Spatial Temporal Coherence; Coherent Undulator Radiationattwood/sxr2009/... · Ch08_F03.ai (8.3) Define a coherence length coh as the distance of propagation over which radiation

Spatial and Temporal Coherence;Coherent Undulator Radiation

David Attwood

University of California, Berkeley

(http://www.coe.berkeley.edu/AST/srms)

d

Ch08_F00.ai

λθ

λ

e–

Pinhole

d

λ

λθ

lcoh = λ2/2∆λ {temporal (longitudinal) coherence}

d θ = λ/2π {spatial (transverse) coherence}

or d 2θFWHM = 0.44 λ

(8.3)

(8.5)

(8.5*)

Pcoh,λ/∆λ = 1– ƒ(K)

(8.6)

(8.9)

Pcoh = Plaser (8.11)

(λ/2π)2

(dxθx)(dyθy)

(λ/2π)2

(dxθx)(dyθy)

ωω0

eλuIη(∆λ/λ)N2

8π0dxdy

Pcoh,N = Pcen

λu

COHERENCE AT SHORT WAVELENGTHSChapter 8

Professor David AttwoodUniv. California, Berkeley

d θ

λλ

CH08_YoungsExprmt_v3.ai

Young’s Double Slit Experiment: Spatial Coherence and the Persistence of Fringes

Persistence of fringes as the source grows from a point source to finite size.


d 2θ|FWHM λ/2

λcoh = λ2/2∆λ = Ncohλ12

Spatial and Spectral Filteringto Produce Coherent Radiation

Ch08_F08.ai

Courtesy of A. Schawlow, Stanford.Professor David AttwoodUniv. California, Berkeley

Ch08_F01.ai

Coherence, Partial Coherence, and Incoherence

θd

λ λ, ∆λ

Point source oscillator– < t <

Source of finite size,divergence, and duration


Spatial and Temporal Coherence

Ch08_Eq1_12_F2.ai

(8.1)

(8.12)

(8.3)

(8.5)

Mutual coherence factor

Longitudinal (temporal) coherence length

Full spatial (transverse) coherence

Normalize degree of spatial coherence(complex coherence factor)

A high degree of coherence (µ → 1)implies an ability to form a high contrastinterference (fringe) pattern. A low degreeof coherence (µ → 0) implies an absenceof interference, except with great care.In general radiation is partially coherent.

Transverse (spatial)coherence

Longitudinalcoherence length

Point source,harmonic oscillator

P1

P2

P2

coh = λ2/2∆λ

P1


Spectral Bandwidth andLongitudinal Coherence Length

Ch08_F03.ai

(8.3)

Define a coherence length coh as the distance of propagation over which radiation of spectral width ∆λ becomes 180° out of phase. For a wavelength λ propagating through N cycles

and for a wavelength λ + ∆λ, a half cycle less (N – )

Equating the two

so that

λ ∆λ

∆λ

λcoh

180 phase shift1.00

coh = Nλ

coh = (N– ) (λ + ∆λ)

N = λ/2∆λ

12

12


• Associate spatial coherence with a spherical wavefront.

• A spherical wavefront implies a point source.

• How small is a “point source”?

Ch08_XBL 915-6740A.ai

From Heisenberg’s Uncertainty

Principle (∆x · ∆p ≥ ), the smallest

source size “d” you can resolve, with

wavelength λ and half angle θ, is

d · θ =λ

2π

d

λ

θ

2

A Practical Interpretationof Spatial Coherence


Ch08_XBL883-8849_modf.ai

Partially Coherent Radiation ApproachesUncertainty Principle Limits

∆x ∆p ≥ /2

quantities1e

∆x k∆θ ≥ 1/2

∆x ∆k ≥ /2

2∆x ∆θ ≥ λ/2π

Standard deviations of Gaussian distributed functions(Tipler, 1978, pp. 174-189)

Spherical wavefronts occurin the limiting case

or(d 2θ)FWHM λ/2 FWHM quantities

Note: ∆p = ∆k ∆k = k∆θ

d = 2∆x

(spatially coherent)

d θ = λ/2π

θ

∆k∆θk

(8.4)


Ch08_F05.ai

Propagation of a Gaussian Beam

r0

Waist

λ

z Gaussian intensitydistribution, sphericallypropagating wave

r(z) θ

In

with waist diameter d = 2r0, we have TEM00 radiation with d θ = λ/2π

(Siegman, Lasers)


Ch08_Heisenberg.aiProfessor David AttwoodUniv. California, Berkeley

Spatially Coherent Undulator Radiation

! = 11.2 nm ! = 13.4 nm

1 !mD pinhole

25 mm wide CCD

at 410 mm

Ch08_Coh_SXR_Sci .PPT

Professor David Attwood

Univ. California, Berkeley

Courtesy of Patrick Naulleau, LBNL.

