Polarized vacuum ultraviolet and X-radiation

NUCLEAR INSTRUMENTS

AND METHODS

152 ( 1 9 7 8 )

225-230

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NORTH-HOLLAND

P U B L I S H I N G CO

POLARIZED VACUUM ULTRAVIOLET AND X-RADIATION JAMES A

R SAMS()N

Behlen Laboratory o/ Physics, University ol Nebraska, Lincoln, A'ebraska 68588, U S A

The most ~ntense source of polarized vacuum UV and X-radiation is synchrotron radmhon, which exhibits a degree of partially polarized hght between about 80-1009. However. the radiation transmitted by vacuum UV monochromators can also be highly polarized The Seya-Namloka type of monochromator can produce partially polarized radiation between 50-807~, For certain experiments ~t ~s necessary to know the degree of polarization of the radmuon being used Also. when synchrotron radmtton and a monochromator are combined the polarization characteristic of both should be known m order to make full use of these polartzahon propemes The polarizing effect of monochromators (~ e diffraction gratings) have been measured at the Seya angle and at grazing angles tor various spectral orders We present the first experimental evidence that the reciprocity law holds for polarization by reflection where the angle of incidence and diffraction are unequal These results will be reviewed along v..th the techmques lot measuring the degree of polarization

I. I n t r o d u c t i o n

Polarized vacuum UV and X-radmuon are being applied to various areas of atomic, molecular and sohd state physics. Inveshgat~ons include such areas as the angular distribution of the ejected photoelectrons, the vectorml effect m photoem~ss~on and the study of optical constants of solids It ~s also an untapped source fbr the production of spin-polarized electrons. The most intense source of polarized vacuum UV and X-radtahon Is synchrotron radiation, which exhibits a degree of partially polarized light between about 80-100% However, the radmtton transmitted by vacuum UV monochromators can also be h~ghly polarized. The Seya-Namloka type of monochromator can produce partially polarized radiation between 50-80~, For certain experiments ~t is necessary to know the degree of polarization of the radmtion being used Also, when synchrotron radlauon and a monochromator are combined the polarization characteristic of both should be known in order to make full use of these polarization properties The polarizing effect of monochromators (i.e dfffracuon gratings) have been measured at the Seya angle and at grazing angles for various spectral orders These results will be reviewed along with the techniques for measuring the degree of polarization 2. P o l a r i z a t i o n

sources

In this review of polarization we will confine our discussion to wavelengths shorter than VII

1000 A Because no blrefrlngent materials exist in this spectral region the production of polarized radiation must be either by reflection or from synchrotron radiation Polarization by reflection is defined as follows (1)

P = (R~-Rp)/(R~+Rp),

where P is the fractional degree of polarization and Rs and R r are the reflectances of the components of the mcldent radiation whose electric vectors vibrate perpendicular (s) and parallel (p) to the plane of incidence, respecuvely R~ and R o can be calculated precisely from the generalized Fresnei equations prowded the optical constants n and k for the mirror material are known, that is. aZ + b 2 - 2 a cos~ + cos2a Rs = aZ+b 2 + 2a cos:~ + cos2~

(2)

and a2+b 2 - 2a Rp = R s a 2 + b 2 + 2 a

sin7 tan~ + sm2a tanZa sm:~ tan~ + smZa tanZa '

(3)

where a¢ is the angle of incidence and a and b are given by 2 a 2 = [ ( n 2 - k 2 - s i n Z o t ) 2 + 4 n 2 k 2 ] !' +

+ (n2-kZ-smZa) and 2b 2 = [(n2-kZ-sm2c02 + 4n2k2] ~ _ - (n 2 - k 2 - s m 20t). Thus, the degree of polarization produced by a single reflection can be determined from eqs. (1) and (3). If we plot the reflectances R S and Rp we

