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Laser- Laboratorium Göttingen e.V. Laser-Laboratorium Göttingen e.V. Hans-Adolf-Krebs Weg 1 D-37077 Göttingen K. Mann J.O. Dette, F. Kühl, U. Leinhos, M. Lübbecke, T. Mey, M. Müller, M. Stubenvoll, J. Sudradjat, B. Schäfer Table-top EUV/Soft X-ray Source and Wavefront Measurements at Short Wavelengths

Table-top EUV/Soft X-ray Source and Wavefront Measurements ... · Soft x-ray microscopy III Applications of ns and ps laser-induced soft x-ray sources dose [mJ/cm² x number of pulses]

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Page 1: Table-top EUV/Soft X-ray Source and Wavefront Measurements ... · Soft x-ray microscopy III Applications of ns and ps laser-induced soft x-ray sources dose [mJ/cm² x number of pulses]

Laser-

Laboratorium

Göttingen e.V.

Laser-Laboratorium Göttingen e.V.

Hans-Adolf-Krebs Weg 1

D-37077 Göttingen

K. Mann

J.O. Dette, F. Kühl, U. Leinhos, M. Lübbecke,

T. Mey, M. Müller, M. Stubenvoll, J. Sudradjat, B. Schäfer

Table-top EUV/Soft X-ray Source and

Wavefront Measurements at Short Wavelengths

Page 2: Table-top EUV/Soft X-ray Source and Wavefront Measurements ... · Soft x-ray microscopy III Applications of ns and ps laser-induced soft x-ray sources dose [mJ/cm² x number of pulses]

2

Dept. “Optics / Short Wavelengths”

Beam propagation

Wavefront

coherence

Optics test (351…193 nm)

(Long term) degradation (109 pulses)

Non-linear processes

LIDT

Absorption / Scatter losses

Wavefront deformation

EUV/XUV technology

Source & Optics

Metrology

Material interaction

Page 3: Table-top EUV/Soft X-ray Source and Wavefront Measurements ... · Soft x-ray microscopy III Applications of ns and ps laser-induced soft x-ray sources dose [mJ/cm² x number of pulses]

pulsed Xenon gas jet

laser

Laser plasma source for extreme UV and soft x-ray radiation

XUV: =1…10nm EUV: = 10…20nm

• Univ. Prag

• Univ. Göttingen

• Max-Planck Inst.

~ 300µm

compact

low debris

long-term stable

versatile

Page 4: Table-top EUV/Soft X-ray Source and Wavefront Measurements ... · Soft x-ray microscopy III Applications of ns and ps laser-induced soft x-ray sources dose [mJ/cm² x number of pulses]

4

LLG-Activities Based on

LPP Source

Direct structuring EUV reflectometry

NEXAFS spectroscopy Soft x-ray microscopy

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 8510

-4

10-3

10-2

10-1

100

Ref

lect

ivit

y

Sample angle

=2.88nm

Page 5: Table-top EUV/Soft X-ray Source and Wavefront Measurements ... · Soft x-ray microscopy III Applications of ns and ps laser-induced soft x-ray sources dose [mJ/cm² x number of pulses]

5

Ablation / damage thresholds

@13.5nm

EUV Schwarzschild objective (Mo/Si):

~ J/cm² @ 13,5 nm

Damage thresholds of

mirrors / substrates single-pulse damage

F. Barkusky, K. Mann et al., Optics Express 18, 4347 (2010)

Page 6: Table-top EUV/Soft X-ray Source and Wavefront Measurements ... · Soft x-ray microscopy III Applications of ns and ps laser-induced soft x-ray sources dose [mJ/cm² x number of pulses]

EUV/XUV plasma source

Isolated Nitrogen line @ = 2.88nm

Peak brillance:

6*1017 [Ph./(s mrad2 mm2 0,1%BW)]

Microscopy @ = 2.88nm

T. Salditt

Univ. Göttingen

Page 7: Table-top EUV/Soft X-ray Source and Wavefront Measurements ... · Soft x-ray microscopy III Applications of ns and ps laser-induced soft x-ray sources dose [mJ/cm² x number of pulses]

