Abstract

Layered synthetic microstructures (LSM) have been shown to be useful in obtaining high reflectivities in the soft x-ray and EUV portions of the spectrum, particularly at angles approaching normal incidence.

© 1986 Optical Society of America

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  1. R. Giacconi, W. P. Reidy, G. S. Vaiana, L. P. Van Speybroeck, T. F. Zehnpfennig, “Grazing Incidence Telescopes for X-Ray Astronomy,” Space. Sci. Rev. 9, 3 (1969).
    [CrossRef]
  2. H. Bräuninger, R. Lenzen, J. Trümper, “X-Ray Optical Properties of a Wolter Type-I Telescope for Rocket Application,” in COSPAR: New Instrumentation for Space Astronomy, K. A. Van der Hucht, G. Vaiana, Eds. (Pergamon, New York, 1978), p. 251.
  3. R. F. Malina, S. Bowyer, D. Finley, W. Cash, “WolterSchwarzchild Optics for the Extreme-Ultraviolet: the Berkeley Stellar Spectrometer and the EUV Explorer,” Proc. Soc. Photo-Opt. Instrum. Eng. 184, 30 (1979).
  4. R. Giacconi et al., “The Einstein (HEAO-2) X-Ray Observatory,” Astrophys. J. 230, 540 (1979).
    [CrossRef]
  5. M. V. Zombeck, “Advanced X-Ray Astrophysics Facility (AXAF)-Performance Requirements and Design Considerations,” Proc. Soc. Photo-Opt. Instrum. Eng. 184, 50 (1979).
  6. H. Wolter, “Spiegelsysteme Streifenden Einfalls als Abbildende Optiken für Röntgenstrahlen,” Ann. Phys. 10, 94 (1952).
    [CrossRef]
  7. H. Wolter, “Verallgemeinerte Schwarzschildsche Spiegelsysteme Streifender Reflexion als Optiken für Röntgenstrahlen,” Ann. Phys. 10, 286 (1952).
    [CrossRef]
  8. P. Gorenstein, “X-ray optics for the LAMAR Facility, an Overview,” Proc. Soc. Photo-Opt. Instrum. Eng. 184, 63 (1979).
  9. P. Kirkpatrick, A. V. Baez, “Formation of Optical Images by X-Rays,” J. Opt. Soc. Am. 38, 766 (1948).
    [CrossRef] [PubMed]
  10. M. C. Hettrick, S. Bowyer, “Variable Line-Space Gratings: New Designs for Use in Grazing Incidence Spectrometers,” Appl. Opt. 22, 3921 (1983).
    [CrossRef] [PubMed]
  11. W. C. Cash, “X-Ray Spectrographs Using Radial Groove Gratings,” Appl. Opt. 22, 3971 (1983).
    [CrossRef] [PubMed]
  12. W. Cash, P. Kohnert, “Very High X-Ray Efficiency from a Blazed Grating,” Appl. Opt. 21, 17 (1982).
    [CrossRef] [PubMed]
  13. W. Cash, “Echelle Spectrographs at Grazing Incidence,” Appl. Opt. 21, 710 (1982).
    [CrossRef] [PubMed]
  14. J. F. Meekins, H. Gursky, R. G. Cruddace, “Optimization of the Rowland Circle Grating for High-Resolution Astrophysical Spectrometers Working at Soft X-Ray and EUV Wavelengths,” Appl. Opt. 24, 2987 (1985).
    [CrossRef] [PubMed]
  15. E. Spiller, “Multilayer Interference Coatings for the Vacuum Ultraviolet,” in Space Optics, Proceedings, Ninth International Congress of the International Commission for Optics, Santa Monica, CA 1972, B. J. Thompson, R. R. Shannon, Eds. (National Academy of Sciences, Washington, DC, 1974), p. 581.
  16. J. H. Underwood, T. W. Barbee, D. L. Shealy, “X-Ray and Extreme Ultraviolet Imaging Using Layered Synthetic Microstructures,” Proc. Soc. Photo-Opt. Instrum. Eng. 316, 79 (1981).
  17. J. P. Henry, E. Spiller, M. Weisskopf, “Imaging Performance of a Normal Incidence X-Ray Telescope Measured at 0.18 keV,” Proc. Soc. Photo-Opt. Instrum. Eng. 316, 166 (1981).
  18. J. F. Meekins, R. G. Cruddace, H. Gursky, “The Optimization of Layered Synthetic Microstructures for Broad-Band Reflectivity at Soft X-Ray and EUV Wavelengths,” submitted to Appl. Opt. (1986).
    [CrossRef] [PubMed]
  19. M. Born, E. Wolf, Principles of Optics–Electromagnetic Theory of Propagation, Interference, and Diffraction of LightPergamon, Oxford, (1980), pp. 51–70, 627–633.
  20. W. R. Hunter, T. L. Mikes, G. Hass, “Deterioration of Reflecting Coatings by Intermetallic Diffusion,” Appl. Opt. 11, 1594 (1972).
    [CrossRef] [PubMed]
  21. B. Vidal, P. Vincent, “Metallic Multilayers for X Rays using Classical Thin-Film Theory,” Appl Opt. 23, 1794 (1984).
    [CrossRef] [PubMed]
  22. W. R. Hunter, Sachs/Freeman Associates, Inc., private communication (1984).
  23. B. L. Henke, P. Lee, T. J. Tanaka, R. L. Shimabukuro, B. K. Fujikawa, “Low-Energy X-Ray Interaction Coefficients: Photoabsorption, Scattering, and Reflection,” At. Data Nucl. Data Tables 27, 1 (1982).
    [CrossRef]