Ch08_SpatialFiltrng.ai

Spatial Filtering of Undulator Radiation

Undulator central radiation cone ( = N ; θ = ):

With spatial filtering (a pinhole and an angular aperture):

(5.41a)

(8.6)

(8.9)

With eq.(5.28), . Convert to photon

energies where for θ = 0, , and where

corresponds to K = 0. For small electron beamdiverence, σ′ << θcen, the spatially coherent power is

λ∆λ

1γ* N

≤ 1 ≤ 1

2 2x,y


500 100 150 200 250 300 350 400 450

5

0

10

15

20

25

30

35

Photon energy (eV)

Tuningcurve

Coh

eren

t pow

er (

mW

)

λ∆λ = N

Pcoh = · Pcen

coh = Nλ/2

(λ/2π)2

(dxθx)(dyθy)

Spatially Filtered Undulator Radiation

Ch08_F09.ai

(8.6)

(8.9)

Using a pinhole-aperture spatial filter, passing only radiation that satisfies d θ = λ/2π

for dx = 2σx, dy = 2σy, θTx → θx, θTy → θy,and σ′2 << θcen.2

Photon energy (eV)

Pce

n (W

)

Tuningcurve

λ∆λ = N

Pcen = ·πeγ 2I0λu

K2f(K)

(1 + K2/2)2

λu = 8 cmN = 551.9 GeV0.4 ampn = 1(only)

0 100 200 300 4000

0.50

1.00

1.50

2.00Undulatorradiation

d

Spatialfilter

Pinhole

N periods

1 γ∗1

Nγ∗

1

Nγ∗

θcen =

θcen = ; = N; γ* = γ/ 1 + K2/2

λ = (1 + + γ2θ2)λu

2γ2

λ∆λ cen

θ

Angularaperture

K2

2

e–

λu


Ch08_SpatialSpectral.ai

Spatial and Spectral Filtering of Undulater Radiation

In addition to the pinhole – angular aperture for spatialfiltering and spatial coherence, add a monochromator for narrowed bandwidth and increased temporal coherence:

which for σ′ << θcen (the undulator condition) gives thespatially and temporally coherent power ( ; )

which we note scales as N2.

(8.10a)

(8.10c)

2 2x,y


Spatially and Spectrally FilteredUndulator Radiation

Ch08_F11_Mar08.ai

(8.10a)

(8.10c)

• Pinhole filtering for full spatial coherence• Monochromator for spectral filtering to λ/∆λ > N

M1planemirror

M2spherical

mirror

Water-cooledbeam definingapertures

8.0 cm periodundulator

EUVinterferometer

166°

Variedline-

spacegrating

Exitslit

166°

M6bendable

EntrancepinholeM5

planeM4

bendable

M3retractable

planemirror

M0retract-

ableplanemirror

EUV/soft x-rayphotoemission

microscope

8.0 cm period, N = 551.9 GeV, 400 mAd θ = λ/2πcoh = 103λ/2η = 10%


0

100

200

300

102 103

Photon Energy (eV)

Pco

h, λ

/∆λ

(µW

)

n = 3λ

∆λ= 103

λ∆λ

= 103

Ch08_CohOptBLwGraf_Feb07.ai

Tuningcurves

8.0 cm period, N = 551.9 GeV, 400 mAd θ = λ/2πcoh = 1000 λ/2ηeuv = 10%, ηsxr = 10%

Coherent Power with a Monochromator

M2spherical2 mirror



Variedline-space

grating

Exitslit172°

M4bendable2 mirror

M3bendable2 mirror

M0retractable

plane2 mirror

Entrancepinhole

CoherentSoft X-ray

End Station

K-Bfocus

system

Coherent Soft X-Ray Beamline: Use of a Higher Harmonic (n = 3) to Access Shorter Wavelengths

0

100

200

300

102 103

Photon Energy (eV)

