 135.6 nm. The optical thickness ratio H/L = 1/3, where H is BaF2 and L is MgF2.

Fig. 6
Fig. 6

Measured (squares) and calculated (diamonds) reflectance of the 35-layer second-order QW stack for a 45° angle of incidence centered at 135.6 nm. H is BaF2, and L is MgF2.

Fig. 7
Fig. 7

Transmittance of the combination of the four 29-layer filters shown in Fig. 5. The bandwidth is 4.3 nm, and a peak transmittance at 135.6 nm is 53.7%.

Fig. 8
Fig. 8

Transmittance of the combination of the six 29-layer filters shown in Fig. 5. The bandwidth is 3.2 nm, and a peak transmittance at 135.6 nm is 39.3%.

Fig. 9
Fig. 9

Measured (squares) and calculated (diamonds) reflectance of the 25-layer QW stack for a 45° angle of incidence centered at 175 nm. H is LaF2 and L is MgF2.

Fig. 10
Fig. 10

Transmittance of combinations of the four (solid curve) and six (dashed curve) 25-layer QW stacks shown in Fig. 9.

Equations (27)

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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 = n S cos θ S
η 0 = cos θ 0 n 0 ,
η S = cos θ S n S
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 l = n l + i k l ,
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 ) .
p = p 0 = π 4 [ tan 1 ( κ H κ L 1 + κ H κ L ) ] 1 ,
κ H = k H n H ,
κ L = k L n L ,
R + A 1 ,
SWR = 1 + R 1 R ,
R K = 1 2 π n 0 k H + k L n H 2 n L 2 ,
n H d H = λ r 6 , n L d L = λ r 3 .
H + L = λ r 2 ,
H = λ r 8 , L = 3 λ r 8 .
H = λ r 6 , L = λ r 3 .
n H d H = λ 10 , n L d L = 4 λ 10 .
n H d H = λ r 8 , n L d L = 3 λ r 8 .
( Δ λ ) H . R . = 1 2 ( m 1 ) + 1 4 λ r π sin 1 ( n H n L n H + n L ) ,

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