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High-Definition X-Ray Polarimetry Berit Marx IOQ Friedrich-Schiller-Universit at Jena Helmholtz-Institut Jena Workshop - EMMI I.Uschmann, S. H ofer, R. Loetzsch, O. Wehrhan, E. F orster, M. Kaluza, G.G. Paulus, C. Detlefs, T. Roth,

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SLIDE 1

High-Definition X-Ray Polarimetry

Berit Marx

IOQ Friedrich-Schiller-Universit¨ at Jena Helmholtz-Institut Jena

Workshop - EMMI

I.Uschmann, S. H¨

  • fer, R. Loetzsch, O. Wehrhan, E. F¨
  • rster, M. Kaluza, G.G. Paulus, C. Detlefs,
  • T. Roth, J. H¨

artwig

Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 1 / 36

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SLIDE 2

Outline

1

Motivation

2

Principles Kinematical theory of diffraction Dynamical theory of diffraction Polarimetry

3

Measurements Polarization measurements at the ESRF Grenoble

4

Summary

5

Outlook

6

Acknowledgement

Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 2 / 36

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SLIDE 3

Motivation

Vacuum birefringence induced by intense laser fields

Experimental setup for the verification of vacuum birefringence:

polarizer analyzer detector laser pulse vacuum X-ray source high electro- magnetic field

  • T. Heinzel et al. 2006

Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 3 / 36

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SLIDE 4

Motivation

Vacuum birefringence induced by intense laser fields

resulting ellipticity δ δ2 ∼ = 2α 15 z0 λ I0 IC κ

  • T. Heinzel et al. 2006

a b

I0-peak intensity λ-probe pulse wavelength z0-Rayleigh length α-fine-structure constant κ-correction factor IC-critical intensity Ellipticity, which would be possible with the petawatt laser system at Jena: I0 = 1022 W

cm2

λ = 0.08nm z0 = 25µm ⇒ δ2 = 4.8 · 10−10

Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 4 / 36

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SLIDE 5

Principles Kinematical theory of diffraction

Outline

1

Motivation

2

Principles Kinematical theory of diffraction Dynamical theory of diffraction Polarimetry

3

Measurements Polarization measurements at the ESRF Grenoble

4

Summary

5

Outlook

6

Acknowledgement

Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 5 / 36

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SLIDE 6

Principles Kinematical theory of diffraction

Kinematical theory

Q R B r ko k R' crystal

fig.: Diffraction

no change of wavenumber in the crystal decrease of intensity of the primary beam is neglected no secondary scattering ⇒ only valid for mosaic crystals and thin crystals Intensity of the diffracted beam at the observation place I( K) ∼ = |A0|2

  • R′2
  • G ρ

G

  • ei(

G− K) rd

r

  • 2

with

  • K =

k − k0

Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 6 / 36

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SLIDE 7

Principles Kinematical theory of diffraction

Diffraction condition

Laue condition

  • G =

k − k0

ko k G

Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 7 / 36

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SLIDE 8

Principles Kinematical theory of diffraction

Diffraction condition

Bragg’s law 2dhklsin(θBhkl) = nλ

Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 8 / 36

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SLIDE 9

Principles Dynamical theory of diffraction

Outline

1

Motivation

2

Principles Kinematical theory of diffraction Dynamical theory of diffraction Polarimetry

3

Measurements Polarization measurements at the ESRF Grenoble

4

Summary

5

Outlook

6

Acknowledgement

Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 9 / 36

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SLIDE 10

Principles Dynamical theory of diffraction

Dynamical theory of diffraction

solves Maxwell’s equations for the propagation of electromagnetic waves in the crystal ⇒is valid for perfect crystals

Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 10 / 36

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SLIDE 11

Principles Dynamical theory of diffraction

Dynamical theory of diffraction

solves Maxwell’s equations for the propagation of electromagnetic waves in the crystal ⇒is valid for perfect crystals

H O nk Lo La k Kh Ko P H O La k kh ko

fig.: —Dispersion surface

Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 10 / 36

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SLIDE 12

Principles Dynamical theory of diffraction

Integrated intensity of a perfect crystal

fig.: Comparison of the rocking curves for · · ·non-absorbing —-absorbing crystals

Integrated intensity Rσ/π = 8Rλ2 |C|

  • |γ|

πVsin(2θB)

  • FhFh

Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 11 / 36

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SLIDE 13

Principles Dynamical theory of diffraction

Integrated intensity of a perfect crystal

fig.: Comparison of the rocking curves for · · ·non-absorbing —-absorbing crystals

Integrated intensity Rσ/π = 8Rλ2 |C|

  • |γ|

πVsin(2θB)

  • FhFh

Polarization factor C =

  • 1

for σ cos2θB for π ⇒ Suppression of the π-polarization at θB = 45◦

Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 11 / 36

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SLIDE 14

Principles Dynamical theory of diffraction

Integrated intensity of a perfect crystal

1 2 3 4 5 0,0 0,2 0,4 0,6 0,8 1,0

σ θ θ θ θ

  • I/I0

∆θ π θ θ θ θ

fig.: Comparison of rocking curves for different Bragg angles

Integrated intensity Rσ/π = 8Rλ2 |C|

  • |γ|

πVsin(2θB)

  • FhFh

Polarization factor C =

  • 1

for σ cos2θB for π ⇒ Suppression of the π-polarization at θB = 45◦

Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 12 / 36

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SLIDE 15

Principles Polarimetry

Outline

1

Motivation

2

Principles Kinematical theory of diffraction Dynamical theory of diffraction Polarimetry

3

Measurements Polarization measurements at the ESRF Grenoble

4

Summary

5

Outlook

6

Acknowledgement

Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 13 / 36

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SLIDE 16

Principles Polarimetry

Polarization purity

Transmitted flux T(π,σ) = I n

(π,σ)(θ, E0+ǫ)B(θ, E0+ǫ)dθdǫ

B(θ, E0 + ǫ)

  • spectral brilliance

E0

  • Bragg energy

θ

  • angle arround θB(Bragg angle)

I(π,σ)(θ, E0 + ǫ)

  • single-crystal reflectivity

n

  • number of reflections inside the channel-cut

Polarization purity δ0 = Tπ Tσ

Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 14 / 36

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SLIDE 17

Principles Polarimetry

Suppression of π -polarization

Si 333, Cu Kα, θB = 47.5◦

  • 6
  • 4
  • 2

2 4 6 8 10 12 1E-5 1E-4 1E-3 0,01 0,1 1

π-polarization 1reflection 4reflections I/I0 θ-θB ["] σ-polarization 1reflection 4reflections

fig.: multiple reflections δ1 = 2, 91 · 10−2 ↔ δ4 = 2, 20 · 10−4

Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 15 / 36

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SLIDE 18

Principles Polarimetry

Multiple scattering

ko k G N kN

fig.: Appearance of multiple scattering demonstrated at the Ewald sphere

Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 16 / 36

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SLIDE 19

Principles Polarimetry

Umweganregungen

ko k G N kN U

fig.: Appearance of indirect reflections demonstrated at the Ewald sphere

Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 17 / 36

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SLIDE 20

Principles Polarimetry

Multiple scattering

n θB incident beam diffracted beam φ

fig.: Kossel cone

  • 1,0
  • 0,8
  • 0,6
  • 0,4
  • 0,2

0,0 0,2 0,4 0,6 0,8 1,0

  • 1,0
  • 0,8
  • 0,6
  • 0,4
  • 0,2

0,0 0,2 0,4 0,6 0,8 1,0

11-2 1-10

fig.: Kossel pattern of a (333) silicon crystal, CuKα, E=8.05keV

Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 18 / 36

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SLIDE 21

Principles Polarimetry

Multiple scattering

n θB incident beam diffracted beam φ φ

fig.: Kossel cone

  • 1,0
  • 0,8
  • 0,6
  • 0,4
  • 0,2

0,0 0,2 0,4 0,6 0,8 1,0

  • 1,0
  • 0,8
  • 0,6
  • 0,4
  • 0,2

0,0 0,2 0,4 0,6 0,8 1,0

11-2 1-10

fig.: Kossel pattern of a (333) silicon crystal, CuKα, E=8.05keV

Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 18 / 36

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SLIDE 22

Principles Polarimetry

Umweganregungen

  • 1,0
  • 0,8
  • 0,6
  • 0,4
  • 0,2

0,0 0,2 0,4 0,6 0,8 1,0

  • 1,0
  • 0,8
  • 0,6
  • 0,4
  • 0,2

0,0 0,2 0,4 0,6 0,8 1,0

001 010

fig.: Kossel pattern of a (400) silicon crystal, FeKα, E=6.4keV, θB = 45, 48◦

Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 19 / 36

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SLIDE 23

Principles Polarimetry

Umweganregungen

  • 1,0
  • 0,8
  • 0,6
  • 0,4
  • 0,2

0,0 0,2 0,4 0,6 0,8 1,0

  • 1,0
  • 0,8
  • 0,6
  • 0,4
  • 0,2

0,0 0,2 0,4 0,6 0,8 1,0

11-2 1-10

fig.: Kossel pattern of a (333) silicon crystal, CuKα, E=8.05keV, θB = 47, 5◦

Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 20 / 36

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SLIDE 24

Principles Polarimetry

Umweganregungen

  • 1,0
  • 0,8
  • 0,6
  • 0,4
  • 0,2

0,0 0,2 0,4 0,6 0,8 1,0

  • 1,0
  • 0,8
  • 0,6
  • 0,4
  • 0,2

0,0 0,2 0,4 0,6 0,8 1,0

11-2 1-10

fig.: Kossel pattern of a (888) silicon crystal, AgKα, E=22.2keV, θB = 45, 53◦

Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 21 / 36

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SLIDE 25

Principles Polarimetry Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 22 / 36

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SLIDE 26

Principles Polarimetry

Polarimeter setup: polarizer

Goniometer (Bragg angle) channel-cut goniometer (Bragg angle) goniometer head wing mirror slit1

Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 23 / 36

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SLIDE 27

Principles Polarimetry

Polarimeter setup: analyzer

channel-cut goniometer (Bragg angle) goniometer (positioning the analyzer) goniometer head with glass plate detector

Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 24 / 36

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SLIDE 28

Measurements Polarization measurements at the ESRF Grenoble

Outline

1

Motivation

2

Principles Kinematical theory of diffraction Dynamical theory of diffraction Polarimetry

3

Measurements Polarization measurements at the ESRF Grenoble

4

Summary

5

Outlook

6

Acknowledgement

Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 25 / 36

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SLIDE 29

Measurements Polarization measurements at the ESRF Grenoble

ESRF

http://www.xfel.eu/ http://www.saxier.org/

Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 26 / 36

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SLIDE 30

Measurements Polarization measurements at the ESRF Grenoble

Source parameters

16 bunch filling mode, I < 90mA beam is premonochromized (Si 111 2 reflections) vertical divergence 4.35µrad horizontal divergence 15.45µrad 2 undulators (< 10keV , > 10keV ) Number of photons: 1010 ph

s − 1012 ph s

Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 27 / 36

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SLIDE 31

Measurements Polarization measurements at the ESRF Grenoble

Setting up the wavelength

Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 28 / 36

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SLIDE 32

Measurements Polarization measurements at the ESRF Grenoble

Principle of measurement

x-ray source detector

Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 29 / 36

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SLIDE 33

Measurements Polarization measurements at the ESRF Grenoble

Principle of measurement

x-ray source detector

Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 29 / 36

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SLIDE 34

Measurements Polarization measurements at the ESRF Grenoble

Principle of measurement

x-ray source detector

Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 29 / 36

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SLIDE 35

Measurements Polarization measurements at the ESRF Grenoble

Results polarization purity

Intensity suppression for Si(400) with E=6.457keV (θB = 45.000◦).

Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 30 / 36

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SLIDE 36

Measurements Polarization measurements at the ESRF Grenoble

Results polarization purity

Intensity suppression for Si(800) with E=12.914keV (θB = 45.000◦).

Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 31 / 36

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SLIDE 37

Measurements Polarization measurements at the ESRF Grenoble

Varying the polarizer azimuth

x-ray source detector

Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 32 / 36

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SLIDE 38

Measurements Polarization measurements at the ESRF Grenoble

Varying the polarizer azimuth

x-ray source detector

Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 32 / 36

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SLIDE 39

Measurements Polarization measurements at the ESRF Grenoble

Varying the polarizer azimuth

x-ray source detector

Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 32 / 36

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SLIDE 40

Measurements Polarization measurements at the ESRF Grenoble

Rocking curves dependending on the analyzer position

Intensity suppression for Si(444) by varying the polarizer azimuth at E=11.1838keV.

Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 33 / 36

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SLIDE 41

Summary

Summary

Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 34 / 36

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SLIDE 42

Outlook

Outlook

polarization measurement at the ESRF using

more reflections (6,8)

  • ther materials

crystal cooling

full theoretical description of the polarimeter

Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 35 / 36

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SLIDE 43

Acknowledgement

Acknowledgement

I.Uschmann1, S. H¨

  • fer, R. Loetzsch, O. Wehrhan, E. F¨
  • rster1,
  • M. Kaluza1, G.G. Paulus1, H. Gies1, H. Marschner

IOQ, Jena; Helmholtz Institut Jena1 Detlefs, T. Roth, J. H¨ artwig ESRF, Grenoble

  • T. S. Toellner

Argonne National Laboratory, Argonne

  • H. Schulte-Schrepping

DESY, Hamburg

  • D. Stachel

OSI, Jena

  • T. K¨

asebier, E.-B. Kley IAP, Jena

Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 36 / 36