Pco

h, λ

/∆λ

(µW

)

n = 1

n = 3

λ∆λ

= 103


Coherent Power at the ALS

Ch08_U8_Feb07.ai

1.9 GeV, 400 mAλu = 80 mm, N = 550.5 ≤ K ≤ 4.0σx = 260 µm, σx′ = 23 µrσy = 16 µm, σy′ = 3.9 µr

0 200 400 600 800 10000

0.5

1.0

1.5

0

10

20

30

40

50

0

100

200

300

102 103102 103

Photon Energy (eV)

Photon Energy (eV)

Photon Energy (eV)

Pco

h, N

(m

W)

Pco

h, λ

/∆λ

(µW

)

Pce

n (W

)

U8

n = 1

n = 3

n = 1

n = 3

n = 1

n = 3

λ∆λ

= 55

λ∆λ = 55

λ∆λ = 165

λ∆λ

= 103

λ∆λ

= 103

ηeuv = 10%ηsxr = 10%


Coherent Power at the ALS

Ch08_U5_Feb07.ai

1.9 GeV, 400 mAλu = 50 mm, N = 890.5 ≤ K ≤ 4.0σx = 260 µm, σx′ = 23 µrσy = 16 µm, σy′ = 3.9 µrη = 10%

U5

0 500

n = 1

n = 3

n = 1

n = 3

n = 1

n = 3

1000 1500 20000

0.5

1.0

1.5

2.0

2.5

0

10

20

30

40

50

0

100

200

300

400

102 103102 103

Photon Energy (eV)Photon Energy (eV)

Photon Energy (eV)

Pco

h, N

(m

W)

Pco

h, λ

/∆λ

(µW

)

Pce

n (W

)

λ∆λ

= 89 λ∆λ

= 103


Ch08_ALS_U5epu_Feb07.ai

1.9 GeV, 400 mAλu = 50 mm, N = 270.5 ≤ K ≤ 4.0σx = 260 µm, σx′ = 23 µrσy = 16 µm, σy′ = 3.9 µrθcen = 61µr @ K = 0.87 (500 eV)

U5 EPU

0 500

n = 1

n = 3

n = 1

n = 3

n = 1

η = 1.3%

n = 3

1000 1500 20000

0.5

1.0

1.5

2.0

2.5

0

5

10

15

20

0

2

4

6

102 103102 103


Photon Energy (eV)

Pco

h, N

(m

W)

Pco

h, λ

/∆λ

(µW

)

Pce

n (W

)

λ∆λ

= 27λ

∆λ = 103


Coherent Power for an EPU at the ALS

Coherent Power Predictedwith SPEAR 3 at SSRL

Ch08_SPEAR3_SSRL_Feb07.ai

3.0 GeV, 500 mAλu = 3.3 cm, N = 1050 ≤ K ≤ 2.2σx = 436 µm, σx′ = 43 µradσy = 30 µm, σy′ = 6.3 µradθcen = 17 µrad @ K = 1η = 10%

Photon Energy (eV)

n = 1

n = 3λ∆λ

= 103

Photon Energy (eV)

Photon Energy (keV)

n = 1

n = 3λ

∆λ= 105

0 2 4 6 8

104103104103

Pco

h, N

(m

W)

Pco

h, λ

/∆λ

(µW

)

Pce

n (W

)

15

10

5

0

0

5

10

n = 1

n = 3

0

50

100


Coherent Power at the Australian Synchrotron

CohPwr_AustralSynch_Feb07.ai

Photon Energy (eV)

n = 1

n = 3λ

∆λ= 103

Photon Energy (eV)

Photon Energy (eV)

n = 1

n = 3

λ∆λ

= 80

λ∆λ

= 80

λ∆λ= 240

0 2,000 4,000 6,000 8,000 10,000

104103104103

Pco

h, N

(m

W)

Pco

h, λ

/∆λ

(µW

)

Pce

n (W

)

8

6

2

0

0

2

4

6

n = 1

n = 3

4

0

10

20

30

40

50

3.0 GeV, 200 mAλu = 22 mm, N = 800 ≤ K ≤ 1.8σx = 320 µm, σx′ = 34 µradσy = 16 µm, σy′ = 6 µradθcen = 23 µrad @ K = 1η = 10%