= Near-edge x-ray absorption fine-structure

Excitation of unoccupied molecular orbitals

NEXAFS Spectroscopy in the „water window“:

„Fingerprint“ of molecules

surface-sensitive chemical analytics

2,0 2,5 3,0 3,5 4,0 4,5 5,0

0,1

1

10

O: 2,28 nm

Ti: 2,73 nm

N: 3,0 nm

Ca: 3,58 nm

C: 4,36 nm

Ti N

Ca

H2O

C

Absorp

tion length

m)

Wavelength (nm)

Accessable absorption edges Spectrum of Krypton plasma

B, C, N, O, F, S, Ca, Ti, Mn, Fe…

Page 8: Table-top EUV/Soft X-ray Source and Wavefront Measurements ... · Soft x-ray microscopy III Applications of ns and ps laser-induced soft x-ray sources dose [mJ/cm² x number of pulses]

Table-top NEXAFS Spectrometer

= 1 …7nm, 10 …20nm

Source sample spectrometer

200 250 300 350 400 450

0

2000

4000

6000

8000

10000

12000

14000

0,0

0,2

0,4

0,6

0,8

1,0

Inte

nsity [C

CD

-Co

un

ts]

Photonenenergy [eV]

without sample

with Polyimid (d=200nm)

Transmission Carbon (CXRO)

Tra

nsm

issio

n

280 290 300 310 3200,0

0,5

1,0

1,5

2,0

*C-N

*C=C

*C=O

*C=O

Optic

al d

ensi

ty [

a.u

.]

Photon energy [eV]

*C=C

Polyimide

C. Peth, K. Mann et al., J. Phys. D 41 (2008) 105202

Carbon

K-edge

Synchrotron

(J. Stöhr)

60 laser pulses

polyimide

sample

(d=200nm):

Laser polychromatic concept („single-shot“)

transmission of thin samples

Page 9: Table-top EUV/Soft X-ray Source and Wavefront Measurements ... · Soft x-ray microscopy III Applications of ns and ps laser-induced soft x-ray sources dose [mJ/cm² x number of pulses]

Compact NEXAFS spectrometer

= 1 …7nm

10 …20nm

pump-probe exp.

measurement in

ambient air

Page 10: Table-top EUV/Soft X-ray Source and Wavefront Measurements ... · Soft x-ray microscopy III Applications of ns and ps laser-induced soft x-ray sources dose [mJ/cm² x number of pulses]

NEXAFS spectroscopy on thin films

Lipid membranes (carbon K-edge)

E. Novakova, C. Peth, K. Mann, T. Salditt et al.: Biointerphases, 3 (2008) FB44

285 290 295 300 305 310 315

0

1

2

3

4

Optic

al d

ensi

ty

Photon energy (eV)

C=C*

DOPS

DOPC

DMPC

4,4 4,3 4,2 4,1 4 3,9

Wavelength [nm]

PCMO (Perovskite-type manganate)

300 400 500 600 700 800 900 10001,0

1,1

1,2

1,3

1,4

1,5

1,6

1,7

1,8

1,9

2,0

Optical T

hic

kness [a.u

.]Photon-Energy (eV)

NEXAFS-Spectrum PCMOCaL 2,3

NK

OK

MnL 2,3

PrM 4,5

: Pr, Ca

: O

: Mn

Every element visible

(single shots)

Pump-probe experiments

phase transitions

Pr1-xCaxMnO3 (S. Techert) (T. Salditt)

P. Grossmann, S. Techert, C. Jooss, K. Mann et al.: Rev. Sci. Instr. 2012

Page 11: Table-top EUV/Soft X-ray Source and Wavefront Measurements ... · Soft x-ray microscopy III Applications of ns and ps laser-induced soft x-ray sources dose [mJ/cm² x number of pulses]

NEXAFS at Fe L2,3 edge

Example:

Prussian Blue

► Iron L2,3 edge ► Carbon K edge

• Photon energy ~ 720eV

• 300 laser pulses

Page 12: Table-top EUV/Soft X-ray Source and Wavefront Measurements ... · Soft x-ray microscopy III Applications of ns and ps laser-induced soft x-ray sources dose [mJ/cm² x number of pulses]

