Abstract

Using numerical optimization algorithm, non-periodic Mo/Si, Mo/Be, and Ni/C broad angular multilayer analyzers have been designed. At the wavelength of 13 nm and the angular range of 45~49°, the Mo/Si and Mo/Be multilayer can provide the plateau s-reflectivity of 65% and 45%, respectively. At 5.7 nm, the s-reflectivity of Ni/C multilayer is 16% in the 44~46° range. The non-periodic Mo/Si broad angular multilayer was also fabricated using DC magnetron sputtering, and characterized using the soft X-ray polarimeter at BESSY. The s-reflectivity is higher than 45.6% over the angular range of 45~49° at 13 nm, where, the degree of polarization is more than 99.98%.

© 2006 Optical Society of America

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  1. J. Bahrdt, A. Gaupp, W. Gudat, M. Mast, K. Molter, W. B. Peatman, M. Scheer, Th. Schroeter, and Ch. Wang, "Circularly polarized synchrotron radiation from the crossed undulator at BESSY," Rev. Sci. Instrum. 63, 339-342 (1992).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  9. C. Morawe, E. Ziegler, J.-C. Peffen, and I. V. Kozhevnikov, "Design and fabrication of depth-graded X-ray multilayers," Nucl. Instrum. Methods Phys. Res. A 493, 189-198 (2002).
    [CrossRef]
  10. F. Schäfers, H.-C. Mertins, A. Gaupp, W. Gudat, M. Mertin, I. Packe, F. Schmolla, S. D. Fonzo, G. Soullié, W. Jark, R. Walker, X. L. Cann, R. Nyholm, and M. Eriksson, "Soft-x-ray polarimeter with multilayer optics: complete analysis of the polarization state of light," Appl. Opt. 38, 4074-4088 (1999).
    [CrossRef]
  11. E. Spiller, "Multilayer interference coatings for the vacuum ultraviolet," in Space Optics, B. J. Thompson and R. R. Shannon, eds. (National Academy of Science, Washington, D.C.,1974).

2004

2002

C. Morawe, E. Ziegler, J.-C. Peffen, and I. V. Kozhevnikov, "Design and fabrication of depth-graded X-ray multilayers," Nucl. Instrum. Methods Phys. Res. A 493, 189-198 (2002).
[CrossRef]

2001

I. V. Kozhevnikov, I. N. Bukreeva, and E. Ziegler, "Design of X-ray supermirrors," Nucl. Instrum. Methods Phys. Res. A 460, 424-443 (2001).
[CrossRef]

2000

Z. Wang, J. Cao, A. G. Michette, "Depth-graded multilayer X-ray optics with broad angular response," Opt. Commun. 177, 25-32 (2000).
[CrossRef]

A. G. Michette and Z. Wang, "Optimisation of depth-graded multilayer coatings for broadband reflectivity in the soft X-ray and EUV regions," Opt. Commun. 177, 47-55 (2000).
[CrossRef]

1999

1996

1993

B. L. Henke, E. M. Gullikson, and J. C. Davis, "X-ray interactions: photoabsorption, scattering, transmission, and reflection at E=50-30000 eV, Z=1-92," At. Data Nucl. Data Tables 54, 181-342 (1993).
[CrossRef]

1992

J. Bahrdt, A. Gaupp, W. Gudat, M. Mast, K. Molter, W. B. Peatman, M. Scheer, Th. Schroeter, and Ch. Wang, "Circularly polarized synchrotron radiation from the crossed undulator at BESSY," Rev. Sci. Instrum. 63, 339-342 (1992).
[CrossRef]

Bahrdt, J.

J. Bahrdt, A. Gaupp, W. Gudat, M. Mast, K. Molter, W. B. Peatman, M. Scheer, Th. Schroeter, and Ch. Wang, "Circularly polarized synchrotron radiation from the crossed undulator at BESSY," Rev. Sci. Instrum. 63, 339-342 (1992).
[CrossRef]

Bajt, S.

Bukreeva, I. N.

I. V. Kozhevnikov, I. N. Bukreeva, and E. Ziegler, "Design of X-ray supermirrors," Nucl. Instrum. Methods Phys. Res. A 460, 424-443 (2001).
[CrossRef]

Cann, X. L.

Cao, J.

Z. Wang, J. Cao, A. G. Michette, "Depth-graded multilayer X-ray optics with broad angular response," Opt. Commun. 177, 25-32 (2000).
[CrossRef]

Chaker, M.

Davis, J. C.

B. L. Henke, E. M. Gullikson, and J. C. Davis, "X-ray interactions: photoabsorption, scattering, transmission, and reflection at E=50-30000 eV, Z=1-92," At. Data Nucl. Data Tables 54, 181-342 (1993).
[CrossRef]

Eriksson, M.

Falco, C. M.

Fonzo, S. D.

Gaupp, A.

F. Schäfers, H.-C. Mertins, A. Gaupp, W. Gudat, M. Mertin, I. Packe, F. Schmolla, S. D. Fonzo, G. Soullié, W. Jark, R. Walker, X. L. Cann, R. Nyholm, and M. Eriksson, "Soft-x-ray polarimeter with multilayer optics: complete analysis of the polarization state of light," Appl. Opt. 38, 4074-4088 (1999).
[CrossRef]

J. Bahrdt, A. Gaupp, W. Gudat, M. Mast, K. Molter, W. B. Peatman, M. Scheer, Th. Schroeter, and Ch. Wang, "Circularly polarized synchrotron radiation from the crossed undulator at BESSY," Rev. Sci. Instrum. 63, 339-342 (1992).
[CrossRef]

Gudat, W.

F. Schäfers, H.-C. Mertins, A. Gaupp, W. Gudat, M. Mertin, I. Packe, F. Schmolla, S. D. Fonzo, G. Soullié, W. Jark, R. Walker, X. L. Cann, R. Nyholm, and M. Eriksson, "Soft-x-ray polarimeter with multilayer optics: complete analysis of the polarization state of light," Appl. Opt. 38, 4074-4088 (1999).
[CrossRef]

J. Bahrdt, A. Gaupp, W. Gudat, M. Mast, K. Molter, W. B. Peatman, M. Scheer, Th. Schroeter, and Ch. Wang, "Circularly polarized synchrotron radiation from the crossed undulator at BESSY," Rev. Sci. Instrum. 63, 339-342 (1992).
[CrossRef]

Gullikson, E. M.

B. L. Henke, E. M. Gullikson, and J. C. Davis, "X-ray interactions: photoabsorption, scattering, transmission, and reflection at E=50-30000 eV, Z=1-92," At. Data Nucl. Data Tables 54, 181-342 (1993).
[CrossRef]

Henke, B. L.

B. L. Henke, E. M. Gullikson, and J. C. Davis, "X-ray interactions: photoabsorption, scattering, transmission, and reflection at E=50-30000 eV, Z=1-92," At. Data Nucl. Data Tables 54, 181-342 (1993).
[CrossRef]

Jark, W.

Kearney, P. A.

Kim, S. K.

J. B. Kortright, M. Rice, S. K. Kim, C. C. Walton, and T. Warwick, "Optics for element-resolved soft X-ray magneto-optical studies," J. Magn. Magn. Mater. 191, 79-89 (1999).
[CrossRef]

Kjornrattanawanich, B.

Kortright, J. B.

J. B. Kortright, M. Rice, S. K. Kim, C. C. Walton, and T. Warwick, "Optics for element-resolved soft X-ray magneto-optical studies," J. Magn. Magn. Mater. 191, 79-89 (1999).
[CrossRef]

Kozhevnikov, I. V.

C. Morawe, E. Ziegler, J.-C. Peffen, and I. V. Kozhevnikov, "Design and fabrication of depth-graded X-ray multilayers," Nucl. Instrum. Methods Phys. Res. A 493, 189-198 (2002).
[CrossRef]

I. V. Kozhevnikov, I. N. Bukreeva, and E. Ziegler, "Design of X-ray supermirrors," Nucl. Instrum. Methods Phys. Res. A 460, 424-443 (2001).
[CrossRef]

Mast, M.

J. Bahrdt, A. Gaupp, W. Gudat, M. Mast, K. Molter, W. B. Peatman, M. Scheer, Th. Schroeter, and Ch. Wang, "Circularly polarized synchrotron radiation from the crossed undulator at BESSY," Rev. Sci. Instrum. 63, 339-342 (1992).
[CrossRef]

Mertin, M.

Mertins, H.-C.

Michette, A. G.

Z. Wang, J. Cao, A. G. Michette, "Depth-graded multilayer X-ray optics with broad angular response," Opt. Commun. 177, 25-32 (2000).
[CrossRef]

A. G. Michette and Z. Wang, "Optimisation of depth-graded multilayer coatings for broadband reflectivity in the soft X-ray and EUV regions," Opt. Commun. 177, 47-55 (2000).
[CrossRef]

Molter, K.

J. Bahrdt, A. Gaupp, W. Gudat, M. Mast, K. Molter, W. B. Peatman, M. Scheer, Th. Schroeter, and Ch. Wang, "Circularly polarized synchrotron radiation from the crossed undulator at BESSY," Rev. Sci. Instrum. 63, 339-342 (1992).
[CrossRef]

Montcalm, C.

Morawe, C.

C. Morawe, E. Ziegler, J.-C. Peffen, and I. V. Kozhevnikov, "Design and fabrication of depth-graded X-ray multilayers," Nucl. Instrum. Methods Phys. Res. A 493, 189-198 (2002).
[CrossRef]

Nyholm, R.

Packe, I.

Peatman, W. B.

J. Bahrdt, A. Gaupp, W. Gudat, M. Mast, K. Molter, W. B. Peatman, M. Scheer, Th. Schroeter, and Ch. Wang, "Circularly polarized synchrotron radiation from the crossed undulator at BESSY," Rev. Sci. Instrum. 63, 339-342 (1992).
[CrossRef]

Peffen, J.-C.

C. Morawe, E. Ziegler, J.-C. Peffen, and I. V. Kozhevnikov, "Design and fabrication of depth-graded X-ray multilayers," Nucl. Instrum. Methods Phys. Res. A 493, 189-198 (2002).
[CrossRef]

Pepin, H.

Rice, M.

J. B. Kortright, M. Rice, S. K. Kim, C. C. Walton, and T. Warwick, "Optics for element-resolved soft X-ray magneto-optical studies," J. Magn. Magn. Mater. 191, 79-89 (1999).
[CrossRef]

Schäfers, F.

Scheer, M.

J. Bahrdt, A. Gaupp, W. Gudat, M. Mast, K. Molter, W. B. Peatman, M. Scheer, Th. Schroeter, and Ch. Wang, "Circularly polarized synchrotron radiation from the crossed undulator at BESSY," Rev. Sci. Instrum. 63, 339-342 (1992).
[CrossRef]

Schmolla, F.

Schroeter, Th.

J. Bahrdt, A. Gaupp, W. Gudat, M. Mast, K. Molter, W. B. Peatman, M. Scheer, Th. Schroeter, and Ch. Wang, "Circularly polarized synchrotron radiation from the crossed undulator at BESSY," Rev. Sci. Instrum. 63, 339-342 (1992).
[CrossRef]

Seely, J. F.

Slaughter, J. M.

Soullié, G.

Sullivan, B. T.

Walker, R.

Walton, C. C.

J. B. Kortright, M. Rice, S. K. Kim, C. C. Walton, and T. Warwick, "Optics for element-resolved soft X-ray magneto-optical studies," J. Magn. Magn. Mater. 191, 79-89 (1999).
[CrossRef]

Wang, Ch.

J. Bahrdt, A. Gaupp, W. Gudat, M. Mast, K. Molter, W. B. Peatman, M. Scheer, Th. Schroeter, and Ch. Wang, "Circularly polarized synchrotron radiation from the crossed undulator at BESSY," Rev. Sci. Instrum. 63, 339-342 (1992).
[CrossRef]

Wang, Z.

Z. Wang, J. Cao, A. G. Michette, "Depth-graded multilayer X-ray optics with broad angular response," Opt. Commun. 177, 25-32 (2000).
[CrossRef]

A. G. Michette and Z. Wang, "Optimisation of depth-graded multilayer coatings for broadband reflectivity in the soft X-ray and EUV regions," Opt. Commun. 177, 47-55 (2000).
[CrossRef]

Warwick, T.

J. B. Kortright, M. Rice, S. K. Kim, C. C. Walton, and T. Warwick, "Optics for element-resolved soft X-ray magneto-optical studies," J. Magn. Magn. Mater. 191, 79-89 (1999).
[CrossRef]

Ziegler, E.

C. Morawe, E. Ziegler, J.-C. Peffen, and I. V. Kozhevnikov, "Design and fabrication of depth-graded X-ray multilayers," Nucl. Instrum. Methods Phys. Res. A 493, 189-198 (2002).
[CrossRef]

I. V. Kozhevnikov, I. N. Bukreeva, and E. Ziegler, "Design of X-ray supermirrors," Nucl. Instrum. Methods Phys. Res. A 460, 424-443 (2001).
[CrossRef]

Appl. Opt.

At. Data Nucl. Data Tables

B. L. Henke, E. M. Gullikson, and J. C. Davis, "X-ray interactions: photoabsorption, scattering, transmission, and reflection at E=50-30000 eV, Z=1-92," At. Data Nucl. Data Tables 54, 181-342 (1993).
[CrossRef]

J. Magn. Magn. Mater.

J. B. Kortright, M. Rice, S. K. Kim, C. C. Walton, and T. Warwick, "Optics for element-resolved soft X-ray magneto-optical studies," J. Magn. Magn. Mater. 191, 79-89 (1999).
[CrossRef]

Nucl. Instrum. Methods Phys. Res. A

I. V. Kozhevnikov, I. N. Bukreeva, and E. Ziegler, "Design of X-ray supermirrors," Nucl. Instrum. Methods Phys. Res. A 460, 424-443 (2001).
[CrossRef]

C. Morawe, E. Ziegler, J.-C. Peffen, and I. V. Kozhevnikov, "Design and fabrication of depth-graded X-ray multilayers," Nucl. Instrum. Methods Phys. Res. A 493, 189-198 (2002).
[CrossRef]

Opt. Commun.

Z. Wang, J. Cao, A. G. Michette, "Depth-graded multilayer X-ray optics with broad angular response," Opt. Commun. 177, 25-32 (2000).
[CrossRef]

A. G. Michette and Z. Wang, "Optimisation of depth-graded multilayer coatings for broadband reflectivity in the soft X-ray and EUV regions," Opt. Commun. 177, 47-55 (2000).
[CrossRef]

Rev. Sci. Instrum.

J. Bahrdt, A. Gaupp, W. Gudat, M. Mast, K. Molter, W. B. Peatman, M. Scheer, Th. Schroeter, and Ch. Wang, "Circularly polarized synchrotron radiation from the crossed undulator at BESSY," Rev. Sci. Instrum. 63, 339-342 (1992).
[CrossRef]

Other

E. Spiller, "Multilayer interference coatings for the vacuum ultraviolet," in Space Optics, B. J. Thompson and R. R. Shannon, eds. (National Academy of Science, Washington, D.C.,1974).

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Figures (4)

Fig. 1.
Fig. 1.

(I): The design of periodic and non-periodic Mo/Si multilayer analyzers working at 13 nm: The non-periodic multilayers were optimized for angular ranges of 45~49° with plateau Rs =0.65 (b) and 43~51° with plateau Rs =0.45 (c). The periodic multilayer (a) was shown just for comparison. (II) Design for other material pairs and wavelength ranges: Mo/Be multilayer at λ=13 nm in 45~49° range with Rs =0.45 (d), and Ni/C multilayer at λ=5.2 nm in 44~46° range with Rs =0.16.

Fig. 2.
Fig. 2.

The layer thickness distribution of the optimized Mo/Si multilayer analyzer.

Fig. 3.
Fig. 3.

The calculated and experimental results of fabricated Mo/Si analyzer shown in Fig. 2.

Fig. 4.
Fig. 4.

The s- and p-reflectivities for broadband Mo/Si multilayer analyzer as function of grazing incident angle at different wavelengths of 14.6 nm (I), 15.5 nm (II), and 16.5 nm (III).

Tables (1)

Tables Icon

Table 1. Calculated and measured results of the Mo/Si broad angular multilayer analyzer in the 45~49° range at wavelength of 13 nm (errors are root-mean-square values).

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

P = R s R p R s + R p ,
and R = R s + R p 2 ,
MF = 1 m j = 1 m ( 1 P ( θ j ) ) 2 ,

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