Coherent Power at the UK’s Diamond Synchrotron Facility

CohPwr_DiamondUK_Feb07.ai

3.0 GeV, 300 mAλu = 2.4 cm, N = 820 ≤ K ≤ 1.4σx = 123 µm, σx′ = 24 µrσy = 6.4 µm, σy′ = 4.2 µrθcen = 23 µr @ K = 1η = 10%1000 5000 900070003000

103 1040

200

300

100

400

500

600

Photon Energy (eV)

Pco

h, λ

/∆λ

(µW

)

Pce

n (W

)

n = 1

n = 3

n = 3

n = 1

n = 3

λ∆λ

= 103

0

2

4

8

6

10

0

10

20

30

40

50

60

103 104

Photon Energy (eV)

Photon Energy (eV)

Pco

h, N

(m

W) n = 1

λ∆λ

= 82

Courtesy of Brian Kennedy (King’s College London),Susan Smith (Daresbury), and Yanwei Liu (LBNL)


Ch08_APS_Feb07.ai

7.00 GeV, 100 mAλu = 33 mm, N = 720.5 ≤ K ≤ 3.0σx = 320 µm, σx′ = 23 µrσy = 50 µm, σy′ = 7 µrη = 10%

0 10 20 30 400

5

10

15

0

0.2

0.4

0.6

0.8

0

2

4

6

104103 105 103 104 105


Photon Energy (eV)

Pco

h, N

(m

W)

Pco

h, λ

/∆λ

(µW

)

Pce

n (W

)

APS

n = 1

n = 3

n = 1

n = 1

n = 3

n = 3

λ∆λ

= 72 λ∆λ

= 103

Coherent Power at the APS


Ch08_SPring8_Feb07.ai

8 GeV, 100 mAλu = 32 mm, N = 1400 ≤ K ≤ 2.46σx = 393 µm, σx′ = 15.7 µrσy = 4.98 µm, σy′ = 1.24 µrη = 10%

n = 1

n = 3

n = 1

n = 3

n = 1

n = 3

λ∆λ

= 103λ∆λ

= 140

0 10 20 30 40 50 600

5

10

15

20

0

5

10

15

20

0

100

200

300

Photon Energy (eV)

Photon Energy (keV)

103 104 105

Photon Energy (eV)103 104 105

Pco

h, N

(m

W)

Pco

h, λ

/∆λ

(µW

)

Pce

n (W

)Coherent Power at SPring-8


Spatially Coherent Undulator Radiation

! = 11.2 nm ! = 13.4 nm

1 !mD pinhole

25 mm wide CCD

at 410 mm

Ch08_Coh_SXR_Sci .PPT



Courtesy of Patrick Naulleau, LBNL.

Undulator Beamline forHigh Spatial Coherence Measurements

BeamlineAperture

GratingUndulator

C. Chang

e–

CCD

Twopinholemask

0 0.2 0.4 0.6

Inte

nsity

Position

13.4 nm420 nmD

5 m sep

0.8 10

0.5

1

Ch08_CohSXRsci.aiProfessor David AttwoodUniv. California, Berkeley

Ch08_CohSXRsciChang.ppt



Courtesy of Chang Chang, UC Berkeley and LBNL.

Spatial Coherence Measurements of Undulator

Radiation Using the Classic 2-Pinhole Technique

! = 13.4 nm, 450 nm diameter pinholes, 1024 x 1024 EUV/CCD at 26 cm ALS, 1.9 GeV, !u = 8 cm, N = 55





Spatial Coherence Measurements of Undulator

Radiation Using the Classic 2-Pinhole Technique






Spatial Coherence Measurements

in the Vertical Plane


Interferogram

Coherent Undulator Radiation is Used for Interferometric

Testing of Multilayer Coated Optics for EUV Lithography

13.4 nm

Wavefront! = 0.52 nm rms = "euv /26

Null test interferogram

1.39 nm

–2.82 nm

Reference wavefront! = 0.044 nm rms = "euv /300

0.25 nm

–0.25 nm

Courtesy of K. Goldberg, P. Naulleau, J. Bokor, et al., LBNL.

Ch08_At_WaveEUV.pptProfessor David Attwood



Univ. California Berkeley Ch08_ETS_optics.ppt

EUV Interferometry of Projection Optics

Fromundulatorbeamline

Turning mirror

Grating beam splitter And phase shifter

EUV CCD

K-B pre-focusing mirrors

PlanarBearingstage

Image stagepinhole array

Object stagepinhole array

Spatially coherent EUV radiation

Courtesy of K. Goldberg, P. Naulleau and P. Batson (LBNL) and J. Bokor (UCB/LBL).

