High-Definition X-Ray Polarimetry Berit Marx IOQ - PowerPoint PPT Presentation

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, J. H¨ artwig Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 1 / 36

Outline Motivation 1 Principles 2 Kinematical theory of diffraction Dynamical theory of diffraction Polarimetry Measurements 3 Polarization measurements at the ESRF Grenoble Summary 4 Outlook 5 Acknowledgement 6 Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 2 / 36

Motivation Vacuum birefringence induced by intense laser fields Experimental setup for the verification of vacuum birefringence: vacuum laser pulse high electro- magnetic field X-ray source detector polarizer analyzer T. Heinzel et al. 2006 Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 3 / 36

Motivation Vacuum birefringence induced by intense laser fields resulting ellipticity δ a = 2 α z 0 I 0 δ 2 ∼ κ 15 λ I C b T. Heinzel et al. 2006 Ellipticity, which would be possible I 0 -peak intensity with the petawatt laser system at λ -probe pulse wavelength Jena: z 0 -Rayleigh length I 0 = 10 22 W α -fine-structure constant cm 2 λ = 0 . 08 nm κ -correction factor z 0 = 25 µ m I C -critical intensity ⇒ δ 2 = 4 . 8 · 10 − 10 Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 4 / 36

Principles Kinematical theory of diffraction Outline Motivation 1 Principles 2 Kinematical theory of diffraction Dynamical theory of diffraction Polarimetry Measurements 3 Polarization measurements at the ESRF Grenoble Summary 4 Outlook 5 Acknowledgement 6 Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 5 / 36

Principles Kinematical theory of diffraction Kinematical theory crystal k no change of wavenumber in the crystal r B R' decrease of intensity of the R primary beam is neglected k o no secondary scattering Q ⇒ only valid for mosaic fig.: Diffraction crystals and thin crystals Intensity of the diffracted beam at the observation place = | A 0 | 2 2 � � K ) ∼ e i ( � G − � I ( � K = � � k − � � K ) � r d � �� G ρ � r with k 0 � � � R ′ 2 G � � Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 6 / 36

Principles Kinematical theory of diffraction Diffraction condition Laue condition � G = � k − � k 0 k G k o Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 7 / 36

Principles Kinematical theory of diffraction Diffraction condition Bragg’s law 2 d hkl sin ( θ B hkl ) = n λ Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 8 / 36

Principles Dynamical theory of diffraction Outline Motivation 1 Principles 2 Kinematical theory of diffraction Dynamical theory of diffraction Polarimetry Measurements 3 Polarization measurements at the ESRF Grenoble Summary 4 Outlook 5 Acknowledgement 6 Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 9 / 36

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

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 L a P L o k K o K h nk L a k O H k o k h O H fig.: —Dispersion surface Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 10 / 36

Principles Dynamical theory of diffraction Integrated intensity of a perfect crystal Integrated intensity R σ/π = 8 R λ 2 | C | � | γ | � F h F h π Vsin (2 θ B ) fig.: Comparison of the rocking curves for · · · non-absorbing —-absorbing crystals Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 11 / 36

Principles Dynamical theory of diffraction Integrated intensity of a perfect crystal Integrated intensity R σ/π = 8 R λ 2 | C | � | γ | � F h F h π Vsin (2 θ B ) Polarization factor � 1 for σ C = cos 2 θ B for π ⇒ Suppression of the fig.: Comparison of the rocking curves for · · · non-absorbing π -polarization at θ B = 45 ◦ —-absorbing crystals Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 11 / 36

� Principles Dynamical theory of diffraction Integrated intensity of a perfect crystal Integrated intensity 1,0 σ ������������� � θ � ���� R σ/π = 8 R λ 2 | C | � 0,8 � θ � ���� | γ | � � θ � ���� F h F h π Vsin (2 θ B ) � θ � ���� 0,6 π ������������� I/I 0 � θ � ���� 0,4 Polarization factor � θ � ���� � θ � ���� 0,2 � θ � ���� � 1 for σ C = 0,0 cos 2 θ B for π 0 1 2 3 4 5 ∆θ ��� ⇒ Suppression of the fig.: Comparison of rocking curves for different π -polarization at θ B = 45 ◦ Bragg angles Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 12 / 36

Principles Polarimetry Outline Motivation 1 Principles 2 Kinematical theory of diffraction Dynamical theory of diffraction Polarimetry Measurements 3 Polarization measurements at the ESRF Grenoble Summary 4 Outlook 5 Acknowledgement 6 Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 13 / 36

Principles Polarimetry Polarization purity Transmitted flux � � I n T ( π,σ ) = ( π,σ ) ( θ, E 0 + ǫ ) B ( θ, E 0 + ǫ ) d θ d ǫ B ( θ, E 0 + ǫ ) - spectral brilliance - Bragg energy E 0 θ - angle arround θ B (Bragg angle) I ( π,σ ) ( θ, E 0 + ǫ ) - single-crystal reflectivity n - number of reflections inside the channel-cut Polarization purity δ 0 = T π T σ Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 14 / 36

Principles Polarimetry Suppression of π -polarization Si 333, Cu K α , θ B = 47 . 5 ◦ 1 π -polarization σ -polarization 1reflection 1reflection 4reflections 4reflections 0,1 0,01 I/I 0 1E-3 1E-4 1E-5 -6 -4 -2 0 2 4 6 8 10 12 θ - θ B ["] fig.: multiple reflections δ 1 = 2 , 91 · 10 − 2 ↔ δ 4 = 2 , 20 · 10 − 4 Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 15 / 36

Principles Polarimetry Multiple scattering k G k o k N N fig.: Appearance of multiple scattering demonstrated at the Ewald sphere Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 16 / 36

Principles Polarimetry Umweganregungen k G U k o k N N fig.: Appearance of indirect reflections demonstrated at the Ewald sphere Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 17 / 36

Principles Polarimetry Multiple scattering n 1,0 0,8 0,6 incident diffracted 0,4 beam beam 0,2 11-2 0,0 θ B -0,2 φ -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 1-10 fig.: Kossel pattern of a (333) silicon crystal, CuK α , E=8.05keV fig.: Kossel cone Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 18 / 36

Principles Polarimetry Multiple scattering n 1,0 0,8 0,6 incident diffracted 0,4 beam beam 0,2 11-2 0,0 θ B -0,2 φ φ -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 1-10 fig.: Kossel pattern of a (333) silicon crystal, CuK α , E=8.05keV fig.: Kossel cone Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 18 / 36

Principles Polarimetry Umweganregungen 1,0 0,8 0,6 0,4 0,2 001 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 1,0 010 fig.: Kossel pattern of a (400) silicon crystal, FeK α , E=6.4keV, θ B = 45 , 48 ◦ Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 19 / 36

Principles Polarimetry Umweganregungen 1,0 0,8 0,6 0,4 0,2 11-2 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 1-10 fig.: Kossel pattern of a (333) silicon crystal, CuK α , E=8.05keV, θ B = 47 , 5 ◦ Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 20 / 36

Principles Polarimetry Umweganregungen 1,0 0,8 0,6 0,4 0,2 11-2 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 1-10 fig.: Kossel pattern of a (888) silicon crystal, AgK α , E=22.2keV, θ B = 45 , 53 ◦ Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 21 / 36

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

Principles Polarimetry Polarimeter setup: polarizer goniometer head wing channel-cut slit1 mirror Goniometer (Bragg angle) goniometer (Bragg angle) Berit Marx (FSU) High-Definition X-Ray Polarimetry Darmstadt 08.06.2010 23 / 36