1985 (1)

1984 (1)

B. Vidal, P. Vincent, “Metallic Multilayers for X Rays using Classical Thin-Film Theory,” Appl Opt. 23, 1794 (1984).
[CrossRef] [PubMed]

1983 (2)

1982 (3)

W. Cash, P. Kohnert, “Very High X-Ray Efficiency from a Blazed Grating,” Appl. Opt. 21, 17 (1982).
[CrossRef] [PubMed]

W. Cash, “Echelle Spectrographs at Grazing Incidence,” Appl. Opt. 21, 710 (1982).
[CrossRef] [PubMed]

B. L. Henke, P. Lee, T. J. Tanaka, R. L. Shimabukuro, B. K. Fujikawa, “Low-Energy X-Ray Interaction Coefficients: Photoabsorption, Scattering, and Reflection,” At. Data Nucl. Data Tables 27, 1 (1982).
[CrossRef]

1981 (2)

J. H. Underwood, T. W. Barbee, D. L. Shealy, “X-Ray and Extreme Ultraviolet Imaging Using Layered Synthetic Microstructures,” Proc. Soc. Photo-Opt. Instrum. Eng. 316, 79 (1981).

J. P. Henry, E. Spiller, M. Weisskopf, “Imaging Performance of a Normal Incidence X-Ray Telescope Measured at 0.18 keV,” Proc. Soc. Photo-Opt. Instrum. Eng. 316, 166 (1981).

1979 (4)

P. Gorenstein, “X-ray optics for the LAMAR Facility, an Overview,” Proc. Soc. Photo-Opt. Instrum. Eng. 184, 63 (1979).

R. F. Malina, S. Bowyer, D. Finley, W. Cash, “WolterSchwarzchild Optics for the Extreme-Ultraviolet: the Berkeley Stellar Spectrometer and the EUV Explorer,” Proc. Soc. Photo-Opt. Instrum. Eng. 184, 30 (1979).

R. Giacconi et al., “The Einstein (HEAO-2) X-Ray Observatory,” Astrophys. J. 230, 540 (1979).
[CrossRef]

M. V. Zombeck, “Advanced X-Ray Astrophysics Facility (AXAF)-Performance Requirements and Design Considerations,” Proc. Soc. Photo-Opt. Instrum. Eng. 184, 50 (1979).

1972 (1)

1969 (1)

R. Giacconi, W. P. Reidy, G. S. Vaiana, L. P. Van Speybroeck, T. F. Zehnpfennig, “Grazing Incidence Telescopes for X-Ray Astronomy,” Space. Sci. Rev. 9, 3 (1969).
[CrossRef]

1952 (2)

H. Wolter, “Spiegelsysteme Streifenden Einfalls als Abbildende Optiken für Röntgenstrahlen,” Ann. Phys. 10, 94 (1952).
[CrossRef]

H. Wolter, “Verallgemeinerte Schwarzschildsche Spiegelsysteme Streifender Reflexion als Optiken für Röntgenstrahlen,” Ann. Phys. 10, 286 (1952).
[CrossRef]

1948 (1)

Baez, A. V.