SPECIFIC

P R O P E R T I E S OF S Y N C H R O T R O N

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226

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A

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see that they are identical only for ~z 0° and 90 ~ At any other angle of incidence they dlffere by varying amounts and so the degree of polarization varies with o~. Fig 1 shows the varmtion of R, and /'{p as a function of 7. for a platinum mirror at 584,~ The values of n and k used were obtained from the results of Hass et al. ]) Their values are about 12% lower than those quoted by Jacobus et al. ~) The resulting degree of polarization for this mirror is shown in fig 2 as a function of ~. along with the degree of polarization produced by reflection from a mirror coated with carbon The n and k values for carbon were taken from the tables prepared by Hagemann et al. 2) and represent the wavelengths 584 A, and 304 ,~. The point of these curves is to show the degree of polarization that can be obtained by a single reflecuon The extinction coefficmnt k ['or carbon at 304 A is nearly zero and therefore the degree of polarization at the Brewster angle is nearly 100%. However, the reflectance is very poor In general, it is more efficient to choose a material that will give a high reflectance and rely on multiple reflectances to provide a reasonable degree of polarization Another advantage of the several reflectances is that it is possible to preserve the direction of the incident beam This is usually accomphshed by three or four reflectances ;-+) [The design criteria for reflection polarizers has been reviewed by HunterV)] The choice of angle of incidence is a compromise between the degree of polarization desired and the transmittance of the polarizer Fig 3 shows a typical three-reflection polarizer =

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Fig 2 "Ihc degree of polarization produced b) mirrors o1 plal m u m , Pt (384,4), and or Carbon, C (584 A) and C (304 3,) a a function of angle of incidence for unpolanzcd hght

The degree of polarization and transmittance o th~s polarizer for gold coated mirrors are shown tt fig 4 as a function of the angle of incidence 0 or the first mirror*). The calculations were performec for 584 A. using n -- 1 07 and k = 0.85 as given b' Canfield et al 9) As we go towards shorter wavelengths th. transmittance of a reflection polarizer decreases To maintain reasonable signals grazing angles o incidence m u s t be used. However, as can be see1 from fig 2 at 85 ° incidence the degree of polarl zatton produced is low Thus, for the extreme U'~ and X-ray region, say for wavelengths belo~ 300 ,~, the only intense source of radmtlon with high degree of polarization is synchrotron radla tton The polarization characteristics of this sourc have been described by several authors6~°-~2). 1

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ANGLE OF INCIDENCE Fig 1 Calculated rer!cctance of platmurn for 384 ,,~ radiation polarized parallel (p) and perpendicular (s) to the plane of mcJdencc as a function of angle or incidence n = 0 85 and k-09t

F~g 3 A three-reflection polarizer that preserves the dtrect]c of the me,dent beam

POLARIZED

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Fig 4 The dcgree o r polarization. P sohd cur~,e, and t r a n s m m a n c e , dashed curve, of a three-reflection polaruzer as a function of the angle o f mc~dence # on the first m~rror, for 584 ,~, mc~dent on gold The single data point 0 ~n the c x p e n m e n t a l value

of P at ~ .-- 76 general the radiation ns elhptically polarized with ~ts major axis of polarization parallel to the orbital plane, but it ts 100% polarized only m the plane of the circulating electrons For fimte angles of acceptance into the monochromator system the dcgree of polarization Is reduced However, values of 80 to 95% can be expected, The actual value produced by the synchrotron Is modified by the monochromators and assocmted focusing mirrors If the plane of maximum polarization ~s parallel to the plane of incidence of the reflecting optics the degree of polarization is reduced as well as the intensity of the emerging beam Thus, m all apphcations usmg synchrotron radiation it is necessary to rotate the plane of m o d e n c e of all mirrors and gratings until they are perpendicular to the orbital plane of the synchrotron tf full use ~s to be made of the high degree of polarlzatzon of the synchrotron radiation

gree of polarization P from the relation P =

1 + R t +R2 - [1 + 4 ( R 1 + R 2 ) ]

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This techmque has been used to construct a compact analyzer that is insensitive to radiation in the v|stble and near U V J-~) A n ~mproved version ~s shown ]n fig. 5 The detector can be either a simple photod~ode or a mtcrochannel plate mult~pher. The m~rror ~s usually a gold coated optical flat. For measurements m the X-ray region the m~cro-

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The degree of polarization m the vacuum UV spectral region ns analyzed by reflection methods 13) The three- and four-reflection polarizers have been used to analyze the incident radiation 3'6) However, the single m~rror method described by Rabmovffch et al ~4) has the advantage that the optical constants of the mirror need not be known provided the reflected hght ~s measured at 45 ° to the mirror normal Two reflection measurements must be made at 90 ° to each other. The measured reflectances R~ and R 2 then give the de-

(4)

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Fig 5 Polarization analyzer utlhzmg a gold mirror M mchned at 45' to the me,dent radiation A photodJode detector D (A1 cathode) ns rotated by shaft S I so that tt can measure the incident and reflected beam mtensltzes Shaft S2 rotates the m~rror and detector system to allow measurements to be made 90: apart

SPECIFIC

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OF SYNCHROTRON

RADIATION

228

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channel plate would be essenual because of the low reflectances at 45: When the quantity 4(Rt +R2),~I, eq (4)can be written with little error a s

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(5)

where /~ and 12 are the lntenstnes reflected from the mirror. These intensities can be arbitrary units No measurement of the incident radlauon is necessary, except to check for constancy during the measurement

SAMSON

than the value for the first order The first order angle of diffraction if 74 c whereas the second order angle ~s 69 5° Clearly the polarization depends upon the angle of diffraction Th)s has been checked for another Pt grating with an angle of incidence of 82.5 '~ with the following results. Degree of polarization (%) Spectral order

304 A

584 A

584 A (calculated)"

0 1 2

30 85

95 31 0 -

16 31 38

4. Polarization by grating monochromators The polarizing effect of diffraction gratings was observed m the visible and infrared spectral region soon after gratings were introduced. However, measurements in the vacuum UV region were not made until 1 9 6 2 and continued through 1968~{4t~-~). The most detailed measurements were made w~th Seya-Namioka type monochromators over the range 400 to 2000 h ~.~.~6) The only measurements reported at grazing angles of mcidence were at five discrete hncs between 304 and 1216.& ~7.{~) However, Arakawa has recently reported measurements at 82 ° for Au and AI gratings over the range 150 to 1200 A ~9) Our present results cover AI and Pt gratings for angles of modence between 80 and 84° and for a Au grating at the Seya angle F~g 6 shows data taken with a new Pt coated grating (1152 h n e s / m m ) at 80~ anglc of incidence. The angle of mcidence remained constant at all wavelengths It can be seen that the degree of pelanzauon decreases with wavelength The polarizaUon of the second order spectrum of the 209 A. line was also measured and ~s considerably greater

* See discussion belov, for calculated values

Again the degree of polarization increases w~th the spectral order. In fig 7 the results are given Ibr a new Pt grating irradiated at a fixed angle of incidence oc-84' and for an aluminized gratmg at an angle of incidence of 82 ° Both gratmgs were ruled with 600 h n e s / m m . The A1 grating was aged and would certainly havc an aluminum oxide coating. However, it was also visibly discolored, presumably be i

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Flg 7 Degree o f polanzauon of (a) a new platmuFn-coate, grating as a funct,on of wavelength (triangular data points] :z=84 °, 600 h n c s / m m , blaze angle= I 5~ and (b) an aged alu mmum-coated graung with carbon conlammauon (sohd dat pomts represent a fixed angle of incidence 6~= 82': sshereas th open data points represent the results when the mc~dcnt hgh ~s reversed to g~ve a variable angle of incidence and a fixe angle of d~ffracnon - 82", 600 h n e s / m m , blaze angle - 2~ Th crosses represent calculated values lot the Pt grating at 584, and 735 A