Improvements (1):

Power density: ns ps laser

Xe (Z = 54)

Single pulse XUV spectra

200 400 600 800 100010

1

102

103

104

200 400 600 800 100010

1

102

103

104

200 400 600 800 1000

101

102

103

200 400 600 800 100010

2

103

104

200 400 600 800 100010

2

103

104

200 400 600 800 100010

2

103

104

Photon energy (eV)

Single-Pulse - Max. Laserpulse-Energy - Al filteredNitrogen Oxygen Neon

Photon energy (eV) Photon energy (eV)

Photon energy (eV)

Argon Krypton Xenon

Photon energy (eV) Photon energy (eV)

Single pulse XUV spectra

Single pulse XUV spectra

Single pulse spectra:

O (Z = 8) Ne (Z = 10) N (Z = 7)

Ar (Z = 18) Kr (Z = 36)

8ns

450mJ

150ps

380mJ

Peak brillance of isolated N line @ = 2.88nm:

6*1017 (ns laser) 1.2*1020 Ph./(s mrad2 mm2 0,1%BW) (ps laser)

Page 13: Table-top EUV/Soft X-ray Source and Wavefront Measurements ... · Soft x-ray microscopy III Applications of ns and ps laser-induced soft x-ray sources dose [mJ/cm² x number of pulses]

Simulation of spectra: Ar

ns laser ps laser

electron temperature [eV]

50.3 66.3

electron density [1019 e/cm³]

7.0 22.4

Calculation with

MHD code

PrismSPECT

measured measured

simulated simulated

ps ns

M. Müller, K. Mann et al.: Opt. Express 21 (2013)

Page 14: Table-top EUV/Soft X-ray Source and Wavefront Measurements ... · Soft x-ray microscopy III Applications of ns and ps laser-induced soft x-ray sources dose [mJ/cm² x number of pulses]

Nitrogen

10 bar

Helium

170 mbar

14

Nitrogen

10 bar

Vacuum

~10-3 mbar

500 µm 500 µm

T. Mey, M. Rein, K. Mann, New J. Phys. 14 (2012) 073045

~10x brilliance

increase

@ = 2.88 nm

Improvements (2): Plasma generation with barrel shock

Schlieren

image

Page 15: Table-top EUV/Soft X-ray Source and Wavefront Measurements ... · Soft x-ray microscopy III Applications of ns and ps laser-induced soft x-ray sources dose [mJ/cm² x number of pulses]

ellipsoidal mirror laser

plasma

caustic measurement

Improvements (3):

Focusing optics for x-ray plasma

Nitrogen plasma, = 2.88nm (monochromatic)

grazing incidence ellipsoidal mirror

focus dia. ~ 500µm

Page 16: Table-top EUV/Soft X-ray Source and Wavefront Measurements ... · Soft x-ray microscopy III Applications of ns and ps laser-induced soft x-ray sources dose [mJ/cm² x number of pulses]

Ablation of PMMA @ =2.88nm

FWHM

≈ 500 µm

focal spot of elliptical mirror:

~ 1 mJ/cm² @ 2.88 nm

≈ 8.5*109 photons/pulse

5000 N2 pulses @ 15 bar,

3 min ultrasonic bath

Kr plasma (3 …6nm): ~ 100mJ/cm²

Page 17: Table-top EUV/Soft X-ray Source and Wavefront Measurements ... · Soft x-ray microscopy III Applications of ns and ps laser-induced soft x-ray sources dose [mJ/cm² x number of pulses]

ellipsoidal mirror laser

plasma

caustic measurement

Improvements (3):

Focusing optics for x-ray plasma

Nitrogen plasma, = 2.88nm (monochromatic)

grazing incidence ellipsoidal mirror

focus dia. ~ 500µm

Optics adjustment: time-consuming…

Page 18: Table-top EUV/Soft X-ray Source and Wavefront Measurements ... · Soft x-ray microscopy III Applications of ns and ps laser-induced soft x-ray sources dose [mJ/cm² x number of pulses]