Barbee, T. W.

J. H. Underwood, T. W. Barbee, D. L. Shealy, “X-Ray and Extreme Ultraviolet Imaging Using Layered Synthetic Microstructures,” Proc. Soc. Photo-Opt. Instrum. Eng. 316, 79 (1981).

Born, M.

M. Born, E. Wolf, Principles of Optics–Electromagnetic Theory of Propagation, Interference, and Diffraction of LightPergamon, Oxford, (1980), pp. 51–70, 627–633.

Bowyer, S.

M. C. Hettrick, S. Bowyer, “Variable Line-Space Gratings: New Designs for Use in Grazing Incidence Spectrometers,” Appl. Opt. 22, 3921 (1983).
[CrossRef] [PubMed]

R. F. Malina, S. Bowyer, D. Finley, W. Cash, “WolterSchwarzchild Optics for the Extreme-Ultraviolet: the Berkeley Stellar Spectrometer and the EUV Explorer,” Proc. Soc. Photo-Opt. Instrum. Eng. 184, 30 (1979).

Bräuninger, H.

H. Bräuninger, R. Lenzen, J. Trümper, “X-Ray Optical Properties of a Wolter Type-I Telescope for Rocket Application,” in COSPAR: New Instrumentation for Space Astronomy, K. A. Van der Hucht, G. Vaiana, Eds. (Pergamon, New York, 1978), p. 251.

Cash, W.

W. Cash, P. Kohnert, “Very High X-Ray Efficiency from a Blazed Grating,” Appl. Opt. 21, 17 (1982).
[CrossRef] [PubMed]

W. Cash, “Echelle Spectrographs at Grazing Incidence,” Appl. Opt. 21, 710 (1982).
[CrossRef] [PubMed]

R. F. Malina, S. Bowyer, D. Finley, W. Cash, “WolterSchwarzchild Optics for the Extreme-Ultraviolet: the Berkeley Stellar Spectrometer and the EUV Explorer,” Proc. Soc. Photo-Opt. Instrum. Eng. 184, 30 (1979).

Cash, W. C.

Cruddace, R. G.

J. F. Meekins, H. Gursky, R. G. Cruddace, “Optimization of the Rowland Circle Grating for High-Resolution Astrophysical Spectrometers Working at Soft X-Ray and EUV Wavelengths,” Appl. Opt. 24, 2987 (1985).
[CrossRef] [PubMed]

J. F. Meekins, R. G. Cruddace, H. Gursky, “The Optimization of Layered Synthetic Microstructures for Broad-Band Reflectivity at Soft X-Ray and EUV Wavelengths,” submitted to Appl. Opt. (1986).
[CrossRef] [PubMed]

Finley, D.

R. F. Malina, S. Bowyer, D. Finley, W. Cash, “WolterSchwarzchild Optics for the Extreme-Ultraviolet: the Berkeley Stellar Spectrometer and the EUV Explorer,” Proc. Soc. Photo-Opt. Instrum. Eng. 184, 30 (1979).

Fujikawa, B. K.

B. L. Henke, P. Lee, T. J. Tanaka, R. L. Shimabukuro, B. K. Fujikawa, “Low-Energy X-Ray Interaction Coefficients: Photoabsorption, Scattering, and Reflection,” At. Data Nucl. Data Tables 27, 1 (1982).
[CrossRef]

Giacconi, R.

R. Giacconi et al., “The Einstein (HEAO-2) X-Ray Observatory,” Astrophys. J. 230, 540 (1979).
[CrossRef]

R. Giacconi, W. P. Reidy, G. S. Vaiana, L. P. Van Speybroeck, T. F. Zehnpfennig, “Grazing Incidence Telescopes for X-Ray Astronomy,” Space. Sci. Rev. 9, 3 (1969).
[CrossRef]

Gorenstein, P.

P. Gorenstein, “X-ray optics for the LAMAR Facility, an Overview,” Proc. Soc. Photo-Opt. Instrum. Eng. 184, 63 (1979).

Gursky, H.