METinterferometry.pptProfessor David Attwood


A 0.30 NA Micro-Exposure Tool (MET) for TestingEUV Resist Patterns to 12 nm Feature Size

Mask

Illumination

Secondary

Wafer

Primary

Fold Flat

Bipods

Bipod

Button

(Courtesy of J. Taylor, LLNL)

MET

NA = 0.30

13.4 nm

5X

200 X 600 µm field



SiN Cr 5nm/Au 12 nm

Plating Base

HSQ Resist

Expose &

develop

HSQNi Plate

HSQ

strip in

HFDry Etch SiN

50 nm50 nm

SEM of

coded 50 nm

pinhole with

HSQ mold

inside

50 nm50 nm

TEM of

coded 25

nm

pinholes

on 500 nm

pitch

300 nm300 nm

25 nm Pinhole Fabrication

(Courtesy of J. Alex Liddle, Deirdre Olynick and Erik Anderson, LBNL)



MET At-Wavelength Interferometry and AlignmentPreparation for Static Microfield Imaging

(Courtesy of K. Goldberg and P. Naulleau, LBNL)

200 x 600 !m

field of view

• Visible-light alignment at Livermore

• EUV interferometry at Berkeley includes PS/PDI and shearing

at 9 points across the field of view and in z.

• Higher-order spherical aberration dominates the wavefront

• A large part of the higher-order spherical is contained in Z35 and Z36.

Higher-order spherical magnitude depends strongly on NA.

2 mirrors

0.3 NA, 5x

13.5 nm

Alignment in progress

September 3, 2003

aberrations

may be reduced

in final alignment

astig

coma

sph ab

trifoil

h-o s.

0.1 nm

0.3 nm

0.4 nm

0.2 nm

0.4 nm

RMS 0.8 nm !/17

central field point

MET

Micro-Exposure Tool


Univ. California Berkeley Ch08_ETS_optics.ppt

Reticle

K-B

K-BObject

pinholes

For Interferometry

Grating

Spherical

mirror

Partial coherence set by

focal spot and angular

scan

(Courtesy of P. Naulleau and P. Denham, LBNL)Wafer

Static Exposures with an Active Coherence Controlling Illuminator

1 State_of_the_art_EUVresists.ppt

Addressing critical EUV lithography issues for Sematechat the ALS: testing state-of-the-art EUV resists

45 nm45 nm 40 nm40 nm 35 nm35 nm

35 nm35 nm

Major support and collaborators include Sematech, Intel, AMD, IBM, Samsung and others.

Mask

Wafer

Two-bounce, 0.3 NA, MET

at ALS Beamline 12.0

Programmable illumination

Annular

22 nm lines and spaces

10mJ/cm2

Courtesy of Patrick Naulleau, CXRO/LBNL.

CoherenceSlides.pptProfessor David Attwood


Coherent Soft X-Ray Science Beamline

Rosfjord (UCB PhD thesis, 2004)

Energy range 200-1000eV

Coherent flux at 600 eV: 2 ! 1011 ph/sec/0.1%BW

" = 2.07 nm (600 eV)

• Wavefront interferomery tomeasure aberrations inzone plate lenses

• Measure material properties(f1 & f2)

• Develop new coherent softx-ray optical techniques(Fourier Optics)

• Coherent scattering frommagnetic nanostructures

K. Rosfjord, Y. Liu, D. Attwood, “Tunable

Coherent Soft X-Rays”, IEEE J. Sel. Top. Quant.

Electr.10, 1405 (Nov/Dec 2004)

Ch08_CohOptBLwGraf2_Feb07.ai

Tuningcurves

8.0 cm period, N = 551.9 GeV, 400 mAd θ = λ/2πcoh = 1000 λ/2ηeuv = 10%, ηsxr = 10%

Coherent Power with a Monochromator

M2spherical2 mirror



Variedline-space

grating

Exitslit172°

M4bendable2 mirror

M3bendable2 mirror

M0retractable

plane2 mirror

Entrancepinhole

CoherentSoft X-ray

End Station

K-Bfocus

system

Coherent Soft X-Ray Beamline: Use of a Higher Harmonic (n = 3) to Access Shorter Wavelengths

0

100

200

300

102 103

Photon Energy (eV)