18

Wavefront measurements

Hartmann-Shack sensor:

wavefront:

Wavefront w(x,y)

= surface Poynting-Vektor S(x,y)

(ISO 15367-2)

directional

distribution

intensity

distribution

Page 19: Table-top EUV/Soft X-ray Source and Wavefront Measurements ... · Soft x-ray microscopy III Applications of ns and ps laser-induced soft x-ray sources dose [mJ/cm² x number of pulses]

Hartmann

plate

Beam characterization of FLASH

Adjustment of beam line optics by

online wavefront monitoring = 5 .. 30nm

Experimental setup at BL2

-0.5

0.29 0.53

0.0

Pitch [mrad]

Yaw

[mrad] 0.5

0.21 0.36

wrms=13nm

wrms=15.5nm

wrms=2.6nm wrms=5.9nm wrms=2.6nm wrms=3.5nm

[1] B. Flöter et al, Beam parameters of FLASH beamline BL1 from Hartmann wavefront

measurements, Nucl. Instrum. Meth. A 635 (2011) 5108-5112

Page 20: Table-top EUV/Soft X-ray Source and Wavefront Measurements ... · Soft x-ray microscopy III Applications of ns and ps laser-induced soft x-ray sources dose [mJ/cm² x number of pulses]

Hartmann

plate

Beam characterization of FLASH

= 5 .. 30nm

Experimental setup at BL2

wrms~ 10nm wrms~ 2.5nm ~ /10

Wavefront

Intensity

after

adjustment

before

adjustment

[2] B. Flöter et al, EUV Hartmann sensor for wavefront measurements at the Free-electron

LASer in Hamburg, New J. Phys. 12 (2010) 083015

Page 21: Table-top EUV/Soft X-ray Source and Wavefront Measurements ... · Soft x-ray microscopy III Applications of ns and ps laser-induced soft x-ray sources dose [mJ/cm² x number of pulses]

Beam profiles and wavefronts of single pulses (no focusing mirror)

Beam propagation parameters X Y wpv [nm] 5.3 ± 0.69

wrms [nm] 0.67 ± 0.09

Beam propagation parameter M2 1.15 ± 0.08 ()

Beam propagation parameter M2i 1.23 ± 0.1 1.1 ± 0.1 ()

Beam width d [mm] 6 ± 0.2 4.4 ± 0.1

Waist position z0,i [m] -109.2 ± 0.9 -99.2 ± 1.4

Rayleigh length zR [mm] 3760 ± 484 5090 ± 731

Waist diameter d0,i [µm] 2nd moment 200 ± 20 223 ± 25 ()

Divergence [µrad] 55 ± 2 44 ± 2 ()

Beam parameters from Hartmann data

FLASH BL2 @=7nm

Page 22: Table-top EUV/Soft X-ray Source and Wavefront Measurements ... · Soft x-ray microscopy III Applications of ns and ps laser-induced soft x-ray sources dose [mJ/cm² x number of pulses]

Beam characterization

at FERMI@Elettra / Triest @ = 32nm

Active KB System

Wavefront sensor

Focal spot size:

Computed PMMA imprint

10x10µm²

Page 23: Table-top EUV/Soft X-ray Source and Wavefront Measurements ... · Soft x-ray microscopy III Applications of ns and ps laser-induced soft x-ray sources dose [mJ/cm² x number of pulses]

Summary:

Laser plasma EUV / soft x-ray source

Clean, stable, compact

=1…20nm, ns…ps pulses

reflectometry, ablation studies, NEXAFS / EXAFS for chemical analysis

spectro-microscopy

Hartmann wavefront sensor (EUV / soft x-rays)

real-time alignment of optics

beam propagation for single pulses

Characterization of partially coherent radiation Wigner distribution

Page 24: Table-top EUV/Soft X-ray Source and Wavefront Measurements ... · Soft x-ray microscopy III Applications of ns and ps laser-induced soft x-ray sources dose [mJ/cm² x number of pulses]

• Dr. B. Schäfer

• Dr. U. Leinhos

• J.O. Dette

• W. Hüttner

• F. Kühl

• M. Lübbecke

• T. Mey

• M. Müller

• G. Steinert

• J. Sudradjat

• M. Stubenvoll

Thank You !