POLARIZED

VACUUM

ULTRAVIOLET

cause ot" carbon accumulation from the oil pumped monochromator Thus, Jt is more realistic to characterlze the aged A1 grating as a carbon coated grating Once again the degree of polarization decreases with wavelength The monochromator with the AI grating (McPherson model 255) could be operated in reverse such that the graung could be illuminated at varying angles of incidence with a fixed angle of diffraction (/.¢= 82 °) This reversal of the light rays maintains the blazed wavelength The results are shown m fig 7 for both modes of operation It is significant to nouce that the degree of polarization remains the same when the rays are reversed Thus, apparently the principle of reversibility of light rays also holds for the degree of polarization produced We propose a simple model for predicting the degree of polarization produced by a grating Namely, that the polarization will be similar to that produced by a plane mirror of the same material where the angle of incidence is chosen to bc equal to the average of the angles of incidence and diffraction, l e = (:z-/3)/2. (~z and /3 have opposite signs when they lie on opposite sides of the grating normal) This is the same angle whether ~ and [3 are measured relative to the grating normal or to the normal of the facets that produce a blaze Thus, this model would include the effects of a triangular groove. Because the wavelengths m the vacuum UV and X-ray region are typically 10 to several hundred times smaller than the spacing between the ruled lines of a grating we assumc that they have little effect on the polarization of the radiation except for their direct influence on the value of/3 With this model the degree of polarization produced by the Pt grating (8¢>), shown in fig 7, has been calculated at 584 and 735/k using the optical constants given by Hass et al ,) The results, shown by crosses in fig. 7, show quahtattve agreement with the extension of the experimental results Unfortunately, there are no measurements of the optical constants for Pt at other wavelengths within this range to allow further calculations However, comparison can bc made with the aged AI grating shown in fig 7 assummg the surface is characteristic of a thin film of evaporated carbon The results arc shown in fig 8 The calculated values are shown by the solid line for a carbon coated grating ruled with 6 0 0 h n e s / m m and by the dashed line for a 300 h i e / r a m grating Our present experimental results are shown with the solid circles and those of VII

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F~g 8 Degree of polarnzauon of c a r b o n c o n t a m m a t c d gratings as a l'unctJon of wavelength The solid data points represent the results lbr the gratmg described m fig 7 for a fixed angle of mcJdence = 8 2 , 600 h n c s / m m and a blaze angle = 2 ] h e open data points are those of Arakawa and W d h a m s for a grating with 300 h i e s / r a m but opcratcd w~th a vattable angle of incidence and a fixed angle of dlffracuon - 82 ~ The sohd hne curve represents the calculated degree of polarization for a 600 l / r a m carbon-coated g r a u n g and the dashed curve represents the calculated values for a 3 0 0 1 / m m grating

Arakawa and Williams ~9) by the open circles. It ts assumed that the aged gratmg used by Arakawa was also carbon coated The overall agreement between the experimental results ts very good. Also, the agreement with the simple model is remarkable good consadermg the actual optical constants of the grating surface were unknown Further, carbon becomes transmitting at wavelengths shorter than 500/~ 20) so the polarization effects at those wavelengths can be mfluenced by the material underneath A further example of the results of the model is shown in fig. 9 for a ~ m Seya monochromator The solid line is the measured degree of polarization of an aged Au coated grating, 1200 h n e s / m m . The grating surface showed the discoloration effects of a carbon coating Thus, the predicted degree of polarization, shown by the dashed line, used the optical constants for carbon 2) The agreement ts very good On the basis of this model we can understand why the degree of polarization increases for higher spectral orders when grazing angles of incidence are used As the diffraction angle decreases (as tt does for higher orders) the value of the average angle of mcldence decreases and hence the degree of polarization increases, as can be seen from fig 2 For example, with 584 A incident on a Pt-coated grating (1152 llnes/mm) at 82 5:: the average angles of incidence for the zero, first, and second

SPECIFIC

PROPERTIES

OF S Y N C H R O T R O N

RADIATION

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p o l a r i z a t i o n in t h e v a c u u m U V w e c a n m a k e t h e general prediction that the degree of polarization p r o d u c e d by g r a t i n g s at g r a z i n g a n g l e s o f i n c i d e n c e will d e c r e a s e w i t h w a v e l e n g t h T h i s is a c o n s e q u e n c e o f t h e fact t h a t at g r a z i n g a n g l e s t h e pol a r i z a t i o n p r o d u c e d by r e f l e c t a n c e d e c r e a s e s as t h e values of the optical constants n and k decrease, s e e fig 10, a n d t h a t for m o s t m a t e r i a l s k d e c r e a s e s with wavelength whde n either remains relatively c o n s t a n t or d e c r e a s e s -~)

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Fig 9 Degree o1" polarization of a Au-coated. but carbon contarmnatcd grating as a f u n c t ) o n of ~avelength m t h e Seya-

mount ]hat ~s, the average angle of incidence ~sconstant and 3525' (sohd line curve) ] b e dashed hnc curve represents the calculated degree of polanzat)on for a carbon-coated grating. 1200 hncs/mm, blaze angle < 2 5 o r d e r s are ( ~ - f l ) / 2 -- 82 5 <:, 75: a n d 70 7 ' , r e s p e c t i v e l y F r o m fig 2 w e w o u l d p r e d i c t t h e d e g r e e o f p o l a r i z a t i o n for t h e zero, first a n d s e c o n d o r d e r s to be 1 6 % , 3 1 % a n d 3 8 5 % , r e s p e c t i v e l y Fora higher o r d e r w h o s e a v e r a g e a n g l e o f i n c i d e n c e is s m a l l er t h a n t h e a n g l e for p e a k p o l a r i z a t i o n t h e d e g r e e o f p o l a r i z a t i o n w o u l d bc e x p e c t e d to d e c r e a s e F o r t h e S c y a m o n o c h r o m a t o r t h e a v e r a g e a n g l e o f inc i d e n c e s t a y s c o n s t a n t at 35 ~ so o u r m o d e l w o u l d p r e d i c t t h e d e g r e e o f . p o l a r i z a t i o n o f h~gher o r d e r s to s t a y c o n s t a n t W e h a v e o b s e r v e d t h i s to be t h e c a s e for all o r d e r s f r o m 0 to 4 t h o r d e r , w i t h o u r c a r b o n c o a t e d g r a t i n g at 584 ,~ t l o w e v e r , t h e S e y a angle coincides with the peak of the polarization c u r v e for c a r b o n at 584 ,~ T h u s , v e r y little c h a n g e m i g h t be e x p e c t e d m t h i s c a s e If w e a s s u m e t h a t t h e r e f l e c t w e c o a t i n g o f t h e g r a t i n g a n d t h e a v e r a g e a n g l e o f i n c i d e n c e are t h e p r i m e p a r a m e t e r s for d e t e r m i n i n g t h e d e g r e e o f

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It is a p l e a s u r e to a c k n o w l e d g e t h e u s e f u l d i s cussions and help of my colleagues K Burgess, H Hancock, G Rayborn and P Pareek This work w a s s u p p o r t e d in part by t h e G o d d a r d S p a c e F l i g h t . C e n t e r u n d e r c o n t r a c t :
References I) G l-lass. J B Ramsc)and H R Hunter. Appl Opt 8

(19691 2255 la) G I- Jacobus. R P Madden and k R Canfield, J Opt Soc Am 53 (1963I 1084 2) I1-J itagemann. W (3udat and C Kunz. Report DESY SR-74 7 (I)ESY, Hamburg. 1974) 3I V G Ilorton, E T Arakawa. R N Hamm and M W Williams, Appl Opt 8 (1969) 667 41 W 11 Hancock and J A R Samson. J Electron Spcctrosc and Related Phenomena 9 11976) 211 ~'} R N Harem, R N MacRac and E T Arakawa, J Opt Soc Am 55 (19651 1460 6) G Rosenbaum. B Feuerbachcr, R PL Godwin and M Sklbowskl, Appl Opt 7 (1968) 1917 7) W R Hunter, Appl Opt. to be pubhshcd 8) j A R Samson. m Methods el eaTwltmental flhvsl(S-Sflf'(tu)s~opy (cd D Wflhams, Academic Press, New York. 19761 Vol 13A, p 204-252 u) L R Canfield. (; Hass and W R Hunter. J de Physique ")5 (19641 124 10) K Codling, Rep Prog Pbys 36 (19731 541 il) K Codhng and R P Madden, J Appl Phys 36 (19651 380 ]2) p Joos, Phys Re', Lett 4 (19601 558 131 For a review of polanzauon m the vacuum UV see J A R Samson, le¢hmques ol i:ucm.n U I" spe~tms¢o/)y (Wiley, New York, 19671 p 296-319 141 K Rablnovltch. L R Canfield and R P Madden. Appl Opt 4 (1965) 1005 i5) j A R Samson. Re', Scl lnstr 47 (1976) 859 i(,) j A R Samson and R B Cairns. Phys Rex 1"/3 (1968) 80 i7) T T Cole and F Oppenheimer. Appl Opt I (1962I 709 181 E Uzan, H Damany and J Romand, C R Aead S,cl 260B (19651 5735 i,)) E T Arakav,a :.rod M W W]lhams. 5th lnt Conr on VUVRadmnon, Phys, Montpelher, lrance 5-9 Sept 1977 2o) j A R Samson, J Opt Soc Am 54 (19641 1491 and Appl Opt 4 1!965) 915