Pco

h, λ

/∆λ

(µW

)

n = 1

n = 3

λ∆λ

= 103


CohSXR_11.05.pptProfessor David Attwood


Courtesy of Kris Rosfjord, CXRO/LBNLK. Rosfjord et al., Coherent Soft X-Rays,

IEEE JSTQE 10, 1405 (Nov/Dec 2004)

!= 2.48 nm

(500 eV)

d = 2.6 !m

t = 40 msec

ALS beamline 12.0.2

Coherent Soft X-Rays

CohSXR_11.05.pptProfessor David Attwood


2 !m vertical separation

|µ| = 1.00

6 !m vertical separation

|µ| = .57d = 500nm diameter individual pinholes at 500eV

Focal spot size of 60um X 9.4um FWHM

Beam Characterization:

Double Pinhole Experimental Results

Courtesy of Kris Rosfjord, CXRO/LBNLK. Rosfjord et al., Coherent Soft X-Rays,

IEEE JSTQE 10, 1405 (Nov/Dec 2004)



Interferometry of Material Properties (f1 and f2)

Using the New XOR Fourier Optic

Combine them!

# $

K. Rosfjord, C. Chang,

R. Miyakawa, H. Barth,

D. Attwood, Applied Optics

(in press)

# = f10(w)

Na re "2

2%

$ = f20(w)

Na re "2

2%



Coherent Soft X-Ray Science Beamline

Rosfjord (UCB PhD thesis, 2004)

Energy range 200-1000eV

Coherent flux at 600 eV: 2 ! 1011 ph/sec/0.1%BW

" = 2.07 nm (600 eV)

• Wavefront interferomery tomeasure aberrations inzone plate lenses

• Measure material properties(f1 & f2)

• Develop new coherent softx-ray optical techniques(Fourier Optics)

• Coherent scattering frommagnetic nanostructures

K. Rosfjord, Y. Liu, D. Attwood, “Tunable

Coherent Soft X-Rays”, IEEE J. Sel. Top. Quant.

Electr.10, 1405 (Nov/Dec 2004)

Coherent Soft X-Ray Scattering

Ch08_CohSXRscattering.ai

Coherent Scatteringfrom a Pt:Co Multilayer

Soft x-ray speckle pattern:diffraction pattern of the magneticdomain structure

(Courtesy of Steve Kevan,University of Oregan)

Smallangleblock

• At a given angle one detects scattering from fluctuations of a specific spatial scale• At that angle, the frequency content tells you the time structure of those fluctuations

|kd| = 2π/d represents a spatial non-uniformity in the medium, such as atoms of periodicity d, a grating, or a density distribution due to a wave motion.

If the density distribution is stationary, or nearstationary, the scattering diagram is isosceles.

ks

ks

Scatteredwave

Incidentwave

2θ

2θ

kd

kd

k i

k i

ωs = ωi + ωd

ks = ki + kd




Coherent Soft X-Ray Magnetic

Scattering Endstation

Scattering

in

Transmission

X rays

Sample

location

Flangosaurus

Courtesy of K.Chesnel, S. Kevan, U. Oregon



Example of Experiment in Transmission:

Coherent Scattering from Nanoparticles

Co Nanoparticles assembly

precipitated on TEM grid

X –ray beam

tuned to Co L3

resonant edge

Diffuse scattering

Pinhole

(coherence)

CCD

Camera

2048x2048

200 400 600 800 1000 1200 1400 1600 1800 2000

200

400

600

800

1000

1200

1400

1600

1800

2000

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

x 104

Scattering ringrelated to

interparticle distance~12nm

Courtesy of K.Chesnel, S. Kevan, U. Oregon

Aperture(OSA)

Detector

Samplescanning

stage

λ

Zone Plate lens

Ch09_ScanSXRMicroscope.aiProfessor David AttwoodUniv. California, Berkeley

The Scanning Soft X-Ray Microscope Requires Spatially Coherent Illumination

Ch09_CohOptcsBL.ai

M2spherical


5.0 cm periodelliptically polarizing

undulatorGrating

Exitslit

M4bendable

M3bendable

M0retractable

plane

Entrancepinhole

CoherentSoft X-rayScanning

Microscope(“STXM”)

K-Bfocus

system

An Undulator Beamline for Scanning X-Ray Microscopy


Ch08_ALS_U5epu_Feb07.ai

1.9 GeV, 400 mAλu = 50 mm, N = 270.5 ≤ K ≤ 4.0σx = 260 µm, σx′ = 23 µrσy = 16 µm, σy′ = 3.9 µrθcen = 61µr @ K = 0.87 (500 eV)

U5 EPU

0 500

n = 1

n = 3

n = 1

n = 3

n = 1

η = 1.3%

n = 3

1000 1500 20000

0.5

1.0

1.5

2.0

2.5

0

5

10

15

20

0

2

4

6

102 103102 103


Photon Energy (eV)

Pco

h, N

(m

W)

Pco

h, λ

/∆λ

(µW

)

Pce

n (W

)

λ∆λ

= 27λ

∆λ = 103


Coherent Power for an EPU at the ALS

ALS_MES.pptProfessor David Attwood


RESULTS

•Ni, Fe, Mn, Ca, K, O, C elemental map,

( there was no sign of Cr.)

•Different oxidation states for Fe and Ni

Protein (gray), Ca, K 700 705 710 715 720 725

OD

1.5

1.0

0.5

0

1 µm

Different oxidation states (minerals) found for Fe & Ni

Fe 2p

5 µm

Tohru Araki, Adam Hitchcock (McMaster University)

Tolek Tyliszczak, LBNL

Sample from: John Lawrence, George Swerhone (NWRI-

Saskatoon), Gary Leppard (NWRI-CCIW)

Biofilm from Saskatoon River

ALS-MES 11.0.2

ALS_MES.pptProfessor David Attwood


Map chemical spectra taken of pure samples

Onto a sample containing both components

M.K. Gilles, R. Planques, S.R. Leone

LBNL

Samples from B. Hinsberg, F. Huele

IBM Almaden

Exposure to UV light results in loss of carbonyl peak

280 eV 290 eV

Courtesy of Mary Gilles, LBNL

Patterned Polymer Photoresists

ALS-MES 11.0.2

Ch08_BESSYII_Nov07.ai

1.7 GeV, 200 mAλu = 49 mm, N = 840 ≤ K ≤ 2.5σx = 314 µm, σx′ = 18 µrσy = 24 µm, σy′ = 2 µrηeuv = 10% ; ηsxr = 10%

0 500 1000 1500 2000

102 1030

50

100

150

Photon Energy (eV)

Pco

h, λ

/∆λ

(µW

)

Pce

n (W

)

n = 1

n = 3

n = 1

n = 3

λ∆λ

= 103

λ∆λ

= 103

0

0.2

0.4

0.6

0.8

1.0

0

5

10

15

102 103

Photon Energy (eV)

Photon Energy (eV)

Pco

h, N

(m

W)

n = 1

n = 3

λ∆λ

= 84

Coherent Power at BESSY II


Lensless Imaging of Magnetic Nanostructures by X-Ray Spectro-Holography

LenslessImagingF1.ai

S. Eisebitt, J. Lüning, W.F. Schlotter, M. Lörgen, O. Hellwig,W. Eberhardt & J. Stöhr / Nature, 16 Dec 2004


X-Ray Hologram at 1.59 nm WavelengthUsing Undulator Radiation at BESSY

LenslessImagingF2.ai

S. Eisebitt, J. Lüning, W.F. Schlotter, M. Lörgen, O. Hellwig,W. Eberhardt & J. Stöhr / Nature, 16 Dec 2004


Recorded Pattern of Magnetic Nanostructuresand Comparison to Scanning X-Ray Microscope

LenslessImagingF3b.ai

S. Eisebitt, J. Lüning, W.F. Schlotter, M. Lörgen, O. Hellwig, W. Eberhardt & J. Stöhr / Nature, 16 Dec 2004

0 500Distance (nm)

1,000 1,500


Undulators, FELs and Coherence

UndulatorsFELsCoh.ai

• Spatial coherence• Temporal coherence• Partial coherence• Full coherence• Spatial filtering• Uncorrelated emitters• Correlated emitters• True phase coherence and mode control• Lasers, amplified spontaneous emission (ASE) and mode control• Undulator radiation• SASE FEL 100+ fsec soft/hard x-rays• Seeded FEL true phase coherent x-rays• High harmonic generation (HHG) compact fsec/asec EUV• EUV lasers and laser seeded HHG• Applications with uncorrelated emitters• Applications with correlated emitters

θ

λλ

YoungsExprmt.ai



d θ

λλ

CH08_YoungsExprmt_v3.ai


Persistence of fringes as the source grows from a point source to finite size.


d 2θ|FWHM λ/2


d θ

λλ

YoungsExprmt_Random_March08.ai

Young’s Double Slit Experiment with Random Emitters: Young did not have a laser


d . 2θ|FWHM ~ λ/2–


N uncorrelatedemitters

• Self-interference only• Electric fields chaotic• Intensities add• Radiated power ~ N

E

t

d

E

t

θ

λλ

YoungsExprmt_PhaseCoh_March08.ai

Young’s Double Slit Experiment with Phase Coherent Emitters (some lasers, or properly seeded FELs)


d . 2θ|FWHM ~ λ/2–


N correlatedemitters

• Phase coherent electric fields• Electric fields from all particles interfere constructively• Radiated power ~ N2

• New phase sensitive probing of matter possible

Ch07_F02_06_Mar08.ai

The Lasing Process Begins withAmplified Spontaneous Emission (ASE)

Gain medium of invertedpopulation density

(Both directions equally likely)

Amplifiedspontaneous

emission

Spontaneousemission

but with spatial and temporal filtering, true phase coherence and mode control can be achieved.

Longitudinalmode selector

Transversemode selector

Gain medium+ flash lampMirror Mirror ~ 10–6

TEMOO

∆λλ

λvis

Undulators and FELs

UndulatorsAndFELs1.ai

Undulator – uncorrelated electronpositions, radiated fields uncorrelated,intensities add, limited coherence,power ~ N.

N

= –e(E + v × B)dpdt


S N S

S N S N

Undulators and FELs



Free Electron Laser (FEL) – very long undulator,electrons are “microbunched” bytheir own radiated fields into strongly correlated waves of electrons, all radiated electric fields now add,spatially coherent, power ~ N2

N




S N S

S N S N

N S N S

S N S N

N S N

S N S

S N

N S

Undulators and FELs



Free Electron Laser (FEL) – very long undulator,electrons are “microbunched” bytheir own radiated fields into strongly correlated waves of electrons, all radiated electric fields now add,spatially coherent, power ~ N2

N




S N S

S N S N

N S N S

S N S N

N S N

S N S

S N

N SCoherentseed pulse

Gain and Saturation in an FEL

Gain_Saturation_FEL_graph.aiProfessor David AttwoodUniv. California, Berkeley

Courtesy of K-J. Kim

FEL Microbunching

FEL_Microbunching.ai

Courtesy of Sven Reiche, UCLA.


Parameters Flash FEL LCLS European XFEL (Hamburg) (Stanford, 2010) (Hamburg, Schenefeld; 2014)

Ee 230/1000 MeV 13.6 GeV 17.5 GeV γ 450/2000 26,600 35,000 λu 2.73 cm 3 cm 5 cm N 500/1100 3700 4000 Lu 30 m 112 m 200 m ω 50-200 eV 1-10 keV 4-12 keV λ/∆λ 100 350 1000 e–/bunch 109 6 109 (1 nC) 6 109

∆τ 25 fsec 160 fsec 100 fsec F 3 1012 ph/pulse 2 1012 ph/pulse 1012 – 1014 ph/pulse rep rate 1 Hz 120 Hz 10 Hz I 1.3 kA 3.4 kA P 0.3 GW 8 GW 20-100 GW B 1 1028 1 1033 5 1033

L 260 m 5 km 3.4 kmˆˆˆ

•

Free Electron Lasers

FreeElectronLasers.aiProfessor David AttwoodUniv. California, Berkeley

Germany March 2008.ppt

FLASH EUV/soft x-ray FEL at DESY Lab, Hamburg

Courtesy of Henry Chapman (LLNL, now Hamburg) and Stefano Marchesini (LLNL, now LBL).

6.5-32 nm wavelength in 1st harmonic

20 fsec, 1012 photons per pulse

Germany March 2008.ppt

Coherent X-ray Diffractive Imaging with the FLASHfree-electron laser (FEL) in Hamburg, Germany

1st shot at full power

Chapman et al, Nature Phys 2 839 (2006)

25 fs diffraction pattern

Reconstruction

1 micron

Documents

Spatial Temporal Coherence; Coherent Undulator Radiationattwood/sxr2009/... · Ch08_F03.ai (8.3) Define a coherence length coh as the distance of propagation over which radiation