Coworkers:

Page 25: Table-top EUV/Soft X-ray Source and Wavefront Measurements ... · Soft x-ray microscopy III Applications of ns and ps laser-induced soft x-ray sources dose [mJ/cm² x number of pulses]

XUV peak brillance

of laser plasma source

400 450 500 550 600 650 700

0

10000

20000

30000

40000

50000

60000

N VII 1s2-1s5p

N VII 1s2-1s4p

N VI 1s2-1s6p

N VI 1s2-1s5p

N VII 1s2-1s3pN VI 1s

2-1s4p

N VII 1s2-1s2p

N VI 1s2-1s2p

CC

D-C

ounts

Photonenenergie (eV)

Stickstoff - Einzelpuls - Al gefiltert

N VI 1s2-1s3p

Isolated N VI 1s2-1s2p line @ 2.8787nm (Ti filtered)

Peak brillance [Photons/(s mrad2 mm2 0,1%BW)]

ns laser: 6*1017 (LLG, T. Wilhein)

ps laser: 1,2*1020 (LLG)

Brightness (ps): ~1014 photons/(pulse x sr)

Page 26: Table-top EUV/Soft X-ray Source and Wavefront Measurements ... · Soft x-ray microscopy III Applications of ns and ps laser-induced soft x-ray sources dose [mJ/cm² x number of pulses]

Comprehensive beam characterization Wigner distribution

= Fourier transform of Mutual Coherence Function

Intensity distribution Beam diameter

CCD camera

Phosphor coated screen

Translation stage

Long working distance

microscope

Caustic of FLASH:

Page 27: Table-top EUV/Soft X-ray Source and Wavefront Measurements ... · Soft x-ray microscopy III Applications of ns and ps laser-induced soft x-ray sources dose [mJ/cm² x number of pulses]

Determination of

Wigner distribution function

ℎ𝑥 𝑥, 𝑢 = ℎ 𝑥, 𝑦, 𝑢, 𝑣 𝑑𝑦𝑑𝑣 ℎ𝑦 𝑦, 𝑣 = ℎ 𝑥, 𝑦, 𝑢, 𝑣 𝑑𝑥𝑑𝑢 mapping measured data into 4D Wigner Fourier space

FFT

Reconstruction

of beam profiles

▼ Wigner distribution

function

comprehensive

beam characterization

beam parameters

coherence function

mode content

wavefront

angular characteristics B. Schäfer, T. Mey, K. Mann, K. Tiedtke et al, Nucl. Inst. Meth. 2011

Page 28: Table-top EUV/Soft X-ray Source and Wavefront Measurements ... · Soft x-ray microscopy III Applications of ns and ps laser-induced soft x-ray sources dose [mJ/cm² x number of pulses]

Spectrum of electromagnetic radiation

Wavelength

Photon energy

EUV Lithography 13.5 nm

Excimer

lasers

Soft x-rays

Hard x-rays

Free electron

lasers

„water window“

1µm 100nm 10nm 1nm 0.1nm

1eV 10eV 100eV 1keV 10keV

Extreme UV

High

Harmonics

Page 29: Table-top EUV/Soft X-ray Source and Wavefront Measurements ... · Soft x-ray microscopy III Applications of ns and ps laser-induced soft x-ray sources dose [mJ/cm² x number of pulses]

Gepulstes Hochdruck-Gastarget

A) monochromatische Strahlung @=2,88nm (N2 + Ti-Filter)

B) Bichromatisches Konzept zur elementspezifischen

Mikroskopie um die Ca-Kante (=3,58 nm)

Spektro-Mikroskopie

Kompaktes Labor-Röntgenmikroskop

Page 30: Table-top EUV/Soft X-ray Source and Wavefront Measurements ... · Soft x-ray microscopy III Applications of ns and ps laser-induced soft x-ray sources dose [mJ/cm² x number of pulses]

NEXAFS measurements at athmospheric pressure

2 – 4mm

Polyimide:

Page 31: Table-top EUV/Soft X-ray Source and Wavefront Measurements ... · Soft x-ray microscopy III Applications of ns and ps laser-induced soft x-ray sources dose [mJ/cm² x number of pulses]

Nitrogen

10 bar

Helium

170 mbar

31

Nitrogen

10 bar

Vacuum

~10-3 mbar

500 µm 500 µm

Improvements (2): Plasma generation with barrel shock

Schlieren

image

Page 32: Table-top EUV/Soft X-ray Source and Wavefront Measurements ... · Soft x-ray microscopy III Applications of ns and ps laser-induced soft x-ray sources dose [mJ/cm² x number of pulses]

Improvements (3):

Barrel shock

10-3mbar

1 bar

Nitrogen

10bar

ambient

pressure:

32

500µm

Schlieren

images:

Page 33: Table-top EUV/Soft X-ray Source and Wavefront Measurements ... · Soft x-ray microscopy III Applications of ns and ps laser-induced soft x-ray sources dose [mJ/cm² x number of pulses]

Beam characterization:

Hartmann-Shack wavefront sensor

Zernike

Analysis:

Beam

parameters:

Propagation

analysis

- Wavefront

Spot distribution - Beam profile

33

2222 4 xx

x xxM

B.Schäfer, K. Mann, Rev. Sci. Instr. 77, 053103 (2006)

Page 34: Table-top EUV/Soft X-ray Source and Wavefront Measurements ... · Soft x-ray microscopy III Applications of ns and ps laser-induced soft x-ray sources dose [mJ/cm² x number of pulses]

EXAFS: Cl L-edge of NaCl

► 200nm NaCl film

► L-edge of Cl (EUV range)

► Bond lengths:

Excellent agreement with

Synchrotron data

EXAFS structures

Streui

iEE

CR

Page 35: Table-top EUV/Soft X-ray Source and Wavefront Measurements ... · Soft x-ray microscopy III Applications of ns and ps laser-induced soft x-ray sources dose [mJ/cm² x number of pulses]

Results and discussion I - Overview

17 November

2013

Emission properties of ns and ps laser-induced soft x-ray sources 35

Page 36: Table-top EUV/Soft X-ray Source and Wavefront Measurements ... · Soft x-ray microscopy III Applications of ns and ps laser-induced soft x-ray sources dose [mJ/cm² x number of pulses]

Results and discussion III – different pulse energies

17 November

2013

Emission properties of ns and ps laser-induced soft x-ray sources 36

N2 Kr

The higher emission intensity of the ps plasma and shift to shorter wavelengths

(considering the same pulse energy of ns and ps laser) is attributed to the higher electron

density and higher electron temperature, respectively.

Page 37: Table-top EUV/Soft X-ray Source and Wavefront Measurements ... · Soft x-ray microscopy III Applications of ns and ps laser-induced soft x-ray sources dose [mJ/cm² x number of pulses]

Results and discussion VI

37

Parameter ns laser ps laser

Wavelength (λ) 1064 nm 1064 nm

Pulse duration (τ) (FWHM) 7 ns 0.17 ns

Laser pulse energy (Q) 450 mJ 380 mJ

Diameter of focal spot 30 µm 20 µm

Maximum power density 2.2 x 1012 W/cm² 1.7 x 1014 W/cm²

Plasma size 470 µm x 190 µm 310 µm x 150 µm

Brightness 5 x 1012 photons/(pulse x sr) 8 x 1013 photons/(pulse x sr)

Peak Brilliance @ 2.88 nm 1 x 1015 photons/(s x mrad² x mm²) 4 x 1018 photons/(s x mrad² x mm²)

Page 38: Table-top EUV/Soft X-ray Source and Wavefront Measurements ... · Soft x-ray microscopy III Applications of ns and ps laser-induced soft x-ray sources dose [mJ/cm² x number of pulses]

38

Soft x-ray microscopy II

caustic measurement

0

10 25

50

-10 -25

-50

z [mm]