J. F. Meekins, H. Gursky, R. G. Cruddace, “Optimization of the Rowland Circle Grating for High-Resolution Astrophysical Spectrometers Working at Soft X-Ray and EUV Wavelengths,” Appl. Opt. 24, 2987 (1985).
[CrossRef] [PubMed]

J. F. Meekins, R. G. Cruddace, H. Gursky, “The Optimization of Layered Synthetic Microstructures for Broad-Band Reflectivity at Soft X-Ray and EUV Wavelengths,” submitted to Appl. Opt. (1986).
[CrossRef] [PubMed]

Hass, G.

Henke, B. L.

B. L. Henke, P. Lee, T. J. Tanaka, R. L. Shimabukuro, B. K. Fujikawa, “Low-Energy X-Ray Interaction Coefficients: Photoabsorption, Scattering, and Reflection,” At. Data Nucl. Data Tables 27, 1 (1982).
[CrossRef]

Henry, J. P.

J. P. Henry, E. Spiller, M. Weisskopf, “Imaging Performance of a Normal Incidence X-Ray Telescope Measured at 0.18 keV,” Proc. Soc. Photo-Opt. Instrum. Eng. 316, 166 (1981).

Hettrick, M. C.

Hunter, W. R.

Kirkpatrick, P.

Kohnert, P.

Lee, P.

B. L. Henke, P. Lee, T. J. Tanaka, R. L. Shimabukuro, B. K. Fujikawa, “Low-Energy X-Ray Interaction Coefficients: Photoabsorption, Scattering, and Reflection,” At. Data Nucl. Data Tables 27, 1 (1982).
[CrossRef]

Lenzen, R.

H. Bräuninger, R. Lenzen, J. Trümper, “X-Ray Optical Properties of a Wolter Type-I Telescope for Rocket Application,” in COSPAR: New Instrumentation for Space Astronomy, K. A. Van der Hucht, G. Vaiana, Eds. (Pergamon, New York, 1978), p. 251.

Malina, R. F.

R. F. Malina, S. Bowyer, D. Finley, W. Cash, “WolterSchwarzchild Optics for the Extreme-Ultraviolet: the Berkeley Stellar Spectrometer and the EUV Explorer,” Proc. Soc. Photo-Opt. Instrum. Eng. 184, 30 (1979).

Meekins, J. F.

J. F. Meekins, H. Gursky, R. G. Cruddace, “Optimization of the Rowland Circle Grating for High-Resolution Astrophysical Spectrometers Working at Soft X-Ray and EUV Wavelengths,” Appl. Opt. 24, 2987 (1985).
[CrossRef] [PubMed]

J. F. Meekins, R. G. Cruddace, H. Gursky, “The Optimization of Layered Synthetic Microstructures for Broad-Band Reflectivity at Soft X-Ray and EUV Wavelengths,” submitted to Appl. Opt. (1986).
[CrossRef] [PubMed]

Mikes, T. L.

Reidy, W. P.

R. Giacconi, W. P. Reidy, G. S. Vaiana, L. P. Van Speybroeck, T. F. Zehnpfennig, “Grazing Incidence Telescopes for X-Ray Astronomy,” Space. Sci. Rev. 9, 3 (1969).
[CrossRef]

Shealy, D. L.

J. H. Underwood, T. W. Barbee, D. L. Shealy, “X-Ray and Extreme Ultraviolet Imaging Using Layered Synthetic Microstructures,” Proc. Soc. Photo-Opt. Instrum. Eng. 316, 79 (1981).

Shimabukuro, R. L.

B. L. Henke, P. Lee, T. J. Tanaka, R. L. Shimabukuro, B. K. Fujikawa, “Low-Energy X-Ray Interaction Coefficients: Photoabsorption, Scattering, and Reflection,” At. Data Nucl. Data Tables 27, 1 (1982).
[CrossRef]

Spiller, E.

J. P. Henry, E. Spiller, M. Weisskopf, “Imaging Performance of a Normal Incidence X-Ray Telescope Measured at 0.18 keV,” Proc. Soc. Photo-Opt. Instrum. Eng. 316, 166 (1981).

E. Spiller, “Multilayer Interference Coatings for the Vacuum Ultraviolet,” in Space Optics, Proceedings, Ninth International Congress of the International Commission for Optics, Santa Monica, CA 1972, B. J. Thompson, R. R. Shannon, Eds. (National Academy of Sciences, Washington, DC, 1974), p. 581.

Tanaka, T. J.

B. L. Henke, P. Lee, T. J. Tanaka, R. L. Shimabukuro, B. K. Fujikawa, “Low-Energy X-Ray Interaction Coefficients: Photoabsorption, Scattering, and Reflection,” At. Data Nucl. Data Tables 27, 1 (1982).
[CrossRef]

Trümper, J.

H. Bräuninger, R. Lenzen, J. Trümper, “X-Ray Optical Properties of a Wolter Type-I Telescope for Rocket Application,” in COSPAR: New Instrumentation for Space Astronomy, K. A. Van der Hucht, G. Vaiana, Eds. (Pergamon, New York, 1978), p. 251.

Underwood, J. H.

J. H. Underwood, T. W. Barbee, D. L. Shealy, “X-Ray and Extreme Ultraviolet Imaging Using Layered Synthetic Microstructures,” Proc. Soc. Photo-Opt. Instrum. Eng. 316, 79 (1981).

Vaiana, G. S.

R. Giacconi, W. P. Reidy, G. S. Vaiana, L. P. Van Speybroeck, T. F. Zehnpfennig, “Grazing Incidence Telescopes for X-Ray Astronomy,” Space. Sci. Rev. 9, 3 (1969).
[CrossRef]

Van Speybroeck, L. P.

R. Giacconi, W. P. Reidy, G. S. Vaiana, L. P. Van Speybroeck, T. F. Zehnpfennig, “Grazing Incidence Telescopes for X-Ray Astronomy,” Space. Sci. Rev. 9, 3 (1969).
[CrossRef]

Vidal, B.

B. Vidal, P. Vincent, “Metallic Multilayers for X Rays using Classical Thin-Film Theory,” Appl Opt. 23, 1794 (1984).
[CrossRef] [PubMed]

Vincent, P.

B. Vidal, P. Vincent, “Metallic Multilayers for X Rays using Classical Thin-Film Theory,” Appl Opt. 23, 1794 (1984).
[CrossRef] [PubMed]

Weisskopf, M.

J. P. Henry, E. Spiller, M. Weisskopf, “Imaging Performance of a Normal Incidence X-Ray Telescope Measured at 0.18 keV,” Proc. Soc. Photo-Opt. Instrum. Eng. 316, 166 (1981).

Wolf, E.

M. Born, E. Wolf, Principles of Optics–Electromagnetic Theory of Propagation, Interference, and Diffraction of LightPergamon, Oxford, (1980), pp. 51–70, 627–633.

Wolter, H.

H. Wolter, “Spiegelsysteme Streifenden Einfalls als Abbildende Optiken für Röntgenstrahlen,” Ann. Phys. 10, 94 (1952).
[CrossRef]

H. Wolter, “Verallgemeinerte Schwarzschildsche Spiegelsysteme Streifender Reflexion als Optiken für Röntgenstrahlen,” Ann. Phys. 10, 286 (1952).
[CrossRef]

Zehnpfennig, T. F.

R. Giacconi, W. P. Reidy, G. S. Vaiana, L. P. Van Speybroeck, T. F. Zehnpfennig, “Grazing Incidence Telescopes for X-Ray Astronomy,” Space. Sci. Rev. 9, 3 (1969).
[CrossRef]

Zombeck, M. V.

M. V. Zombeck, “Advanced X-Ray Astrophysics Facility (AXAF)-Performance Requirements and Design Considerations,” Proc. Soc. Photo-Opt. Instrum. Eng. 184, 50 (1979).

Ann. Phys. (2)

H. Wolter, “Spiegelsysteme Streifenden Einfalls als Abbildende Optiken für Röntgenstrahlen,” Ann. Phys. 10, 94 (1952).
[CrossRef]

H. Wolter, “Verallgemeinerte Schwarzschildsche Spiegelsysteme Streifender Reflexion als Optiken für Röntgenstrahlen,” Ann. Phys. 10, 286 (1952).
[CrossRef]

Appl Opt. (1)

B. Vidal, P. Vincent, “Metallic Multilayers for X Rays using Classical Thin-Film Theory,” Appl Opt. 23, 1794 (1984).
[CrossRef] [PubMed]

Appl. Opt. (6)

Astrophys. J. (1)

R. Giacconi et al., “The Einstein (HEAO-2) X-Ray Observatory,” Astrophys. J. 230, 540 (1979).
[CrossRef]

At. Data Nucl. Data Tables (1)

B. L. Henke, P. Lee, T. J. Tanaka, R. L. Shimabukuro, B. K. Fujikawa, “Low-Energy X-Ray Interaction Coefficients: Photoabsorption, Scattering, and Reflection,” At. Data Nucl. Data Tables 27, 1 (1982).
[CrossRef]

J. Opt. Soc. Am. (1)

Proc. Soc. Photo-Opt. Instrum. Eng. (5)

R. F. Malina, S. Bowyer, D. Finley, W. Cash, “WolterSchwarzchild Optics for the Extreme-Ultraviolet: the Berkeley Stellar Spectrometer and the EUV Explorer,” Proc. Soc. Photo-Opt. Instrum. Eng. 184, 30 (1979).

P. Gorenstein, “X-ray optics for the LAMAR Facility, an Overview,” Proc. Soc. Photo-Opt. Instrum. Eng. 184, 63 (1979).

M. V. Zombeck, “Advanced X-Ray Astrophysics Facility (AXAF)-Performance Requirements and Design Considerations,” Proc. Soc. Photo-Opt. Instrum. Eng. 184, 50 (1979).

J. H. Underwood, T. W. Barbee, D. L. Shealy, “X-Ray and Extreme Ultraviolet Imaging Using Layered Synthetic Microstructures,” Proc. Soc. Photo-Opt. Instrum. Eng. 316, 79 (1981).

J. P. Henry, E. Spiller, M. Weisskopf, “Imaging Performance of a Normal Incidence X-Ray Telescope Measured at 0.18 keV,” Proc. Soc. Photo-Opt. Instrum. Eng. 316, 166 (1981).

Space. Sci. Rev. (1)

R. Giacconi, W. P. Reidy, G. S. Vaiana, L. P. Van Speybroeck, T. F. Zehnpfennig, “Grazing Incidence Telescopes for X-Ray Astronomy,” Space. Sci. Rev. 9, 3 (1969).
[CrossRef]

Other (5)

H. Bräuninger, R. Lenzen, J. Trümper, “X-Ray Optical Properties of a Wolter Type-I Telescope for Rocket Application,” in COSPAR: New Instrumentation for Space Astronomy, K. A. Van der Hucht, G. Vaiana, Eds. (Pergamon, New York, 1978), p. 251.

J. F. Meekins, R. G. Cruddace, H. Gursky, “The Optimization of Layered Synthetic Microstructures for Broad-Band Reflectivity at Soft X-Ray and EUV Wavelengths,” submitted to Appl. Opt. (1986).
[CrossRef] [PubMed]

M. Born, E. Wolf, Principles of Optics–Electromagnetic Theory of Propagation, Interference, and Diffraction of LightPergamon, Oxford, (1980), pp. 51–70, 627–633.

E. Spiller, “Multilayer Interference Coatings for the Vacuum Ultraviolet,” in Space Optics, Proceedings, Ninth International Congress of the International Commission for Optics, Santa Monica, CA 1972, B. J. Thompson, R. R. Shannon, Eds. (National Academy of Sciences, Washington, DC, 1974), p. 581.

W. R. Hunter, Sachs/Freeman Associates, Inc., private communication (1984).

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Figures (5)

Fig. 1
Fig. 1

Comparison of reflection coefficients of an optimized periodic LSM (triangles) and an optimized nonperiodic LSM (solid circles) at a wavelength of 200 Å. The reflectivity of the nonperiodic LSM has been maximized for ten pairs of film layers. Each point is labeled with the number of pairs of films deposited on the substrate. The open circle is the asymptotic reflection coefficient for both LSMs.

Fig. 2
Fig. 2

Optical constants (n and k) of silicon, iridium, and platinum from Hunter22 and Henke et al.23: (a) silicon; (b) iridium; (c) platinum.

Fig. 3
Fig. 3

Reflectivity at normal incidence of a nonperiodic seven-layer iridium–silicon LSM optimized over a narrow band of wavelengths centered at 450 Å.

Fig. 4
Fig. 4

Reflectivity at normal incidence of a nonperiodic seventeen-layer platinum–silicon LSM optimized over a narrow band of wavelengths centered at 200 Å.

Fig. 5
Fig. 5

Reflectivity at normal incidence of the nonperiodic platinum–silicon LSM formed by taking the first five films and the substrate from Table II.

Tables (2)

Tables Icon

Table I Film Thickness of a LSM Optimized at 200 Å

Tables Icon

Table II Film Thicknesses of Optimized LSMs

Equations (31)

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E = e ^ x U ( z ) exp [ i ( k 0 α y - ω t ) ] , H = [ e ^ y V ( z ) - e ^ z ( α / μ ) U ( z ) ] exp [ i ( k 0 α y - ω t ) ] ,
d U / d z = i μ k 0 V , d V / d z = i k 0 ( c - α 2 / μ ) U ,
[ U ( 0 ) V ( 0 ) ] = M ( z ) [ U ( z ) V ( z ) ] ,
M ( z ) = [ cos ( γ z ) - i p - 1 sin ( γ z ) - i p sin ( γ z ) cos ( γ z ) ] ,
H j + H j = ( c j / μ j ) 1 / 2 ( s ^ j × E j + s ^ j × E j ) .
M ( z J ) = M 1 ( h 1 ) M 2 ( h 2 ) M J ( h J ) ,
U ( 0 ) = A + R ,             V ( 0 ) = p 0 ( A - R ) , U ( z J ) = T ,             V ( z J ) = p s T ,
r = [ ( m 11 + m 12 p s ) p 0 - m 21 - m 22 p s ] [ ( m 11 + m 12 p s ) p 0 + m 21 + m 22 p s ] t = 2 p 0 / [ ( m 11 + m 12 p s ) p 0 + m 21 + m 22 p s ] ,
R = r 2 , T = [ ( p s + p s * ) / ( p 0 + p 0 * ) ] t 2 .
M = N K ,
N = M 1 ( h 1 ) M 2 ( h 2 ) M L ( h L )
[ 1 + r p 0 ( 1 - r ) ] = N K [ t p s t ] .
r ¯ = ( A - B ) / ( A + B ) , t = 2 p 0 / ( A + B ) ,
[ 1 + r ¯ p 0 ( 1 - r ¯ ) ] = N M [ t p s t ]
r ¯ = ( A - B ) / ( A + B ) , t = 2 p 0 / ( A + B ) ,
[ 1 + r ¯ p 0 ( 1 - r ¯ ) ] = Λ - 1 N M [ t p s t ]
Λ [ 1 + r ¯ p 0 ( 1 - r ¯ ) ] = N [ 1 + r ¯ p 0 ( 1 - r ¯ ) ] .
( n 11 - Λ ) ( n 22 - Λ ) - n 12 n 21 = 0 ,
Λ ± = ( ½ ) { n 11 + n 22 ± [ ( n 11 + n 22 ) 2 - 4 ] 1 / 2 } ,
Λ a 2 1
r ¯ = [ 2 p 0 Λ a - ( a + b ) ] / ( a - b ) ,
[ 1 + r K p 0 ( 1 - r K ) ] = N K [ t K p s t K ]
Λ K [ 1 + r K p 0 ( 1 - r K ) ] = N [ 1 + r K - 1 p 0 ( 1 - r K - 1 ) ] ,
[ Λ a ( 1 + r ¯ ) Λ K ( 1 + r K ) Λ a p 0 ( 1 - r ¯ ) Λ K p 0 ( 1 - r K ) ] = N [ 1 + r ¯ 1 + r K - 1 p 0 ( 1 - r ¯ ) p 0 ( 1 - r K - 1 ) ] .
Λ a Λ K ( r ¯ - r K ) = r ¯ - r K - 1 .
Λ a - Λ K = Const ( r ¯ - r K - 1 ) ,
Λ + 2 = ¼ { Q 2 + Q exp ( - i ϕ ) [ Q 2 exp ( 2 i ϕ ) - 4 ] 1 / 2 + Q exp ( i ϕ ) [ Q 2 exp ( - 2 i ϕ ) - 4 ] 1 / 2 + ( Q 4 - 8 Q 2 cos 2 ϕ + 16 ) 1 / 2 } ,
Λ K + 1 + Λ K - 1 = Λ a + Λ a - 1 = n 11 + n 22 .
Λ K + 1 2 - 2 Λ K + 1 ( n 11 + n 22 ) cos α + ( n 11 + n 22 ) 2 = Λ K - 2 ,
ρ 2 = λ ( 1 - R λ ) 2 ,
h odd = h odd ( ) - A odd exp ( - α N 1 / 2 ) , h even = h even ( ) + A even exp ( - α N 1 / 2 ) ,

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