Abstract

In the laboratory of the Physikalisch-Technische Bundesanstalt (PTB) at the Berlin electron-storage ring BESSY II, aprocedure has been developed to investigate the dependence of vacuum-ultraviolet reflection on polarization. It is based on characterizing the elliptically polarized synchrotron radiation at PTB's normal-incidence monochromator beamline for reflectometry by means of polarization-sensitive photodetectors. For this purpose, the polarization dependency in the detector responsivity was determined at a small, low, solid angle of acceptance for the synchrotron radiation, i.e., within the orbital plane of the storage ring where the degree of linear polarization is known to be almost 100%. Our method allows the polarization dependence of reflection samples to be measured with relative standard uncertainties ranging from 2.4% to 11% in the spectral range between 60 and 160  nm. The method has been applied to the optimization of polarizing mirrors at the Lyman-α wavelength of 121.6   nm.

© 2007 Optical Society of America

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References

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2007 (3)

M. Yang, C. Cobet, and N. Esser,"Tunable thin film polarizer for the vacuum ultraviolet and soft x-ray spectral regions," J. Appl. Phys. 101, 053114 (2007).
[CrossRef]

F. Bridou, M. Cuniot-Ponsard, and J-M. Desvignes,"Experimental determination of optical constants in the vacuum ultra violet wavelength region between 80 and 140 nm: a reflectance versus thickness method and its application to ZnSe," Opt. Commun. 271, 353-360 (2007).
[CrossRef]

G. Brandt, J. Eden, R. Fliegauf, A. Gottwald, A. Hoehl, R. Klein, R. Müller, M. Richter, F. Scholze, R. Thornagel, G. Ulm, K. Bürkmann, J. Rahn, and G. Wüstefeld,"The metrology light source--the new dedicated electron storage ring of PTB," Nucl. Instrum. Methods Phys. Res. B 258, 445-452 (2007).
[CrossRef]

2006 (3)

2004 (3)

2003 (1)

M. Letz, L. Parthier, A. Gottwald, and M. Richter,"Spatial anisotropy of the exciton level in CaF2 at 11.1 eV and its relation to the weak optical anisotropy at 157 nm," Phys. Rev. B 67, 233101 (2003).
[CrossRef]

2002 (1)

R. Klein, M. Krumrey, M. Richter, F. Scholze, R. Thornagel, and G. Ulm,"Radiometry with synchrotron radiation at the PTB laboratory at BESSY II," Synchrotron Radiat. News 15, 23-29 (2002).
[CrossRef]

2001 (2)

J. H. Burnett, Z. H. Levine, and E. L. Shirley,"Intrinsic birefringence in calcium fluoride and barium fluoride," Phys. Rev. B 64, 241102R (2001).
[CrossRef]

M. Richter, J. Hollandt, U. Kroth, W. Paustian, H. Rabus, R. Thornagel, and G. Ulm,"The two normal-incidence monochromator beam lines of PTB at BESSY II," Nucl. Instrum. Methods Phys. Res. A 467-468, 605-608 (2001).
[CrossRef]

1999 (1)

1995 (1)

J. B. Kortright, M. Rice, and K. D. Franck,"Tunable multilayer EUV/soft x-ray polarimeter," Rev. Sci. Instrum. 66, 1567-1569 (1995).
[CrossRef]

1991 (1)

M. Krumrey, M. Kühne, P. Müller, and F. Scholze,"Precision soft x-ray reflectometry of curved multilayer optics," Proc. SPIE 1547, 136-143 (1991).
[CrossRef]

1990 (1)

F. Bridou and B. Pardo,"Automatic characterization of layers stacks from reflectivity measurements. Application to the study of the validity conditions of the grazing X-rays reflectometry," J. Opt. 21, 183-191 (1990).
[CrossRef]

1980 (1)

E. I. Ivanov, L. B. Lopatina, V. L. Sukhanov, V. V. Tuchkevich, and N. M. Schmidt,"Silicon p-n junctions with the current-voltage characteristic of an 'ideal' Shockley diode," Sov. Tech. Phys. Lett. 6, 377-378 (1980).

1978 (1)

1965 (1)

1949 (1)

J. Schwinger,"On the classical radiation of accelerated electrons," Phys. Rev. 75, 1912-1925 (1949).
[CrossRef]

Adv. Space Res. (1)

M. Richter, A. Gottwald, F. Scholze, R. Thornagel, and G. Ulm,"Calibration of space instrumentation with synchrotron radiation," Adv. Space Res. 37, 265-272 (2006).
[CrossRef]

Appl. Opt. (6)

J. Appl. Phys. (1)

M. Yang, C. Cobet, and N. Esser,"Tunable thin film polarizer for the vacuum ultraviolet and soft x-ray spectral regions," J. Appl. Phys. 101, 053114 (2007).
[CrossRef]

J. Opt. (1)

F. Bridou and B. Pardo,"Automatic characterization of layers stacks from reflectivity measurements. Application to the study of the validity conditions of the grazing X-rays reflectometry," J. Opt. 21, 183-191 (1990).
[CrossRef]

J. Opt. Soc. Am. (1)

Nucl. Instrum. Methods Phys. Res. A (1)

M. Richter, J. Hollandt, U. Kroth, W. Paustian, H. Rabus, R. Thornagel, and G. Ulm,"The two normal-incidence monochromator beam lines of PTB at BESSY II," Nucl. Instrum. Methods Phys. Res. A 467-468, 605-608 (2001).
[CrossRef]

Nucl. Instrum. Methods Phys. Res. B (1)

G. Brandt, J. Eden, R. Fliegauf, A. Gottwald, A. Hoehl, R. Klein, R. Müller, M. Richter, F. Scholze, R. Thornagel, G. Ulm, K. Bürkmann, J. Rahn, and G. Wüstefeld,"The metrology light source--the new dedicated electron storage ring of PTB," Nucl. Instrum. Methods Phys. Res. B 258, 445-452 (2007).
[CrossRef]

Opt. Commun. (1)

F. Bridou, M. Cuniot-Ponsard, and J-M. Desvignes,"Experimental determination of optical constants in the vacuum ultra violet wavelength region between 80 and 140 nm: a reflectance versus thickness method and its application to ZnSe," Opt. Commun. 271, 353-360 (2007).
[CrossRef]

Phys. Rev. (1)

J. Schwinger,"On the classical radiation of accelerated electrons," Phys. Rev. 75, 1912-1925 (1949).
[CrossRef]

Phys. Rev. B (2)

J. H. Burnett, Z. H. Levine, and E. L. Shirley,"Intrinsic birefringence in calcium fluoride and barium fluoride," Phys. Rev. B 64, 241102R (2001).
[CrossRef]

M. Letz, L. Parthier, A. Gottwald, and M. Richter,"Spatial anisotropy of the exciton level in CaF2 at 11.1 eV and its relation to the weak optical anisotropy at 157 nm," Phys. Rev. B 67, 233101 (2003).
[CrossRef]

Proc. SPIE (2)

M. Krumrey, M. Kühne, P. Müller, and F. Scholze,"Precision soft x-ray reflectometry of curved multilayer optics," Proc. SPIE 1547, 136-143 (1991).
[CrossRef]

A. Gottwald, U. Kroth, M. Letz, H. Schöppe, and M. Richter,"High-accuracy VUV reflectometry at selectable sample temperatures," Proc. SPIE 5538, 157-164 (2004).
[CrossRef]

Rev. Sci. Instrum. (1)

J. B. Kortright, M. Rice, and K. D. Franck,"Tunable multilayer EUV/soft x-ray polarimeter," Rev. Sci. Instrum. 66, 1567-1569 (1995).
[CrossRef]

Sov. Tech. Phys. Lett. (1)

E. I. Ivanov, L. B. Lopatina, V. L. Sukhanov, V. V. Tuchkevich, and N. M. Schmidt,"Silicon p-n junctions with the current-voltage characteristic of an 'ideal' Shockley diode," Sov. Tech. Phys. Lett. 6, 377-378 (1980).

Synchrotron Radiat. News (1)

R. Klein, M. Krumrey, M. Richter, F. Scholze, R. Thornagel, and G. Ulm,"Radiometry with synchrotron radiation at the PTB laboratory at BESSY II," Synchrotron Radiat. News 15, 23-29 (2002).
[CrossRef]

Other (1)

F. Schäfers and M. Krumrey,"REFLEC," Tech. Rep. BESSY 201/96 (Berliner Elektronenspeicherring-Gesellschaft für Synchrotronstrahlung, m.b.h., 1996).

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Figures (7)

Fig. 1
Fig. 1

(Color online) Scheme of the VUV reflectometry beamline at the PTB laboratory at BESSY II.

Fig. 2
Fig. 2

(Color online) Schematic view of the s- and p-polarization ( Ψ = 90 ° and 0°, respectively) measurement geometries using the PTB VUV reflectometer.

Fig. 3
Fig. 3

(Color online) Geometry of the tilted photodiode used for the polarization measurements.

Fig. 4
Fig. 4

(Color online) (a) Photodiode signal (normalized to ring current and maximum) with linearly polarized radiation at wavelengths of 120 (open symbols) and 160   nm (closed symbols) versus rotation angle Ψ D . The lines are the results of a cosine function fit to the data points. (b) Responsivity polarization of the photodiode with 50° tilted mounting versus wavelength. The arrows mark the wavelengths of 120 and 160   nm where the measurements in (a) were taken.

Fig. 5
Fig. 5

(Color online) (a) Photodiode signal (normalized to ring current and maximum) with elliptically polarized radiation of the VUV reflectometry beamline at wavelengths of 120 (open symbols) and 160   nm (closed symbols) versus rotation angle Ψ D . The lines are the results of a cosine function fit to the data points. The arrows indicate the resulting measurement positions for s- and p-polarization (80° and 10 ° ). (b) Polarization of the VUV reflectometry beamline for different optical configurations in the 80 to 160   nm wavelength regime. The optical surfaces (i.e., premirror, grating) are coated either with aluminum (Al, squares) or silicon carbide (SiC, circles), and for spectral purity filtering either an argon gas (Ar, open symbols) or a lithium fluoride filter (LiF, closed symbols) is used. The line is a calculation based on Schwinger's theory (see text).

Fig. 6
Fig. 6

Experimental (symbols) and fitted (continuous curve) grazing reflectance versus incidence angle at λ = 0.154   nm (x-ray reflectometry) of a MgF 2 / SiO 2 sample.

Fig. 7
Fig. 7

(Color online) Measured polarization P R (diamonds), and total reflectance R (dots), polarization-dependent reflectances R s (squares), and R p (circles) with respective fitted values (continuous curves) of a MgF 2 / SiO 2 sample at the H Ly-α ( 121.6   nm ) wavelength.

Tables (2)

Tables Icon

Table 1 Main Contributions to the Uncertainty Budget in the Determination of Reflectance Polarization at the Wavelengths of 121.6 and 160 nm

Tables Icon

Table 2 Fit Parameters for the MgF 2 ∕SiO 2 Sample Properties From X-ray Reflectometry Data at 0.154 nm (Fig. 6) and VUV Reflectometry Data at 121.6 nm (Fig. 7) a

Equations (12)

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P R  :=  R s R p R s + R p .
R s = ( 1 + P R ) R ,
R p = ( 1 P R ) R ,
R = ( R s + R p ) / 2 .
P D  :=  s s s p s s + s p ,
P Φ  :=  Φ Φ Φ + Φ .
P Φ , R = P Φ P R = R s Φ + R p Φ R p Φ R s Φ R s Φ + R p Φ + R p Φ + R s Φ .
Φ R , Ψ = 0 ° = R s Φ + R p Φ .
Φ R , Ψ = 90 ° = R p Φ + R s Φ .
P Φ , R = Φ R , Ψ = 90 ° Φ R , Ψ = 0 ° Φ R , Ψ = 90 ° + Φ R , Ψ = 0 ° .
P I D = P Φ P D = s s Φ + s p Φ s p Φ s s Φ s s Φ + s p Φ + s p Φ + s s Φ .
P I , Φ = 0 D = s s Φ s p Φ s s Φ + s p Φ = s s s p s s + s p = P D .

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