FWHM

≈ 500 µm

Page 39: Table-top EUV/Soft X-ray Source and Wavefront Measurements ... · Soft x-ray microscopy III Applications of ns and ps laser-induced soft x-ray sources dose [mJ/cm² x number of pulses]

17 November

2013

39

Soft x-ray microscopy III

Applications of ns and ps laser-induced soft x-ray sources

dose [mJ/cm² x number of pulses]

de

pth

[n

m]

EUV energy density [mJ/cm²]

ablation

fragmentation

Ablation of PMMA @ 2.88nm

energy density between 0.3 mJ/cm² -

0.5 mJ/cm² @ 2.88 nm in the focal

spot of the elliptical mirror

≈ 8.5*109 photons/pulse 5000 pulses, N2 @ 15 bar,

3 min ultrasonic bath

@ 13.5 nm

Page 40: Table-top EUV/Soft X-ray Source and Wavefront Measurements ... · Soft x-ray microscopy III Applications of ns and ps laser-induced soft x-ray sources dose [mJ/cm² x number of pulses]

17 November

2013

40

Soft x-ray microscopy IV

Applications of ns and ps laser-induced soft x-ray sources

2.3*1012 photons/(sr*pulse ) 1.8*1011 photons/(sr*pulse )

R ≈ 8%

Page 41: Table-top EUV/Soft X-ray Source and Wavefront Measurements ... · Soft x-ray microscopy III Applications of ns and ps laser-induced soft x-ray sources dose [mJ/cm² x number of pulses]

Caustic of HHG Source

25. Harmonic (=32nm)

x y

Waist diameter d0 91.5 µm 243.4 µm

Waist position z0 312.6 mm 402.6 mm

Rayleigh length zR 10.7 mm 30.1 mm

Beam propagation factor M² 19.7 50.0

90.0 mm

z0y

d0y

√2·d0y

zRy

Aberrations !

Page 42: Table-top EUV/Soft X-ray Source and Wavefront Measurements ... · Soft x-ray microscopy III Applications of ns and ps laser-induced soft x-ray sources dose [mJ/cm² x number of pulses]

Real-time wavefront measurement

25. Harmonic (=32nm)

42

Yaw angle

Pitch angle !

Page 43: Table-top EUV/Soft X-ray Source and Wavefront Measurements ... · Soft x-ray microscopy III Applications of ns and ps laser-induced soft x-ray sources dose [mJ/cm² x number of pulses]

Spatial coherence:

interference of elementary waves

𝑥 − 𝑠 /2

𝑥 + 𝑠 /2

𝑑

43

𝑠

2𝑎

Young´s experiment:

Contrast of fringes

local degree of coherence 𝛾 𝑥 , 𝑠 :

Page 44: Table-top EUV/Soft X-ray Source and Wavefront Measurements ... · Soft x-ray microscopy III Applications of ns and ps laser-induced soft x-ray sources dose [mJ/cm² x number of pulses]

Caustic of Free Electron Laser FLASH / DESY

Beam

parameter Value

Waist position

z0x / z0y [mm] 131.1 / 132.6

Waist diameter

d0x / d0y [µm] 65.5 / 35.9

Rayleigh length

zRx / zRy [mm] 11.8 / 5.7

Beam propagation

factor M²x / M²y 21 / 13

coherence ???

z0x

d0x √2·d0x

zRx

44

Page 45: Table-top EUV/Soft X-ray Source and Wavefront Measurements ... · Soft x-ray microscopy III Applications of ns and ps laser-induced soft x-ray sources dose [mJ/cm² x number of pulses]

angular coordinate 𝑢 =𝑢𝑣

spatial coordinate 𝑥 =

𝑥𝑦

Wigner distribution

ℎ 𝑥 , 𝑢 = 1

2𝜋

2

⋅ Γ 𝑥 , 𝑠 ⋅ 𝑒−𝑖𝑢⋅𝑠 𝑑2𝑠

Wigner distribution mutual coherence function

x

y

z v

Interpretation: radiance at position 𝑥 in direction of 𝑢

ℎ = Wm² ⋅ sr

M. J. Bastiaans, 1986, Opt. Acta 28 1215-24

h = Fourier transform of Mutual Coherence Function: