Polarization analyses of elliptically-polarized vacuum-ultraviolet undulator radiation

NUCLEAR INSTRUMENTS & METHODS IN PHYSICS RESEARCH

Nuclear Instruments and Methods in Physics Research A 336 (1993) 368-372 North-Holland

Section A

Polarization analyses of elliptically-polarized vacuum-ultraviolet undulator radiation Tsuneharu Koide

a,

Tetsuo Shidara

a

and Masatada Yuri

b, I

" Photon Factory, National Laboratory for High Energy Physics, 1-1 Oho, Tsukuba, Ibarakc 305, Japan n Tokyo University of Technology, Ichihara, Chiba 290-01, Japan

Received

28

June

1993

Polarization measurements have been performed using a reflection polarimeter in the 50-80 eV region for elliptically polarized synchrotron radiation from a helical undulator installed on beamline BL-28 at the Photon Factory. The degree of circular polarization (Pc) was found to strongly depend on the photon energy, indicating the importance of a correction for P,- m applications of the undulator radiation The measured Stokes parameters were compared with numerical calculations The results are discussed m relation to the effects on the polarization of the beamline optics and of the mixing of the bending-magnet radiation. 1. Introduction The availability of circularly polarized synchrotron radiation (CPSR) above and below the ring orbit plane from bending-magnet sources has recently made it possible to observe the magnetic circular dichroism (MCD) in both core-level photoabsorption [1-5] and photoemission [6,7] as well as circular dichroism in the angular distribution in core-level photoemission [8]. A new technique called magnetic microscopy [9], which combines core-level MCD effects with photoelectron microscopy, has also been reported very recently . In most of these studies [1,2,4-9], calculated or estimated .) were values of the degree of circular polarization (P, relied upon for analyzing the results. However, an experimental determination of Pc, (more generally, that of the Stokes parameters) is indeed desirable in order to make a quantitative comparison between theory and experiment . Rapidly growing interest in the applications of CPSR has recently led to both proposals and implementation of new insertion devices [10-19] (wigglers and undulators) which can produce intense CPSR (strictly speaking, elliptically polarized (EP) SR). At the Photon Factory, a helical undulator [14] is now in operation on bcamline BL-28A [20], which is intended for the exclusive use of CPSR in the vacuum ultraviolet (VUV) and soft X-ray (SX) regions . However, no polarization meac Present address: Electrotechnical Laboratory, 1-1-4 Umezono, Tsukuba, Ibarakc 305, Japan. 0168-9002/93/$06.00 © 1993 -

Elsevier Science Publishers

surement has been successful up to now for helical undulator radiation . In the case of EPSR from bending-magnet sources, the value of Pc is not much dependent upon the photon energy for a given observation angle with respect to the ring orbit plane at a constant acceptance angle. This aspect, in part, justified the use of constant values for the calculated [1,2,4-9] or measured [3] P, in the recent core-level MCD studies. In contrast, the state of the polarization of the EPSR emitted by the helical undulator is anticipated to strongly depend upon the photon energy [14] . The polarization state of the beam emerging from the bcamline will be affected, more or less, by both reflection and diffraction on the bcamline optical elements ; there are seven optical elements in beamline BL-28A [20] . Moreover, predominantly linearly polarized radiation from bending-magnet sources just upstream and downstream of the helical undulator will be mixed into the undulator radiation . This could result in an effective decrease in the Pc- of the emerging beam in energy regions far from the undulator-harmonic-peak energy . For a quantitative analysis of the experimental results obtained using the helical undulator radiation, a correction will be indispensable for the expected energy-dependent Pc-. Therefore, a polarization analysis is more important for the EPSR from the helical undulator than for the off-plane EPSR from bending-magnet sources. Only a few complete polarization analyses [19,21-26] have been reported to date in the VUV and SX regions. This is mainly because of the lack of a convenient phase shifter, in sharp contrast to the commercial

B.V. All

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T. Koede et al. / Elliptically-polarized VUV undulator radiation TRPI

TRP2

PHS1 (PHS2)

VP

Hi

closed open Fig. 1. Schematic drawing of the present reflection polarimeter. TRPI and TRP2 : triple-reflection polarizers ; D: GaAsP photodiode detector; PHS1 and PHS2 : pinhole slits, CBP: cylindrical base pipe ; M: mirror ; P prisms; VP : view port . The lower panel shows the closed and open positions of PHSI and PHS2 with the reader looking into the beam . availability of a complete quarter-wave retarder for the visible and ultraviolet regions. By utilizing a reflection polarimeter which incorporated a phase shifter, we recently performed an experimental determination of the Stokes parameters of the off-plane EPSR on the bending-magnet beamlines for the VUV and SX regions [23,24]. We present here the results of polarization analyses for EPSR from the helical undulator, carried out using an improved reflection polarimeter . A comparison was also made using numerical calculations which took into account the light-source (i .e ., helical-undulator) polarization characteristics, the influence on the polarization of the beamline optical elements, and the effect on the polarization of the mixing of the bending-magnet radiation. 2. Experiment and theoretical background The reflection polarimeter used in the present measurements is schematically shown in fig. 1. It mainly comprises two triple-reflection polarizers (TRPI and TRP2) and a GaAsP photodiode detector (D). The upstream TRPI functions as a phase shifter and the downstream TRP2 acts as a quasi-linear polarization analyzer . They can be rotated by 360° under an ultrahigh vacuum, driven by stepping motors attached outside of the vacuum chamber. Their rotational axes precisely coincided with the center axis of a cylindrical base pipe (CBP). Polarization measurements with a reflection polarimeter require an accurate adjustment of the polarimeter axis (i .e ., the rotational axis of TRPI and TRP2 in the present case) with the beam axis . To fulfill this requirement is very important in order to suppress

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any possible deviation of the outgoing beam direction at the detector position upon the rotation of TRPI and TRP2 . On the other hand, the monochromator on BL-28A for the VUV and SX regions had a problem in that the emerging beam was vertically deflected as the wavelength was scanned. This necessitated a polarimeter-axis adjustment with monochromatized light, not with zeroth-order light. In order to cope with this serious problem we improved the previous polarimeter regarding two essential aspects. First, the present polarimeter was designed so as to incorporate two pinhole slits (PHS1 and PHS2) in its vacuum chamber (fig. 1) . The center of the pinholes (1 mm in diameter) was mechanically precisely coincident with the center axis of the CBP. A mechanism similar to that used for monochromator slits was employed for PHS1 and PHS2, allowing them to be opened and closed ; pinholes are formed at the closed position (shown in the lower panel of fig. 1) . The entire polarimeter vacuum chamber can be adjusted by using stepping motors in the horizontal and vertical translations as well as in the horizontal and vertical tiltings . Second, a sliding mechanism was employed for the prisms of TRPI and TRP2, permitting them to slide along the direction perpendicular to the rotational axis of the polarimeter . This made it possible to choose a straight-through position (i .e., no prisms) as well as to interchange prisms having different roof angles . With this combination of two new mechanisms, an adjustment of the polarimeter axis to the monochromatized beam could be achieved under a vacuum by monitoring the intensity of light transmitted through the pinholes (with TRPI and TRP2 set at the straight-through position). The theory and analytical procedure of a polarization analysis involving a reflection polarimeter were previously described in detail [23] . We present here only the salient features of the theoretical background . When the Stokes vector of the light beam emerging from a beamline is S = {S  , S1 , S2, S3}, its polarization state is completely specified by three ratios : S1/S, S2/S . and S3/S  [27] . These Stokes parameters are to be determined in the present experiment . The polarizing characteristics of TRPI and TRP2 are represented by p, = rp,/rs, (i = 1 and 2) and d, = S P, - S4, (t = 1 and 2), where rP, and rs, are the amplitude reflectances for all three reflections in TRPI and TRP2 for p and s polarizations, respectively; SP, and SS, are the corresponding phase shifts . Let the rotation angles of TRPI and TRP2 be a and /3, respectively . The light intensity detected after transmission through the polarimeter (I) can be expressed as a function of seven unknowns (S 1 /So , S2/S o, S3/So, p 1 , p2, d i and a proportional factor) with a and /3 being parameters [23] . Hence, three light-polarization-related quantities (S1/So, S2/So and SS/S o) can be determined together

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T. Koede et al / Elliptically-polarized VUV undulator radiation

with the polarimeter-related quantities (p,, pz and 4,) by measuring ID for seven independent pairs of rotation angles (a, /3) [23] . Although it is indeed, in principle, possible to calculate p,, pZ and 1 1 using the optical constants of the coating material (Pt) for the mirrors and prisms of TRP1 and TRP2, the present method does not require any prior knowledge concerning these quantities . The measurements were carried out at 50, 55, 60, 65, 70, 75 and 80 eV with the helical undulator set at a right-handed CP mode, and with its first harmonic energy kept at - 75 eV . The on-axis beam was extracted using horizontal and vertical slits installed in the beamline . Data were recorded for a given rotation angle of TRPI (a) by varying the rotation angle of TRP2 (/3) by 360° in steps of 0/3 = 5°. Angle a was changed by 360° in steps of Aa = 45°. 3. Results and discussion Fig. 2 shows an example of the measured intensity (I D ) as a function of ß for a = 0°, 45° and 90°. The data were taken at 65 eV . There is a geometrically equivalent angle of a + 180° for angle a. Hence, the data points in fig. 2 represent values averaged for two equivalent angles of a : a = 0° and 180°, a = 45° and 225°, and a = 90° and 270°. Since the dark current of the photodiode detector was found to be lower than 0.5 pA, its undesirable effect is almost completely negligible . The intensity (I D ) as a function of a and /3 can be represented as ID(a, ß) =1p(a) +I,(a) sin 2(3 +I,(a) tos 2/3 . The data points given in fig. 2 seem to satisfy this relationship fairly well . Any deviations from this functional form are attributable to deviations in the direc-

Angle, ß (° ) Fig. 2. Typical data of the light intensities detected at 65 eV as a function of the rotation angle of TRP2 (0). The values averaged for two equivalent angles (a and a+180°) are shown.

Fig. 3. (a) Measured and calculated degree of circular polarization, Pc = S3 IS O. The solid and dash-dotted curves are guides to the eye . (b) Measured and calculated undulator spectra. The energy position of the first harmonic peak of the undulator radiation is denoted by a vertical arrow. Calc . 1 is based on the undulator-radiation characteristics alone, talc . 2 takes into account the effect of the beamline optics as well, and talc . 3 takes further account of the influence of the mixing of the bending radiation. tion of the beam outgoing from the polarimeter upon the rotation of TRPI and TRP2 and to the position dependence of the detector sensitivity. Best fits to the measured ID curves yielded the Stokes parameters of the beam emerging from BL-28A . Figs . 3 and 4 show the Stokes parameters thus determined, compared with those obtained from numerical calculations . Fig. 3a displays the result for the degree of circular polarization (P. = S3/S o ) . Figs . 4a and 4b show the results for the degree of horizontal linear polarization (S,/So) and for the azimuthal angle of the polarization ellipse ((h = z tan -'(SZ/S,)), respectively . For a comparison, the measured and calculated undulator spectra are also displayed in fig. 3b . The measured spectrum was obtained by monitoring the photocurrent from an Au-coated postfocusing mirror in the beamline . The energy position of the first harmonic peak of the undulator radiation (hp, -75 eV) is indicated by a vertical arrow in the figure . In figs . 3 and 4, the calculated results are indicated by dashed curves for the case of the undulator-radiation characteristics

T. Koute et al. / Elliptically-polarized VUVundulator radiation 04

02

-02

-04

-06 40 20 0 ÎN -20 a -40 50

60 Photon

70

Energy (eV)

80

Fig. 4. (a) Measured and calculated degree of horizontal linear polarization, S, /So. (b) Measured and calculated azimuthal angle of the polarization ellipse, ~6= z tan-1 (S2/S,), Calculations 1, 2 and 3 refer to the same calculations as in fig. 3. The solid and dash-dotted curves are guides to the eye. alone (calc. 1) and by open circles for the case of considering the influence on the polarization of the reflection and diffraction on the beamline optical elements as well (calc. 2) . The effect on the polarization of the diffraction on a grating was approximated by that of the reflection on a mirror, in which the angle of incidence (0) for the mirror was equal to the average of the angles of incidence (B,) and diffraction (6 p) for the grating, i.e ., 0 = (01 + B p )/2 (Samson's model [281). We also made a calculation in which the influence on the polarization of the mixing of the bending-magnet radiation was taken into account; the result is indicated by double open circles for the given energies (calc. 3) . The measured P, exhibited high values (> 90%) at -hv, and at lower energies within -10 eV of hv I (fig . 3a). This indicates that only a small correction for PC, is necessary in order to analyze the experimental results, such as MCD studies, as far as this narrow energy region is concerned. However, the measured P,, rapidly decreased in regions higher than hv l and lower than - 65 eV . A correction for Pc would have a considerably important effect on the results of energy-

371

scanning experiments in these regions of low undulator-radiation intensity. This strong energy dependence of Pc is in sharp contrast to the rather flat PC of bending-magnet radiation, which was previously reported [231 . The calculated Pc only based on the undulatorradiation characteristics (cale. 1) was found to be higher than the measured Pc over the entire energy range, as can be naturally expected (fig . 3a). The Pc calculated by taking into account the effect of the beam line optics on the polarization (calc. 2) shows a better agreement with the measured Pc. However, a discrepancy still remains in regions of low-intensity undulator radiation. The disagreement between theory and experiment is more clearly noticed for other Stokes parameters . As shown in fig. 4a, the calculated St/So based on the undulator characteristics alone (calc. 1) does not agree with the measured one, even in sign . It was found that a calculation which included the effect of the beamline optics (calc. 2) resulted in a considerably improved agreement . In particular, fairly good agreement was achieved at - hv, and at lower energies within - 10 eV of hv l . However, the discrepancy rapidly increases with both increasing and further decreasing energies . The same tendency was also noticed for (b = z tan -1 (S z/S 1) in fig. 4b . In this case, the sign reversal at - 65 eV in the calculated spectrum (calc. 2) corresponds to that in the calculated S,IS, (see fig. 4a). The main origin of these remaining discrepancies could be a mixing of the bending-magnet radiation into undulator radiation . In fact, its influence was observed in the undulator spectra given in fig. 3b . Namely, though the measured spectrum is lower than the calculated one in the neighborhood of hv 1 , their relative intensity is reversed in regions far from by 1. In order to take into account the mixing of bending-magnet radiation, we now represent the intensities of the undulator radiation and of the bending-magnet radiation by Sâ°d and S0 , respectively, and let r=Sôend/S0 Calculations were carried out for 50, 60 and 80 eV with r being a parameter. The results (calc. 3) are shown for r = 0.35 (50 eV), r = 0.13 (60 eV) and r = 0.30 (80 eV) in figs . 3a, 4a and 4b . It can be seen that a much better agreement with the experimental results was achieved in the calculation . This result clearly shows that the polarization state of the beam emerging from the beamline was influenced by the mixing of the bendingmagnet radiation in the regions of low intensity of the undulator radiation. 4. Conclusions We have experimentally determined the Stokes parameters for helical undulator radiation in the 50-80

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T Koide et al / Elliptically-polarized VUV undulator radiation

eV region using a renovated reflection polarimeter. The degree of circular polarization (PC = S3 /S o ) was shown to strongly depend on the photon energy, indi-

[10]

cating the significance of a correction for Pc in applications concerning helical undulator radiation . A com-

parison of the experimental results with calculations

for all of the Stokes parameters showed that the effects

on the polarization of both the beamline optics and the

mixing of the bending-magnet radiation cannot be neglected, particularly in the regions of low-intensity undulator radiation.

Acknowledgements The authors thank H. Kttamura for providing a

[1l] [12]

[13]

[l4] [15]

computer program for calculating the undulator-radia-

[l6]

for their advice concerning the design of the present polarimeter . The staff of the Photon Factory is also

[17]

tion characteristics, and T. Miyahara and N. Kandaka

acknowledged for machine operation.

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